Average Error: 0.0 → 0.0
Time: 8.8s
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 r1422 = re;
        double r1423 = r1422 * r1422;
        double r1424 = im;
        double r1425 = r1424 * r1424;
        double r1426 = r1423 - r1425;
        return r1426;
}
↓
double f(double re, double im) {
        double r1427 = re;
        double r1428 = im;
        double r1429 = r1427 - r1428;
        double r1430 = r1427 + r1428;
        double r1431 = r1429 * r1430;
        return r1431;
}

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 2020046 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))