Average Error: 0.0 → 0.0
Time: 1.1s
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 r190997 = x;
        double r190998 = y;
        double r190999 = r190997 * r190998;
        double r191000 = 1.0;
        double r191001 = r191000 - r190997;
        double r191002 = z;
        double r191003 = r191001 * r191002;
        double r191004 = r190999 + r191003;
        return r191004;
}
↓
double f(double x, double y, double z) {
        double r191005 = x;
        double r191006 = y;
        double r191007 = 1.0;
        double r191008 = r191007 - r191005;
        double r191009 = z;
        double r191010 = r191008 * r191009;
        double r191011 = fma(r191005, r191006, r191010);
        return r191011;
}

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 2020100 +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)))