Average Error: 0.0 → 0.0
Time: 1.3s
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 r210396 = x;
        double r210397 = y;
        double r210398 = r210396 * r210397;
        double r210399 = 1.0;
        double r210400 = r210399 - r210396;
        double r210401 = z;
        double r210402 = r210400 * r210401;
        double r210403 = r210398 + r210402;
        return r210403;
}
↓
double f(double x, double y, double z) {
        double r210404 = x;
        double r210405 = y;
        double r210406 = 1.0;
        double r210407 = r210406 - r210404;
        double r210408 = z;
        double r210409 = r210407 * r210408;
        double r210410 = fma(r210404, r210405, r210409);
        return r210410;
}

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 2020043 +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)))