Average Error: 0.0 → 0.0
Time: 11.5s
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 r10934304 = x;
        double r10934305 = y;
        double r10934306 = r10934304 * r10934305;
        double r10934307 = 1.0;
        double r10934308 = r10934307 - r10934304;
        double r10934309 = z;
        double r10934310 = r10934308 * r10934309;
        double r10934311 = r10934306 + r10934310;
        return r10934311;
}
↓
double f(double x, double y, double z) {
        double r10934312 = 1.0;
        double r10934313 = x;
        double r10934314 = r10934312 - r10934313;
        double r10934315 = z;
        double r10934316 = y;
        double r10934317 = r10934313 * r10934316;
        double r10934318 = fma(r10934314, r10934315, r10934317);
        return r10934318;
}

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 2019163 +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)))