Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re - im\right) \cdot \left(re + im\right)\]
re \cdot re - im \cdot im
↓
\left(re - im\right) \cdot \left(re + im\right)
double f(double re, double im) {
        double r176 = re;
        double r177 = r176 * r176;
        double r178 = im;
        double r179 = r178 * r178;
        double r180 = r177 - r179;
        return r180;
}
↓
double f(double re, double im) {
        double r181 = re;
        double r182 = im;
        double r183 = r181 - r182;
        double r184 = r181 + r182;
        double r185 = r183 * r184;
        return r185;
}

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

    \[re \cdot re - im \cdot im\]

  2. Simplified0.0

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

  3. Final simplification0.0

    \[\leadsto \left(re - im\right) \cdot \left(re + im\right)\]

Reproduce

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