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 r8152 = re;
        double r8153 = r8152 * r8152;
        double r8154 = im;
        double r8155 = r8154 * r8154;
        double r8156 = r8153 - r8155;
        return r8156;
}
↓
double f(double re, double im) {
        double r8157 = re;
        double r8158 = im;
        double r8159 = r8157 - r8158;
        double r8160 = r8157 + r8158;
        double r8161 = r8159 * r8160;
        return r8161;
}

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 2019209 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))