Average Error: 0.1 → 0.1
Time: 12.3s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[\frac{1 \cdot 1 - \left(x \cdot 0.2530000000000000026645352591003756970167\right) \cdot \left(x \cdot 0.2530000000000000026645352591003756970167\right)}{1 + x \cdot 0.2530000000000000026645352591003756970167} - x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
\frac{1 \cdot 1 - \left(x \cdot 0.2530000000000000026645352591003756970167\right) \cdot \left(x \cdot 0.2530000000000000026645352591003756970167\right)}{1 + x \cdot 0.2530000000000000026645352591003756970167} - x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)
double f(double x) {
        double r55686 = 1.0;
        double r55687 = x;
        double r55688 = 0.253;
        double r55689 = 0.12;
        double r55690 = r55687 * r55689;
        double r55691 = r55688 + r55690;
        double r55692 = r55687 * r55691;
        double r55693 = r55686 - r55692;
        return r55693;
}
↓
double f(double x) {
        double r55694 = 1.0;
        double r55695 = r55694 * r55694;
        double r55696 = x;
        double r55697 = 0.253;
        double r55698 = r55696 * r55697;
        double r55699 = r55698 * r55698;
        double r55700 = r55695 - r55699;
        double r55701 = r55694 + r55698;
        double r55702 = r55700 / r55701;
        double r55703 = 0.12;
        double r55704 = r55696 * r55703;
        double r55705 = r55696 * r55704;
        double r55706 = r55702 - r55705;
        return r55706;
}

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. Using strategy rm

  6. Applied flip--0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))