math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 5.3s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r10963 = re;
        double r10964 = im;
        double r10965 = r10963 * r10964;
        double r10966 = r10964 * r10963;
        double r10967 = r10965 + r10966;
        return r10967;
}

↓

double f(double re, double im) {
        double r10968 = im;
        double r10969 = re;
        double r10970 = r10969 + r10969;
        double r10971 = r10968 * r10970;
        return r10971;
}

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 0.1

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019149 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))