Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
Cost: 448
\[re \cdot re - im \cdot im\]
↓
\[\left(re + im\right) \cdot \left(re - im\right)\]
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 (re * re) - (im * im);
}
↓
double code(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

Alternatives

Alternative 1
Error12.8
Cost849
\[\begin{array}{l} \mathbf{if}\;re \leq -3.224450515213971 \cdot 10^{-37} \lor \neg \left(re \leq -5.926855860335571 \cdot 10^{-51} \lor \neg \left(re \leq -5.2058524450127765 \cdot 10^{-65}\right) \land re \leq 7.150922772501069 \cdot 10^{-13}\right):\\ \;\;\;\;re \cdot re\\ \mathbf{else}:\\ \;\;\;\;-im \cdot im\\ \end{array}\]
Alternative 2
Error28.5
Cost192
\[re \cdot re\]
Alternative 3
Error55.3
Cost64
\[0\]
Alternative 4
Error61.8
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

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

  3. Applied difference-of-squares_binary640.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

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