Average Error: 0.0 → 0.0
Time: 6.5s
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 r1490 = re;
        double r1491 = r1490 * r1490;
        double r1492 = im;
        double r1493 = r1492 * r1492;
        double r1494 = r1491 - r1493;
        return r1494;
}
↓
double f(double re, double im) {
        double r1495 = re;
        double r1496 = im;
        double r1497 = r1495 - r1496;
        double r1498 = r1495 + r1496;
        double r1499 = r1497 * r1498;
        return r1499;
}

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)))