Average Error: 0.0 → 0.0
Time: 950.0ms
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 r1291 = re;
        double r1292 = im;
        double r1293 = r1291 * r1292;
        double r1294 = r1292 * r1291;
        double r1295 = r1293 + r1294;
        return r1295;
}
↓
double f(double re, double im) {
        double r1296 = re;
        double r1297 = im;
        double r1298 = r1296 * r1297;
        double r1299 = r1297 * r1296;
        double r1300 = r1298 + r1299;
        return r1300;
}

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 2020089 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))