Average Error: 0.1 → 0.2
Time: 50.7s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(0.2530000000000000026645352591003756970167 \cdot x + \left(x \cdot x\right) \cdot 0.1199999999999999955591079014993738383055\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - \left(0.2530000000000000026645352591003756970167 \cdot x + \left(x \cdot x\right) \cdot 0.1199999999999999955591079014993738383055\right)
double f(double x) {
        double r3310779 = 1.0;
        double r3310780 = x;
        double r3310781 = 0.253;
        double r3310782 = 0.12;
        double r3310783 = r3310780 * r3310782;
        double r3310784 = r3310781 + r3310783;
        double r3310785 = r3310780 * r3310784;
        double r3310786 = r3310779 - r3310785;
        return r3310786;
}
↓
double f(double x) {
        double r3310787 = 1.0;
        double r3310788 = 0.253;
        double r3310789 = x;
        double r3310790 = r3310788 * r3310789;
        double r3310791 = r3310789 * r3310789;
        double r3310792 = 0.12;
        double r3310793 = r3310791 * r3310792;
        double r3310794 = r3310790 + r3310793;
        double r3310795 = r3310787 - r3310794;
        return r3310795;
}

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 flip-+0.1

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

  4. Taylor expanded around 0 0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))