Average Error: 0.0 → 0.0
Time: 48.8s
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 r336660 = re;
        double r336661 = r336660 * r336660;
        double r336662 = im;
        double r336663 = r336662 * r336662;
        double r336664 = r336661 - r336663;
        return r336664;
}
↓
double f(double re, double im) {
        double r336665 = re;
        double r336666 = im;
        double r336667 = r336665 + r336666;
        double r336668 = r336665 - r336666;
        double r336669 = r336667 * r336668;
        return r336669;
}

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 2019200 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))