Average Error: 0.0 → 0.0
Time: 589.0ms
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 r281021 = x;
        double r281022 = y;
        double r281023 = r281021 * r281022;
        double r281024 = 1.0;
        double r281025 = r281024 - r281021;
        double r281026 = z;
        double r281027 = r281025 * r281026;
        double r281028 = r281023 + r281027;
        return r281028;
}
↓
double f(double x, double y, double z) {
        double r281029 = x;
        double r281030 = y;
        double r281031 = 1.0;
        double r281032 = r281031 - r281029;
        double r281033 = z;
        double r281034 = r281032 * r281033;
        double r281035 = fma(r281029, r281030, r281034);
        return r281035;
}

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 2020020 +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)))