Average Error: 0.0 → 0.0
Time: 1.3s
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 r1292 = re;
        double r1293 = r1292 * r1292;
        double r1294 = im;
        double r1295 = r1294 * r1294;
        double r1296 = r1293 - r1295;
        return r1296;
}
↓
double f(double re, double im) {
        double r1297 = re;
        double r1298 = im;
        double r1299 = r1297 + r1298;
        double r1300 = r1297 - r1298;
        double r1301 = r1299 * r1300;
        return r1301;
}

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. Using strategy rm

  3. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(re + im\right) \cdot \left(re - im\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(re + im\right) \cdot \left(re - im\right)\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))