Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r34120 = re;
        double r34121 = r34120 * r34120;
        double r34122 = im;
        double r34123 = r34122 * r34122;
        double r34124 = r34121 - r34123;
        return r34124;
}
↓
double f(double re, double im) {
        double r34125 = im;
        double r34126 = re;
        double r34127 = r34125 + r34126;
        double r34128 = r34126 - r34125;
        double r34129 = r34127 * r34128;
        return r34129;
}

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

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

Reproduce

herbie shell --seed 2019121 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))