Average Error: 0.0 → 0.0
Time: 1.1s
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 r209480 = x;
        double r209481 = y;
        double r209482 = r209480 * r209481;
        double r209483 = 1.0;
        double r209484 = r209483 - r209480;
        double r209485 = z;
        double r209486 = r209484 * r209485;
        double r209487 = r209482 + r209486;
        return r209487;
}
↓
double f(double x, double y, double z) {
        double r209488 = x;
        double r209489 = y;
        double r209490 = 1.0;
        double r209491 = r209490 - r209488;
        double r209492 = z;
        double r209493 = r209491 * r209492;
        double r209494 = fma(r209488, r209489, r209493);
        return r209494;
}

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 2020062 +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)))