Average Error: 0.0 → 0.0
Time: 3.2s
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 r1504 = re;
        double r1505 = r1504 * r1504;
        double r1506 = im;
        double r1507 = r1506 * r1506;
        double r1508 = r1505 - r1507;
        return r1508;
}
↓
double f(double re, double im) {
        double r1509 = re;
        double r1510 = im;
        double r1511 = r1509 - r1510;
        double r1512 = r1509 + r1510;
        double r1513 = r1511 * r1512;
        return r1513;
}

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