Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(z, y - x, x\right)\]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(z, y - x, x\right)
double f(double x, double y, double z) {
        double r113228 = x;
        double r113229 = y;
        double r113230 = r113229 - r113228;
        double r113231 = z;
        double r113232 = r113230 * r113231;
        double r113233 = r113228 + r113232;
        return r113233;
}
↓
double f(double x, double y, double z) {
        double r113234 = z;
        double r113235 = y;
        double r113236 = x;
        double r113237 = r113235 - r113236;
        double r113238 = fma(r113234, r113237, r113236);
        return r113238;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x + \left(y - x\right) \cdot z\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))