math.square on complex, imaginary part

Average Error: 0.0 → 0.0

Time: 379.0ms

Precision: 64

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

Math

\[re \cdot im + im \cdot re\]

↓

\[im \cdot \left(re + re\right)\]

C

double f(double re, double im) {
        double r1609 = re;
        double r1610 = im;
        double r1611 = r1609 * r1610;
        double r1612 = r1610 * r1609;
        double r1613 = r1611 + r1612;
        return r1613;
}

↓

double f(double re, double im) {
        double r1614 = im;
        double r1615 = re;
        double r1616 = r1615 + r1615;
        double r1617 = r1614 * r1616;
        return r1617;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.0

   \[re \cdot im + im \cdot re\]

2. Simplified 0.0

   \[\leadsto \color{blue}{im \cdot \left(re + re\right)}\]

3. Final simplification 0.0

   \[\leadsto im \cdot \left(re + re\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))