Average Error: 0.1 → 0.1
Time: 13.8s
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 r57499 = 1.0;
        double r57500 = x;
        double r57501 = 0.253;
        double r57502 = 0.12;
        double r57503 = r57500 * r57502;
        double r57504 = r57501 + r57503;
        double r57505 = r57500 * r57504;
        double r57506 = r57499 - r57505;
        return r57506;
}
↓
double f(double x) {
        double r57507 = 1.0;
        double r57508 = x;
        double r57509 = 0.253;
        double r57510 = r57508 * r57509;
        double r57511 = 0.12;
        double r57512 = r57508 * r57511;
        double r57513 = r57508 * r57512;
        double r57514 = r57510 + r57513;
        double r57515 = r57507 - r57514;
        return r57515;
}

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)))))