Average Error: 0.0 → 0.0
Time: 571.0ms
Precision: binary64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot \left(im + im\right)\]
re \cdot im + im \cdot re
↓
re \cdot \left(im + im\right)
(FPCore (re im) :precision binary64 (+ (* re im) (* im re)))
↓
(FPCore (re im) :precision binary64 (* re (+ im im)))
double code(double re, double im) {
	return ((double) (((double) (re * im)) + ((double) (im * re))));
}
↓
double code(double re, double im) {
	return ((double) (re * ((double) (im + im))));
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 0.0 bits

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

  2. SimplifiedError: 0.0 bits

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

  3. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))