Average Error: 0.1 → 0.1
Time: 3.1s
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 r81055 = 1.0;
        double r81056 = x;
        double r81057 = 0.253;
        double r81058 = 0.12;
        double r81059 = r81056 * r81058;
        double r81060 = r81057 + r81059;
        double r81061 = r81056 * r81060;
        double r81062 = r81055 - r81061;
        return r81062;
}
↓
double f(double x) {
        double r81063 = 1.0;
        double r81064 = x;
        double r81065 = 0.253;
        double r81066 = r81065 * r81065;
        double r81067 = 0.12;
        double r81068 = r81064 * r81067;
        double r81069 = r81068 * r81068;
        double r81070 = r81066 - r81069;
        double r81071 = r81065 - r81068;
        double r81072 = r81070 / r81071;
        double r81073 = r81064 * r81072;
        double r81074 = r81063 - r81073;
        return r81074;
}

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)))))