Average Error: 0.0 → 0.0
Time: 2.2s
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 r197347 = x;
        double r197348 = y;
        double r197349 = r197347 * r197348;
        double r197350 = 1.0;
        double r197351 = r197350 - r197347;
        double r197352 = z;
        double r197353 = r197351 * r197352;
        double r197354 = r197349 + r197353;
        return r197354;
}
↓
double f(double x, double y, double z) {
        double r197355 = x;
        double r197356 = y;
        double r197357 = 1.0;
        double r197358 = r197357 - r197355;
        double r197359 = z;
        double r197360 = r197358 * r197359;
        double r197361 = fma(r197355, r197356, r197360);
        return r197361;
}

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)))