Average Error: 0.0 → 0.0
Time: 3.2s
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 r175937 = x;
        double r175938 = y;
        double r175939 = r175937 * r175938;
        double r175940 = 1.0;
        double r175941 = r175940 - r175937;
        double r175942 = z;
        double r175943 = r175941 * r175942;
        double r175944 = r175939 + r175943;
        return r175944;
}
↓
double f(double x, double y, double z) {
        double r175945 = x;
        double r175946 = y;
        double r175947 = 1.0;
        double r175948 = r175947 - r175945;
        double r175949 = z;
        double r175950 = r175948 * r175949;
        double r175951 = fma(r175945, r175946, r175950);
        return r175951;
}

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 2020034 +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)))