math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 4.3s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r10122 = re;
        double r10123 = im;
        double r10124 = r10122 * r10123;
        double r10125 = r10123 * r10122;
        double r10126 = r10124 + r10125;
        return r10126;
}

↓

double f(double re, double im) {
        double r10127 = im;
        double r10128 = r10127 + r10127;
        double r10129 = re;
        double r10130 = r10128 * r10129;
        return r10130;
}

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

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019164 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))