Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[\left(2 \cdot im\right) \cdot re\]
re \cdot im + im \cdot re
↓
\left(2 \cdot im\right) \cdot re
double f(double re, double im) {
        double r8035 = re;
        double r8036 = im;
        double r8037 = r8035 * r8036;
        double r8038 = r8036 * r8035;
        double r8039 = r8037 + r8038;
        return r8039;
}
↓
double f(double re, double im) {
        double r8040 = 2.0;
        double r8041 = im;
        double r8042 = r8040 * r8041;
        double r8043 = re;
        double r8044 = r8042 * r8043;
        return r8044;
}

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

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

  3. Final simplification0.0

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

Reproduce

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