math.square on complex, imaginary part

Average Error: 0.0 → 0.0

Time: 3.5s

Precision: binary64

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

Math

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

↓

\[2 \cdot \left(im \cdot re\right)\]

C

double code(double re, double im) {
	return ((double) (((double) (re * im)) + ((double) (im * re))));
}

↓

double code(double re, double im) {
	return ((double) (2.0 * ((double) (im * re))));
}

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

   \[\leadsto \color{blue}{2 \cdot \left(im \cdot re\right)}\]

3. Final simplification 0.0

   \[\leadsto 2 \cdot \left(im \cdot re\right)\]

Reproduce

herbie shell --seed 2020182 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))