Average Error: 0.0 → 0.0
Time: 6.4s
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 r256429 = x;
        double r256430 = y;
        double r256431 = r256429 * r256430;
        double r256432 = 1.0;
        double r256433 = r256432 - r256429;
        double r256434 = z;
        double r256435 = r256433 * r256434;
        double r256436 = r256431 + r256435;
        return r256436;
}
↓
double f(double x, double y, double z) {
        double r256437 = x;
        double r256438 = y;
        double r256439 = 1.0;
        double r256440 = r256439 - r256437;
        double r256441 = z;
        double r256442 = r256440 * r256441;
        double r256443 = fma(r256437, r256438, r256442);
        return r256443;
}

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 2020045 +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)))