Average Error: 0.0 → 0.0
Time: 2.0s
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 r209011 = x;
        double r209012 = y;
        double r209013 = r209011 * r209012;
        double r209014 = 1.0;
        double r209015 = r209014 - r209011;
        double r209016 = z;
        double r209017 = r209015 * r209016;
        double r209018 = r209013 + r209017;
        return r209018;
}
↓
double f(double x, double y, double z) {
        double r209019 = x;
        double r209020 = y;
        double r209021 = 1.0;
        double r209022 = r209021 - r209019;
        double r209023 = z;
        double r209024 = r209022 * r209023;
        double r209025 = fma(r209019, r209020, r209024);
        return r209025;
}

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 2020065 +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)))