Average Error: 0.1 → 0.1
Time: 2.5s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - x \cdot \left(x \cdot 0.12 + 0.253\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - x \cdot \left(x \cdot 0.12 + 0.253\right)
double f(double x) {
        double r69590 = 1.0;
        double r69591 = x;
        double r69592 = 0.253;
        double r69593 = 0.12;
        double r69594 = r69591 * r69593;
        double r69595 = r69592 + r69594;
        double r69596 = r69591 * r69595;
        double r69597 = r69590 - r69596;
        return r69597;
}
↓
double f(double x) {
        double r69598 = 1.0;
        double r69599 = x;
        double r69600 = 0.12;
        double r69601 = r69599 * r69600;
        double r69602 = 0.253;
        double r69603 = r69601 + r69602;
        double r69604 = r69599 * r69603;
        double r69605 = r69598 - r69604;
        return r69605;
}

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 +-commutative0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))