Average Error: 0.0 → 0.0
Time: 1.2s
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 r224041 = x;
        double r224042 = y;
        double r224043 = r224041 * r224042;
        double r224044 = 1.0;
        double r224045 = r224044 - r224041;
        double r224046 = z;
        double r224047 = r224045 * r224046;
        double r224048 = r224043 + r224047;
        return r224048;
}
↓
double f(double x, double y, double z) {
        double r224049 = x;
        double r224050 = y;
        double r224051 = 1.0;
        double r224052 = r224051 - r224049;
        double r224053 = z;
        double r224054 = r224052 * r224053;
        double r224055 = fma(r224049, r224050, r224054);
        return r224055;
}

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 2020060 +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)))