Average Error: 0.0 → 0.0
Time: 740.0ms
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 r228016 = x;
        double r228017 = y;
        double r228018 = r228016 * r228017;
        double r228019 = 1.0;
        double r228020 = r228019 - r228016;
        double r228021 = z;
        double r228022 = r228020 * r228021;
        double r228023 = r228018 + r228022;
        return r228023;
}
↓
double f(double x, double y, double z) {
        double r228024 = x;
        double r228025 = y;
        double r228026 = 1.0;
        double r228027 = r228026 - r228024;
        double r228028 = z;
        double r228029 = r228027 * r228028;
        double r228030 = fma(r228024, r228025, r228029);
        return r228030;
}

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 2020024 +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)))