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

Average Error: 0.0 → 0.0

Time: 3.2s

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 r212773 = x;
        double r212774 = y;
        double r212775 = r212774 - r212773;
        double r212776 = z;
        double r212777 = r212775 * r212776;
        double r212778 = r212773 + r212777;
        return r212778;
}

↓

double f(double x, double y, double z) {
        double r212779 = z;
        double r212780 = y;
        double r212781 = x;
        double r212782 = r212780 - r212781;
        double r212783 = fma(r212779, r212782, r212781);
        return r212783;
}

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 2020042 +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)))