Average Error: 0.0 → 0.0
Time: 9.0s
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 r113589 = x;
        double r113590 = y;
        double r113591 = r113590 - r113589;
        double r113592 = z;
        double r113593 = r113591 * r113592;
        double r113594 = r113589 + r113593;
        return r113594;
}
↓
double f(double x, double y, double z) {
        double r113595 = z;
        double r113596 = y;
        double r113597 = x;
        double r113598 = r113596 - r113597;
        double r113599 = fma(r113595, r113598, r113597);
        return r113599;
}

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 2019235 +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)))