Average Error: 0.0 → 0.0
Time: 1.2s
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 r1235 = re;
        double r1236 = r1235 * r1235;
        double r1237 = im;
        double r1238 = r1237 * r1237;
        double r1239 = r1236 - r1238;
        return r1239;
}
↓
double f(double re, double im) {
        double r1240 = re;
        double r1241 = im;
        double r1242 = r1240 + r1241;
        double r1243 = r1240 - r1241;
        double r1244 = r1242 * r1243;
        return r1244;
}

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 2020046 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))