Average Error: 0.0 → 0.0
Time: 2.3s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)
double f(double x, double y, double z) {
        double r164524 = x;
        double r164525 = y;
        double r164526 = r164524 * r164525;
        double r164527 = 1.0;
        double r164528 = r164527 - r164524;
        double r164529 = z;
        double r164530 = r164528 * r164529;
        double r164531 = r164526 + r164530;
        return r164531;
}
↓
double f(double x, double y, double z) {
        double r164532 = x;
        double r164533 = y;
        double r164534 = 1.0;
        double r164535 = r164534 - r164532;
        double r164536 = z;
        double r164537 = r164535 * r164536;
        double r164538 = fma(r164532, r164533, r164537);
        return r164538;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(1 - x\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1 x) z)))