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

Average Error: 0.0 → 0.0

Time: 3.7s

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 r202022 = x;
        double r202023 = y;
        double r202024 = r202023 - r202022;
        double r202025 = z;
        double r202026 = r202024 * r202025;
        double r202027 = r202022 + r202026;
        return r202027;
}

↓

double f(double x, double y, double z) {
        double r202028 = z;
        double r202029 = y;
        double r202030 = x;
        double r202031 = r202029 - r202030;
        double r202032 = fma(r202028, r202031, r202030);
        return r202032;
}

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 2020043 +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)))