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

Average Error: 0.0 → 0.0

Time: 6.4s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r239574 = x;
        double r239575 = y;
        double r239576 = r239575 - r239574;
        double r239577 = z;
        double r239578 = r239576 * r239577;
        double r239579 = r239574 + r239578;
        return r239579;
}

↓

double f(double x, double y, double z) {
        double r239580 = z;
        double r239581 = y;
        double r239582 = x;
        double r239583 = r239581 - r239582;
        double r239584 = fma(r239580, r239583, r239582);
        return r239584;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019351 +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)))