Average Error: 0.0 → 0.0
Time: 11.1s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(y - x, z, x\right)\]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(y - x, z, x\right)
double f(double x, double y, double z) {
        double r5365094 = x;
        double r5365095 = y;
        double r5365096 = r5365095 - r5365094;
        double r5365097 = z;
        double r5365098 = r5365096 * r5365097;
        double r5365099 = r5365094 + r5365098;
        return r5365099;
}
↓
double f(double x, double y, double z) {
        double r5365100 = y;
        double r5365101 = x;
        double r5365102 = r5365100 - r5365101;
        double r5365103 = z;
        double r5365104 = fma(r5365102, r5365103, r5365101);
        return r5365104;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))