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

Average Error: 0.0 → 0.0

Time: 2.6s

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 r134384 = x;
        double r134385 = y;
        double r134386 = r134385 - r134384;
        double r134387 = z;
        double r134388 = r134386 * r134387;
        double r134389 = r134384 + r134388;
        return r134389;
}

↓

double f(double x, double y, double z) {
        double r134390 = z;
        double r134391 = y;
        double r134392 = x;
        double r134393 = r134391 - r134392;
        double r134394 = fma(r134390, r134393, r134392);
        return r134394;
}

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 2019350 +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)))