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 r178401 = x;
        double r178402 = y;
        double r178403 = r178401 * r178402;
        double r178404 = 1.0;
        double r178405 = r178404 - r178401;
        double r178406 = z;
        double r178407 = r178405 * r178406;
        double r178408 = r178403 + r178407;
        return r178408;
}
↓
double f(double x, double y, double z) {
        double r178409 = x;
        double r178410 = y;
        double r178411 = 1.0;
        double r178412 = r178411 - r178409;
        double r178413 = z;
        double r178414 = r178412 * r178413;
        double r178415 = fma(r178409, r178410, r178414);
        return r178415;
}

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 2020089 +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)))