Average Error: 0.0 → 0.0
Time: 8.6s
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 r8028227 = x;
        double r8028228 = y;
        double r8028229 = r8028227 * r8028228;
        double r8028230 = 1.0;
        double r8028231 = r8028230 - r8028227;
        double r8028232 = z;
        double r8028233 = r8028231 * r8028232;
        double r8028234 = r8028229 + r8028233;
        return r8028234;
}
↓
double f(double x, double y, double z) {
        double r8028235 = x;
        double r8028236 = y;
        double r8028237 = 1.0;
        double r8028238 = r8028237 - r8028235;
        double r8028239 = z;
        double r8028240 = r8028238 * r8028239;
        double r8028241 = fma(r8028235, r8028236, r8028240);
        return r8028241;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(1 - x\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  (+ (* x y) (* (- 1.0 x) z)))