Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot im + im \cdot re\]
re \cdot im + im \cdot re
↓
re \cdot im + im \cdot re
double f(double re, double im) {
        double r13298 = re;
        double r13299 = im;
        double r13300 = r13298 * r13299;
        double r13301 = r13299 * r13298;
        double r13302 = r13300 + r13301;
        return r13302;
}
↓
double f(double re, double im) {
        double r13303 = re;
        double r13304 = im;
        double r13305 = r13303 * r13304;
        double r13306 = r13304 * r13303;
        double r13307 = r13305 + r13306;
        return r13307;
}

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. Final simplification0.0

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

Reproduce

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