Average Error: 0.0 → 0.0
Time: 10.0s
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 r162798 = x;
        double r162799 = y;
        double r162800 = r162798 * r162799;
        double r162801 = 1.0;
        double r162802 = r162801 - r162798;
        double r162803 = z;
        double r162804 = r162802 * r162803;
        double r162805 = r162800 + r162804;
        return r162805;
}
↓
double f(double x, double y, double z) {
        double r162806 = x;
        double r162807 = y;
        double r162808 = 1.0;
        double r162809 = r162808 - r162806;
        double r162810 = z;
        double r162811 = r162809 * r162810;
        double r162812 = fma(r162806, r162807, r162811);
        return r162812;
}

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 2019323 +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)))