Average Error: 0.0 → 0.0
Time: 2.0s
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 r292418 = x;
        double r292419 = y;
        double r292420 = r292418 * r292419;
        double r292421 = 1.0;
        double r292422 = r292421 - r292418;
        double r292423 = z;
        double r292424 = r292422 * r292423;
        double r292425 = r292420 + r292424;
        return r292425;
}
↓
double f(double x, double y, double z) {
        double r292426 = x;
        double r292427 = y;
        double r292428 = 1.0;
        double r292429 = r292428 - r292426;
        double r292430 = z;
        double r292431 = r292429 * r292430;
        double r292432 = fma(r292426, r292427, r292431);
        return r292432;
}

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 2020057 +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)))