Average Error: 0.0 → 0.0
Time: 9.0s
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 r167241 = x;
        double r167242 = y;
        double r167243 = r167241 * r167242;
        double r167244 = 1.0;
        double r167245 = r167244 - r167241;
        double r167246 = z;
        double r167247 = r167245 * r167246;
        double r167248 = r167243 + r167247;
        return r167248;
}
↓
double f(double x, double y, double z) {
        double r167249 = x;
        double r167250 = y;
        double r167251 = 1.0;
        double r167252 = r167251 - r167249;
        double r167253 = z;
        double r167254 = r167252 * r167253;
        double r167255 = fma(r167249, r167250, r167254);
        return r167255;
}

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 2019323 +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)))