Average Error: 0.0 → 0.0
Time: 9.2s
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 r166267 = x;
        double r166268 = y;
        double r166269 = r166267 * r166268;
        double r166270 = 1.0;
        double r166271 = r166270 - r166267;
        double r166272 = z;
        double r166273 = r166271 * r166272;
        double r166274 = r166269 + r166273;
        return r166274;
}
↓
double f(double x, double y, double z) {
        double r166275 = x;
        double r166276 = y;
        double r166277 = 1.0;
        double r166278 = r166277 - r166275;
        double r166279 = z;
        double r166280 = r166278 * r166279;
        double r166281 = fma(r166275, r166276, r166280);
        return r166281;
}

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 2019303 +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)))