Average Error: 0.0 → 0.0
Time: 3.7s
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 r231115 = x;
        double r231116 = y;
        double r231117 = r231115 * r231116;
        double r231118 = 1.0;
        double r231119 = r231118 - r231115;
        double r231120 = z;
        double r231121 = r231119 * r231120;
        double r231122 = r231117 + r231121;
        return r231122;
}
↓
double f(double x, double y, double z) {
        double r231123 = x;
        double r231124 = y;
        double r231125 = 1.0;
        double r231126 = r231125 - r231123;
        double r231127 = z;
        double r231128 = r231126 * r231127;
        double r231129 = fma(r231123, r231124, r231128);
        return r231129;
}

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 2020042 +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)))