Average Error: 0.0 → 0.0
Time: 16.8s
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 r167167 = x;
        double r167168 = y;
        double r167169 = r167167 * r167168;
        double r167170 = 1.0;
        double r167171 = r167170 - r167167;
        double r167172 = z;
        double r167173 = r167171 * r167172;
        double r167174 = r167169 + r167173;
        return r167174;
}
↓
double f(double x, double y, double z) {
        double r167175 = x;
        double r167176 = y;
        double r167177 = 1.0;
        double r167178 = r167177 - r167175;
        double r167179 = z;
        double r167180 = r167178 * r167179;
        double r167181 = fma(r167175, r167176, r167180);
        return r167181;
}

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 2019235 +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)))