Average Error: 0.0 → 0.0
Time: 4.1s
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 r147368 = x;
        double r147369 = y;
        double r147370 = r147369 - r147368;
        double r147371 = z;
        double r147372 = r147370 * r147371;
        double r147373 = r147368 + r147372;
        return r147373;
}
↓
double f(double x, double y, double z) {
        double r147374 = z;
        double r147375 = y;
        double r147376 = x;
        double r147377 = r147375 - r147376;
        double r147378 = fma(r147374, r147377, r147376);
        return r147378;
}

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 2019347 +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)))