Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 1.7s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r106122 = x;
        double r106123 = y;
        double r106124 = z;
        double r106125 = r106124 + r106122;
        double r106126 = r106123 * r106125;
        double r106127 = r106122 + r106126;
        return r106127;
}

↓

double f(double x, double y, double z) {
        double r106128 = z;
        double r106129 = x;
        double r106130 = r106128 + r106129;
        double r106131 = y;
        double r106132 = fma(r106130, r106131, r106129);
        return r106132;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))