Average Error: 0.0 → 0.0
Time: 12.4s
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 r136281 = x;
        double r136282 = y;
        double r136283 = r136281 * r136282;
        double r136284 = 1.0;
        double r136285 = r136284 - r136281;
        double r136286 = z;
        double r136287 = r136285 * r136286;
        double r136288 = r136283 + r136287;
        return r136288;
}
↓
double f(double x, double y, double z) {
        double r136289 = x;
        double r136290 = y;
        double r136291 = 1.0;
        double r136292 = r136291 - r136289;
        double r136293 = z;
        double r136294 = r136292 * r136293;
        double r136295 = fma(r136289, r136290, r136294);
        return r136295;
}

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 2019212 +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)))