Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Average Error: 0.0 → 0.0

Time: 8.1s

Precision: 64

Math

\[x + \left(y - x\right) \cdot z\]

↓

\[\mathsf{fma}\left(y - x, z, x\right)\]

C

double f(double x, double y, double z) {
        double r8511610 = x;
        double r8511611 = y;
        double r8511612 = r8511611 - r8511610;
        double r8511613 = z;
        double r8511614 = r8511612 * r8511613;
        double r8511615 = r8511610 + r8511614;
        return r8511615;
}

↓

double f(double x, double y, double z) {
        double r8511616 = y;
        double r8511617 = x;
        double r8511618 = r8511616 - r8511617;
        double r8511619 = z;
        double r8511620 = fma(r8511618, r8511619, r8511617);
        return r8511620;
}

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. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z, x\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(y - x, z, x\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))