Average Error: 0.0 → 0.0
Time: 833.0ms
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 r171522 = x;
        double r171523 = y;
        double r171524 = r171523 - r171522;
        double r171525 = z;
        double r171526 = r171524 * r171525;
        double r171527 = r171522 + r171526;
        return r171527;
}
↓
double f(double x, double y, double z) {
        double r171528 = z;
        double r171529 = y;
        double r171530 = x;
        double r171531 = r171529 - r171530;
        double r171532 = fma(r171528, r171531, r171530);
        return r171532;
}

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 2020001 +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)))