Average Error: 0.0 → 0.0
Time: 9.3s
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 r104079 = x;
        double r104080 = y;
        double r104081 = r104079 * r104080;
        double r104082 = 1.0;
        double r104083 = r104082 - r104079;
        double r104084 = z;
        double r104085 = r104083 * r104084;
        double r104086 = r104081 + r104085;
        return r104086;
}
↓
double f(double x, double y, double z) {
        double r104087 = x;
        double r104088 = y;
        double r104089 = 1.0;
        double r104090 = r104089 - r104087;
        double r104091 = z;
        double r104092 = r104090 * r104091;
        double r104093 = fma(r104087, r104088, r104092);
        return r104093;
}

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 2019326 +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)))