Average Error: 0.0 → 0.0
Time: 2.5s
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 r203549 = x;
        double r203550 = y;
        double r203551 = r203550 - r203549;
        double r203552 = z;
        double r203553 = r203551 * r203552;
        double r203554 = r203549 + r203553;
        return r203554;
}
↓
double f(double x, double y, double z) {
        double r203555 = z;
        double r203556 = y;
        double r203557 = x;
        double r203558 = r203556 - r203557;
        double r203559 = fma(r203555, r203558, r203557);
        return r203559;
}

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 2019353 +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)))