math.square on complex, imaginary part

Average Error: 0.0 → 0.0

Time: 7.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double re, double im) {
        double r5678 = re;
        double r5679 = im;
        double r5680 = r5678 * r5679;
        double r5681 = r5679 * r5678;
        double r5682 = r5680 + r5681;
        return r5682;
}

↓

double f(double re, double im) {
        double r5683 = re;
        double r5684 = im;
        double r5685 = r5683 * r5684;
        double r5686 = r5684 * r5683;
        double r5687 = r5685 + r5686;
        return r5687;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))