Average Error: 0.0 → 0.0
Time: 21.2s
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 r9375 = re;
        double r9376 = r9375 * r9375;
        double r9377 = im;
        double r9378 = r9377 * r9377;
        double r9379 = r9376 - r9378;
        return r9379;
}
↓
double f(double re, double im) {
        double r9380 = re;
        double r9381 = im;
        double r9382 = r9380 - r9381;
        double r9383 = r9380 + r9381;
        double r9384 = r9382 * r9383;
        return r9384;
}

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 2019304 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))