Average Error: 0.0 → 0.0
Time: 15.6s
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 r138988 = x;
        double r138989 = y;
        double r138990 = r138988 * r138989;
        double r138991 = 1.0;
        double r138992 = r138991 - r138988;
        double r138993 = z;
        double r138994 = r138992 * r138993;
        double r138995 = r138990 + r138994;
        return r138995;
}
↓
double f(double x, double y, double z) {
        double r138996 = x;
        double r138997 = y;
        double r138998 = 1.0;
        double r138999 = r138998 - r138996;
        double r139000 = z;
        double r139001 = r138999 * r139000;
        double r139002 = fma(r138996, r138997, r139001);
        return r139002;
}

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 2019209 +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)))