Average Error: 0.0 → 0.0
Time: 610.0ms
Precision: binary64
Cost: 320
\[re \cdot im + im \cdot re\]
↓
\[re \cdot \left(im + im\right)\]
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 (re * im) + (im * re);
}
↓
double code(double re, double im) {
	return re * (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

Alternatives

Alternative 1
Error53.4
Cost64
\[0\]
Alternative 2
Error61.6
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))