Average Error: 0.1 → 0.1
Time: 15.8s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(x \cdot 0.2530000000000000026645352591003756970167 + x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - \left(x \cdot 0.2530000000000000026645352591003756970167 + x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)\right)
double f(double x) {
        double r52874 = 1.0;
        double r52875 = x;
        double r52876 = 0.253;
        double r52877 = 0.12;
        double r52878 = r52875 * r52877;
        double r52879 = r52876 + r52878;
        double r52880 = r52875 * r52879;
        double r52881 = r52874 - r52880;
        return r52881;
}
↓
double f(double x) {
        double r52882 = 1.0;
        double r52883 = x;
        double r52884 = 0.253;
        double r52885 = r52883 * r52884;
        double r52886 = 0.12;
        double r52887 = r52883 * r52886;
        double r52888 = r52883 * r52887;
        double r52889 = r52885 + r52888;
        double r52890 = r52882 - r52889;
        return r52890;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))