Average Error: 0.0 → 0.0
Time: 5.7s
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 r1522 = re;
        double r1523 = r1522 * r1522;
        double r1524 = im;
        double r1525 = r1524 * r1524;
        double r1526 = r1523 - r1525;
        return r1526;
}
↓
double f(double re, double im) {
        double r1527 = re;
        double r1528 = im;
        double r1529 = r1527 - r1528;
        double r1530 = r1527 + r1528;
        double r1531 = r1529 * r1530;
        return r1531;
}

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)))