Average Error: 0.0 → 0.0
Time: 1.5s
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 r267569 = x;
        double r267570 = y;
        double r267571 = r267569 * r267570;
        double r267572 = 1.0;
        double r267573 = r267572 - r267569;
        double r267574 = z;
        double r267575 = r267573 * r267574;
        double r267576 = r267571 + r267575;
        return r267576;
}
↓
double f(double x, double y, double z) {
        double r267577 = x;
        double r267578 = y;
        double r267579 = 1.0;
        double r267580 = r267579 - r267577;
        double r267581 = z;
        double r267582 = r267580 * r267581;
        double r267583 = fma(r267577, r267578, r267582);
        return r267583;
}

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)))