Average Error: 0.0 → 0.0
Time: 7.0s
Precision: 64
\[x \cdot y + \left(1.0 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(1.0 - x, z, x \cdot y\right)\]
x \cdot y + \left(1.0 - x\right) \cdot z
↓
\mathsf{fma}\left(1.0 - x, z, x \cdot y\right)
double f(double x, double y, double z) {
        double r7495273 = x;
        double r7495274 = y;
        double r7495275 = r7495273 * r7495274;
        double r7495276 = 1.0;
        double r7495277 = r7495276 - r7495273;
        double r7495278 = z;
        double r7495279 = r7495277 * r7495278;
        double r7495280 = r7495275 + r7495279;
        return r7495280;
}
↓
double f(double x, double y, double z) {
        double r7495281 = 1.0;
        double r7495282 = x;
        double r7495283 = r7495281 - r7495282;
        double r7495284 = z;
        double r7495285 = y;
        double r7495286 = r7495282 * r7495285;
        double r7495287 = fma(r7495283, r7495284, r7495286);
        return r7495287;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(1.0 - x\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.0 - x, z, y \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(1.0 - x, z, x \cdot y\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  (+ (* x y) (* (- 1.0 x) z)))