Average Error: 0.0 → 0.0
Time: 2.5s
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 r214532 = x;
        double r214533 = y;
        double r214534 = r214532 * r214533;
        double r214535 = 1.0;
        double r214536 = r214535 - r214532;
        double r214537 = z;
        double r214538 = r214536 * r214537;
        double r214539 = r214534 + r214538;
        return r214539;
}
↓
double f(double x, double y, double z) {
        double r214540 = x;
        double r214541 = y;
        double r214542 = 1.0;
        double r214543 = r214542 - r214540;
        double r214544 = z;
        double r214545 = r214543 * r214544;
        double r214546 = fma(r214540, r214541, r214545);
        return r214546;
}

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 2020025 +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)))