Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)
double f(double x) {
        double r82474 = 1.0;
        double r82475 = x;
        double r82476 = 0.253;
        double r82477 = 0.12;
        double r82478 = r82475 * r82477;
        double r82479 = r82476 + r82478;
        double r82480 = r82475 * r82479;
        double r82481 = r82474 - r82480;
        return r82481;
}
↓
double f(double x) {
        double r82482 = x;
        double r82483 = -r82482;
        double r82484 = 0.12;
        double r82485 = 0.253;
        double r82486 = fma(r82484, r82482, r82485);
        double r82487 = 1.0;
        double r82488 = fma(r82483, r82486, r82487);
        return r82488;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)\]

Reproduce

herbie shell --seed 2020046 +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)))))