math.square on complex, real part

Average Error: 0.0 → 0.0

Time: 14.2s

Precision: 64

Math

\[re \cdot re - im \cdot im\]

↓

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

C

double f(double re, double im) {
        double r221119 = re;
        double r221120 = r221119 * r221119;
        double r221121 = im;
        double r221122 = r221121 * r221121;
        double r221123 = r221120 - r221122;
        return r221123;
}

↓

double f(double re, double im) {
        double r221124 = im;
        double r221125 = re;
        double r221126 = r221124 + r221125;
        double r221127 = r221125 - r221124;
        double r221128 = r221126 * r221127;
        return r221128;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.0

   \[re \cdot re - im \cdot im\]
2. Using strategy rm

3. Applied difference-of-squares 0.0

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

4. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))