Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot im + re \cdot im\]
re \cdot im + im \cdot re
↓
re \cdot im + re \cdot im
double f(double re, double im) {
        double r8043 = re;
        double r8044 = im;
        double r8045 = r8043 * r8044;
        double r8046 = r8044 * r8043;
        double r8047 = r8045 + r8046;
        return r8047;
}
↓
double f(double re, double im) {
        double r8048 = re;
        double r8049 = im;
        double r8050 = r8048 * r8049;
        double r8051 = r8050 + r8050;
        return r8051;
}

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

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))