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

Average Error: 0.0 → 0.0

Time: 10.9s

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 r232509 = x;
        double r232510 = y;
        double r232511 = r232510 - r232509;
        double r232512 = z;
        double r232513 = r232511 * r232512;
        double r232514 = r232509 + r232513;
        return r232514;
}

↓

double f(double x, double y, double z) {
        double r232515 = z;
        double r232516 = y;
        double r232517 = x;
        double r232518 = r232516 - r232517;
        double r232519 = fma(r232515, r232518, r232517);
        return r232519;
}

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 2020047 +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)))