Average Error: 0.0 → 0.0
Time: 2.3s
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 r203123 = x;
        double r203124 = y;
        double r203125 = r203123 * r203124;
        double r203126 = 1.0;
        double r203127 = r203126 - r203123;
        double r203128 = z;
        double r203129 = r203127 * r203128;
        double r203130 = r203125 + r203129;
        return r203130;
}
↓
double f(double x, double y, double z) {
        double r203131 = x;
        double r203132 = y;
        double r203133 = 1.0;
        double r203134 = r203133 - r203131;
        double r203135 = z;
        double r203136 = r203134 * r203135;
        double r203137 = fma(r203131, r203132, r203136);
        return r203137;
}

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 2020064 +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)))