Average Error: 0.0 → 0.0
Time: 5.1s
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 r271088 = x;
        double r271089 = y;
        double r271090 = r271088 * r271089;
        double r271091 = 1.0;
        double r271092 = r271091 - r271088;
        double r271093 = z;
        double r271094 = r271092 * r271093;
        double r271095 = r271090 + r271094;
        return r271095;
}
↓
double f(double x, double y, double z) {
        double r271096 = x;
        double r271097 = y;
        double r271098 = 1.0;
        double r271099 = r271098 - r271096;
        double r271100 = z;
        double r271101 = r271099 * r271100;
        double r271102 = fma(r271096, r271097, r271101);
        return r271102;
}

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 2020047 +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)))