Average Error: 0.1 → 0.1
Time: 8.0s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(0.2530000000000000026645352591003756970167 \cdot x + \left(x \cdot 0.1199999999999999955591079014993738383055\right) \cdot x\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - \left(0.2530000000000000026645352591003756970167 \cdot x + \left(x \cdot 0.1199999999999999955591079014993738383055\right) \cdot x\right)
double f(double x) {
        double r56750 = 1.0;
        double r56751 = x;
        double r56752 = 0.253;
        double r56753 = 0.12;
        double r56754 = r56751 * r56753;
        double r56755 = r56752 + r56754;
        double r56756 = r56751 * r56755;
        double r56757 = r56750 - r56756;
        return r56757;
}
↓
double f(double x) {
        double r56758 = 1.0;
        double r56759 = 0.253;
        double r56760 = x;
        double r56761 = r56759 * r56760;
        double r56762 = 0.12;
        double r56763 = r56760 * r56762;
        double r56764 = r56763 * r56760;
        double r56765 = r56761 + r56764;
        double r56766 = r56758 - r56765;
        return r56766;
}

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. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))