Average Error: 0.0 → 0.0
Time: 8.5s
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 r7426731 = x;
        double r7426732 = y;
        double r7426733 = r7426732 - r7426731;
        double r7426734 = z;
        double r7426735 = r7426733 * r7426734;
        double r7426736 = r7426731 + r7426735;
        return r7426736;
}
↓
double f(double x, double y, double z) {
        double r7426737 = y;
        double r7426738 = x;
        double r7426739 = r7426737 - r7426738;
        double r7426740 = z;
        double r7426741 = fma(r7426739, r7426740, r7426738);
        return r7426741;
}

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 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))