Average Error: 0.1 → 0.1
Time: 3.3s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - x \cdot \frac{0.253 \cdot 0.253 - \left(x \cdot 0.12\right) \cdot \left(x \cdot 0.12\right)}{0.253 - x \cdot 0.12}\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - x \cdot \frac{0.253 \cdot 0.253 - \left(x \cdot 0.12\right) \cdot \left(x \cdot 0.12\right)}{0.253 - x \cdot 0.12}
double f(double x) {
        double r109759 = 1.0;
        double r109760 = x;
        double r109761 = 0.253;
        double r109762 = 0.12;
        double r109763 = r109760 * r109762;
        double r109764 = r109761 + r109763;
        double r109765 = r109760 * r109764;
        double r109766 = r109759 - r109765;
        return r109766;
}
↓
double f(double x) {
        double r109767 = 1.0;
        double r109768 = x;
        double r109769 = 0.253;
        double r109770 = r109769 * r109769;
        double r109771 = 0.12;
        double r109772 = r109768 * r109771;
        double r109773 = r109772 * r109772;
        double r109774 = r109770 - r109773;
        double r109775 = r109769 - r109772;
        double r109776 = r109774 / r109775;
        double r109777 = r109768 * r109776;
        double r109778 = r109767 - r109777;
        return r109778;
}

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

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
  2. Using strategy rm

  3. Applied flip-+0.1

    \[\leadsto 1 - x \cdot \color{blue}{\frac{0.253 \cdot 0.253 - \left(x \cdot 0.12\right) \cdot \left(x \cdot 0.12\right)}{0.253 - x \cdot 0.12}}\]

  4. Final simplification0.1

    \[\leadsto 1 - x \cdot \frac{0.253 \cdot 0.253 - \left(x \cdot 0.12\right) \cdot \left(x \cdot 0.12\right)}{0.253 - x \cdot 0.12}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))