Average Error: 0.1 → 0.1
Time: 2.9s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - x \cdot \left(0.1199999999999999955591079014993738383055 \cdot x + 0.2530000000000000026645352591003756970167\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - x \cdot \left(0.1199999999999999955591079014993738383055 \cdot x + 0.2530000000000000026645352591003756970167\right)
double f(double x) {
        double r81964 = 1.0;
        double r81965 = x;
        double r81966 = 0.253;
        double r81967 = 0.12;
        double r81968 = r81965 * r81967;
        double r81969 = r81966 + r81968;
        double r81970 = r81965 * r81969;
        double r81971 = r81964 - r81970;
        return r81971;
}
↓
double f(double x) {
        double r81972 = 1.0;
        double r81973 = x;
        double r81974 = 0.12;
        double r81975 = r81974 * r81973;
        double r81976 = 0.253;
        double r81977 = r81975 + r81976;
        double r81978 = r81973 * r81977;
        double r81979 = r81972 - r81978;
        return r81979;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]

  2. Taylor expanded around 0 0.1

    \[\leadsto 1 - x \cdot \color{blue}{\left(0.1199999999999999955591079014993738383055 \cdot x + 0.2530000000000000026645352591003756970167\right)}\]

  3. Final simplification0.1

    \[\leadsto 1 - x \cdot \left(0.1199999999999999955591079014993738383055 \cdot x + 0.2530000000000000026645352591003756970167\right)\]

Reproduce

herbie shell --seed 2019347 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))