Average Error: 0.0 → 0.0
Time: 6.1s
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 r253927 = x;
        double r253928 = y;
        double r253929 = r253927 * r253928;
        double r253930 = 1.0;
        double r253931 = r253930 - r253927;
        double r253932 = z;
        double r253933 = r253931 * r253932;
        double r253934 = r253929 + r253933;
        return r253934;
}
↓
double f(double x, double y, double z) {
        double r253935 = x;
        double r253936 = y;
        double r253937 = 1.0;
        double r253938 = r253937 - r253935;
        double r253939 = z;
        double r253940 = r253938 * r253939;
        double r253941 = fma(r253935, r253936, r253940);
        return r253941;
}

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 2019351 +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)))