Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot \left(2 \cdot im\right)\]
re \cdot im + im \cdot re
↓
re \cdot \left(2 \cdot im\right)
double f(double re, double im) {
        double r13268 = re;
        double r13269 = im;
        double r13270 = r13268 * r13269;
        double r13271 = r13269 * r13268;
        double r13272 = r13270 + r13271;
        return r13272;
}
↓
double f(double re, double im) {
        double r13273 = re;
        double r13274 = 2.0;
        double r13275 = im;
        double r13276 = r13274 * r13275;
        double r13277 = r13273 * r13276;
        return r13277;
}

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

    \[\leadsto \color{blue}{2 \cdot \left(im \cdot re\right)}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.0

    \[\leadsto \color{blue}{\left(1 \cdot 2\right)} \cdot \left(im \cdot re\right)\]

  5. Applied associate-*l*0.0

    \[\leadsto \color{blue}{1 \cdot \left(2 \cdot \left(im \cdot re\right)\right)}\]

  6. Simplified0.0

    \[\leadsto 1 \cdot \color{blue}{\left(re \cdot \left(2 \cdot im\right)\right)}\]

  7. Final simplification0.0

    \[\leadsto re \cdot \left(2 \cdot im\right)\]

Reproduce

herbie shell --seed 2020045 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))