Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot \left(im + im\right)\]
re \cdot im + im \cdot re
↓
re \cdot \left(im + im\right)
double f(double re, double im) {
        double r56530 = re;
        double r56531 = im;
        double r56532 = r56530 * r56531;
        double r56533 = r56531 * r56530;
        double r56534 = r56532 + r56533;
        return r56534;
}
↓
double f(double re, double im) {
        double r56535 = re;
        double r56536 = im;
        double r56537 = r56536 + r56536;
        double r56538 = r56535 * r56537;
        return r56538;
}

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

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

  2. Simplified0.0

    \[\leadsto \color{blue}{re \cdot im + re \cdot im}\]

  3. Taylor expanded around -inf 0.0

    \[\leadsto \color{blue}{2 \cdot \left(re \cdot im\right)}\]

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019149 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))