Average Error: 0.0 → 0.0
Time: 1.1s
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 r200253 = x;
        double r200254 = y;
        double r200255 = r200253 * r200254;
        double r200256 = 1.0;
        double r200257 = r200256 - r200253;
        double r200258 = z;
        double r200259 = r200257 * r200258;
        double r200260 = r200255 + r200259;
        return r200260;
}
↓
double f(double x, double y, double z) {
        double r200261 = x;
        double r200262 = y;
        double r200263 = 1.0;
        double r200264 = r200263 - r200261;
        double r200265 = z;
        double r200266 = r200264 * r200265;
        double r200267 = fma(r200261, r200262, r200266);
        return r200267;
}

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 2020056 +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)))