Average Error: 0.0 → 0.0
Time: 2.9s
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 r204342 = x;
        double r204343 = y;
        double r204344 = r204342 * r204343;
        double r204345 = 1.0;
        double r204346 = r204345 - r204342;
        double r204347 = z;
        double r204348 = r204346 * r204347;
        double r204349 = r204344 + r204348;
        return r204349;
}
↓
double f(double x, double y, double z) {
        double r204350 = x;
        double r204351 = y;
        double r204352 = 1.0;
        double r204353 = r204352 - r204350;
        double r204354 = z;
        double r204355 = r204353 * r204354;
        double r204356 = fma(r204350, r204351, r204355);
        return r204356;
}

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 2020036 +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)))