Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(\left|im\right| + re\right) \cdot \left(re - \left|im\right|\right)\]
re \cdot re - im \cdot im
↓
\left(\left|im\right| + re\right) \cdot \left(re - \left|im\right|\right)
double code(double re, double im) {
	return ((double) (((double) (re * re)) - ((double) (im * im))));
}
↓
double code(double re, double im) {
	return ((double) (((double) (((double) fabs(im)) + re)) * ((double) (re - ((double) fabs(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 0.0

    \[re \cdot re - im \cdot im\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto re \cdot re - \color{blue}{\sqrt{im \cdot im} \cdot \sqrt{im \cdot im}}\]

  4. Applied difference-of-squares0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))