Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot im + im \cdot re\]
re \cdot im + im \cdot re
↓
re \cdot im + im \cdot re
double f(double re, double im) {
        double r11379 = re;
        double r11380 = im;
        double r11381 = r11379 * r11380;
        double r11382 = r11380 * r11379;
        double r11383 = r11381 + r11382;
        return r11383;
}
↓
double f(double re, double im) {
        double r11384 = re;
        double r11385 = im;
        double r11386 = r11384 * r11385;
        double r11387 = r11385 * r11384;
        double r11388 = r11386 + r11387;
        return r11388;
}

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

    \[re \cdot im + im \cdot re\]

  2. Final simplification0.0

    \[\leadsto re \cdot im + im \cdot re\]

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))