diff --git a/REFERENCE.md b/REFERENCE.md index e463f53..e1ccded 100644 --- a/REFERENCE.md +++ b/REFERENCE.md @@ -12,7 +12,7 @@ in this file. All operations in input files are assumed to be over real numbers. FPTaylor models floating-point arithmetic with rounding operations. The basic analysis which FPTaylor performs is the following. Suppose the input file contains an expression `expr` -containing some variables (for simplicity, assume that is depends on +containing some variables (for simplicity, assume that it depends on one variable `x`) and some rounding operations. FPTaylor constructs another expression `expr'` without rounding operations and estimates the maximum value of the difference @@ -233,7 +233,7 @@ It is equivalent to ### Constraints -Each variable have lower and upper bounds. Additional constraints can +Each variable has lower and upper bounds. Additional constraints can be defined in the following section Constraints @@ -349,7 +349,7 @@ if `type` is `up`, `down`, or `zero`. There is one special value for FPTaylor also can work with an improved rounded model where the expression `f e` is replaced with `p2(f)e`. The function `p2` is a special function which improves the result of the rounding -approximation. In general, the imporved rounding model leads to more +approximation. In general, the improved rounding model leads to more complicated problems for FPTaylor to solve. It can be turned on with a special option. @@ -456,7 +456,7 @@ error. Possible values: `true`, `false`. -Turns on or off the impoved rounding model. The improved rounding +Turns on or off the improved rounding model. The improved rounding model yields better error estimation results but it also produces harder problems for optimization backends to solve. It may be not supported by some optimization backends.