Average Error: 0.0 → 0.0
Time: 3.4s
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 r118112 = x;
        double r118113 = y;
        double r118114 = r118112 * r118113;
        double r118115 = 1.0;
        double r118116 = r118115 - r118112;
        double r118117 = z;
        double r118118 = r118116 * r118117;
        double r118119 = r118114 + r118118;
        return r118119;
}
↓
double f(double x, double y, double z) {
        double r118120 = x;
        double r118121 = y;
        double r118122 = 1.0;
        double r118123 = r118122 - r118120;
        double r118124 = z;
        double r118125 = r118123 * r118124;
        double r118126 = fma(r118120, r118121, r118125);
        return r118126;
}

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 2019322 +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)))