Average Error: 0.1 → 0.1
Time: 3.5s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - x \cdot \left(0.12 \cdot x + 0.253\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - x \cdot \left(0.12 \cdot x + 0.253\right)
double f(double x) {
        double r74588 = 1.0;
        double r74589 = x;
        double r74590 = 0.253;
        double r74591 = 0.12;
        double r74592 = r74589 * r74591;
        double r74593 = r74590 + r74592;
        double r74594 = r74589 * r74593;
        double r74595 = r74588 - r74594;
        return r74595;
}
↓
double f(double x) {
        double r74596 = 1.0;
        double r74597 = x;
        double r74598 = 0.12;
        double r74599 = r74598 * r74597;
        double r74600 = 0.253;
        double r74601 = r74599 + r74600;
        double r74602 = r74597 * r74601;
        double r74603 = r74596 - r74602;
        return r74603;
}

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. Taylor expanded around 0 0.1

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

  3. Final simplification0.1

    \[\leadsto 1 - x \cdot \left(0.12 \cdot x + 0.253\right)\]

Reproduce

herbie shell --seed 2020081 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))