math.square on complex, imaginary part

Average Error: 0.0 → 0.0

Time: 398.0ms

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 r293 = re;
        double r294 = im;
        double r295 = r293 * r294;
        double r296 = r294 * r293;
        double r297 = r295 + r296;
        return r297;
}

↓

double f(double re, double im) {
        double r298 = im;
        double r299 = re;
        double r300 = r299 + r299;
        double r301 = r298 * r300;
        return r301;
}

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 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))