Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[im \cdot \left(re + re\right)\]
re \cdot im + im \cdot re
↓
im \cdot \left(re + re\right)
double f(double re, double im) {
        double r250094 = re;
        double r250095 = im;
        double r250096 = r250094 * r250095;
        double r250097 = r250095 * r250094;
        double r250098 = r250096 + r250097;
        return r250098;
}
↓
double f(double re, double im) {
        double r250099 = im;
        double r250100 = re;
        double r250101 = r250100 + r250100;
        double r250102 = r250099 * r250101;
        return r250102;
}

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

    \[\leadsto \color{blue}{im \cdot re + im \cdot re}\]
  3. Using strategy rm

  4. Applied distribute-lft-out0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))