Average Error: 0.0 → 0.0
Time: 6.4s
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 r6794720 = x;
        double r6794721 = y;
        double r6794722 = r6794721 - r6794720;
        double r6794723 = z;
        double r6794724 = r6794722 * r6794723;
        double r6794725 = r6794720 + r6794724;
        return r6794725;
}
↓
double f(double x, double y, double z) {
        double r6794726 = y;
        double r6794727 = x;
        double r6794728 = r6794726 - r6794727;
        double r6794729 = z;
        double r6794730 = fma(r6794728, r6794729, r6794727);
        return r6794730;
}

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 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))