Average Error: 4.1 → 0.0
Time: 1.2s
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_sqr (re im) :precision binary64 (- (* re re) (* im im)))
↓
(FPCore re_sqr (re im) :precision binary64 (* (+ re im) (- re im)))
double re_sqr(double re, double im) {
	return (re * re) - (im * im);
}
↓
double re_sqr(double re, double im) {
	return (re + im) * (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 4.1

    \[re \cdot re - im \cdot im \]

  2. Applied difference-of-squares_binary640.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022067 
(FPCore re_sqr (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))