Average Error: 0.0 → 0.0
Time: 10.8s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(1 - x, z, x \cdot y\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
\mathsf{fma}\left(1 - x, z, x \cdot y\right)
double f(double x, double y, double z) {
        double r15366119 = x;
        double r15366120 = y;
        double r15366121 = r15366119 * r15366120;
        double r15366122 = 1.0;
        double r15366123 = r15366122 - r15366119;
        double r15366124 = z;
        double r15366125 = r15366123 * r15366124;
        double r15366126 = r15366121 + r15366125;
        return r15366126;
}
↓
double f(double x, double y, double z) {
        double r15366127 = 1.0;
        double r15366128 = x;
        double r15366129 = r15366127 - r15366128;
        double r15366130 = z;
        double r15366131 = y;
        double r15366132 = r15366128 * r15366131;
        double r15366133 = fma(r15366129, r15366130, r15366132);
        return r15366133;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(1 - x, z, y \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(1 - x, z, x \cdot y\right)\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  (+ (* x y) (* (- 1.0 x) z)))