Average Error: 0.0 → 0.0
Time: 5.9s
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 r255121 = x;
        double r255122 = y;
        double r255123 = r255121 * r255122;
        double r255124 = 1.0;
        double r255125 = r255124 - r255121;
        double r255126 = z;
        double r255127 = r255125 * r255126;
        double r255128 = r255123 + r255127;
        return r255128;
}
↓
double f(double x, double y, double z) {
        double r255129 = x;
        double r255130 = y;
        double r255131 = 1.0;
        double r255132 = r255131 - r255129;
        double r255133 = z;
        double r255134 = r255132 * r255133;
        double r255135 = fma(r255129, r255130, r255134);
        return r255135;
}

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)))