Average Error: 0.1 → 0.2
Time: 2.2s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[\left(1 - 0.2530000000000000026645352591003756970167 \cdot x\right) - {x}^{2} \cdot 0.1199999999999999955591079014993738383055\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
\left(1 - 0.2530000000000000026645352591003756970167 \cdot x\right) - {x}^{2} \cdot 0.1199999999999999955591079014993738383055
double f(double x) {
        double r110983 = 1.0;
        double r110984 = x;
        double r110985 = 0.253;
        double r110986 = 0.12;
        double r110987 = r110984 * r110986;
        double r110988 = r110985 + r110987;
        double r110989 = r110984 * r110988;
        double r110990 = r110983 - r110989;
        return r110990;
}
↓
double f(double x) {
        double r110991 = 1.0;
        double r110992 = 0.253;
        double r110993 = x;
        double r110994 = r110992 * r110993;
        double r110995 = r110991 - r110994;
        double r110996 = 2.0;
        double r110997 = pow(r110993, r110996);
        double r110998 = 0.12;
        double r110999 = r110997 * r110998;
        double r111000 = r110995 - r110999;
        return r111000;
}

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. Applied associate--r+0.1

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

  5. Simplified0.1

    \[\leadsto \color{blue}{\left(1 - 0.2530000000000000026645352591003756970167 \cdot x\right)} - x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)\]
  6. Using strategy rm

  7. Applied associate-*r*0.2

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

  8. Simplified0.2

    \[\leadsto \left(1 - 0.2530000000000000026645352591003756970167 \cdot x\right) - \color{blue}{{x}^{2}} \cdot 0.1199999999999999955591079014993738383055\]

  9. Final simplification0.2

    \[\leadsto \left(1 - 0.2530000000000000026645352591003756970167 \cdot x\right) - {x}^{2} \cdot 0.1199999999999999955591079014993738383055\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))