Average Error: 0.0 → 0.0
Time: 2.7s
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 r159677 = x;
        double r159678 = y;
        double r159679 = r159678 - r159677;
        double r159680 = z;
        double r159681 = r159679 * r159680;
        double r159682 = r159677 + r159681;
        return r159682;
}
↓
double f(double x, double y, double z) {
        double r159683 = z;
        double r159684 = y;
        double r159685 = x;
        double r159686 = r159684 - r159685;
        double r159687 = fma(r159683, r159686, r159685);
        return r159687;
}

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 2020025 +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)))