math.square on complex, imaginary part

Average Error: 0.1 → 0.1

Time: 3.7s

Precision: 64

Math

\[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]

↓

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

C

double f(double re, double im) {
        double r8549 = re;
        double r8550 = im;
        double r8551 = r8549 * r8550;
        double r8552 = r8550 * r8549;
        double r8553 = r8551 + r8552;
        return r8553;
}

↓

double f(double re, double im) {
        double r8554 = re;
        double r8555 = im;
        double r8556 = r8554 * r8555;
        double r8557 = r8555 * r8554;
        double r8558 = r8556 + r8557;
        return r8558;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.1

   \[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019135 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))