Average Error: 0.0 → 0.0
Time: 2.0s
Precision: binary64
\[re \cdot re - im \cdot im\]
↓
\[\left(re + im\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(re + im\right) \cdot \left(re - im\right)
(FPCore (re im) :precision binary64 (- (* re re) (* im im)))
↓
(FPCore (re im) :precision binary64 (* (+ re im) (- re im)))
double code(double re, double im) {
	return ((double) (((double) (re * re)) - ((double) (im * im))));
}
↓
double code(double re, double im) {
	return ((double) (((double) (re + im)) * ((double) (re - 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

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

  3. Applied difference-of-squaresError: 0.0 bits

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

  4. Final simplificationError: 0.0 bits

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

Reproduce

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