math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 4.7s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r8975 = re;
        double r8976 = im;
        double r8977 = r8975 * r8976;
        double r8978 = r8976 * r8975;
        double r8979 = r8977 + r8978;
        return r8979;
}

↓

double f(double re, double im) {
        double r8980 = re;
        double r8981 = im;
        double r8982 = r8981 + r8981;
        double r8983 = r8980 * r8982;
        return r8983;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.2

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

2. Simplified 0.2

   \[\leadsto \color{blue}{\frac{\left(im \cdot re\right)}{\left(im \cdot re\right)}}\]
3. Using strategy rm

4. Applied distribute-rgt-out 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))