Average Error: 2.1 → 2.1
Time: 11.4s
Precision: 64
\[\left(0.5\right) \cdot \left(\sqrt{\left(\left(2.0\right) \cdot \left(\frac{\left(\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}\right)}{re}\right)\right)}\right)\]
↓
\[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{\left(\mathsf{qma}\left(\left(\left(re \cdot re\right)\right), im, im\right)\right)} + re\right)}\]
\left(0.5\right) \cdot \left(\sqrt{\left(\left(2.0\right) \cdot \left(\frac{\left(\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}\right)}{re}\right)\right)}\right)
↓
0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{\left(\mathsf{qma}\left(\left(\left(re \cdot re\right)\right), im, im\right)\right)} + re\right)}
double f(double re, double im) {
        double r396382 = 0.5;
        double r396383 = /* ERROR: no posit support in C */;
        double r396384 = 2.0;
        double r396385 = /* ERROR: no posit support in C */;
        double r396386 = re;
        double r396387 = r396386 * r396386;
        double r396388 = im;
        double r396389 = r396388 * r396388;
        double r396390 = r396387 + r396389;
        double r396391 = sqrt(r396390);
        double r396392 = r396391 + r396386;
        double r396393 = r396385 * r396392;
        double r396394 = sqrt(r396393);
        double r396395 = r396383 * r396394;
        return r396395;
}
↓
double f(double re, double im) {
        double r396396 = 0.5;
        double r396397 = 2.0;
        double r396398 = re;
        double r396399 = r396398 * r396398;
        double r396400 = /*Error: no posit support in C */;
        double r396401 = im;
        double r396402 = /*Error: no posit support in C */;
        double r396403 = /*Error: no posit support in C */;
        double r396404 = sqrt(r396403);
        double r396405 = r396404 + r396398;
        double r396406 = r396397 * r396405;
        double r396407 = sqrt(r396406);
        double r396408 = r396396 * r396407;
        return r396408;
}

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 2.1

    \[\left(0.5\right) \cdot \left(\sqrt{\left(\left(2.0\right) \cdot \left(\frac{\left(\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}\right)}{re}\right)\right)}\right)\]
  2. Using strategy rm

  3. Applied introduce-quire2.1

    \[\leadsto \left(0.5\right) \cdot \left(\sqrt{\left(\left(2.0\right) \cdot \left(\frac{\left(\sqrt{\left(\frac{\color{blue}{\left(\left(\left(re \cdot re\right)\right)\right)}}{\left(im \cdot im\right)}\right)}\right)}{re}\right)\right)}\right)\]

  4. Applied insert-quire-fdp-add2.1

    \[\leadsto \left(0.5\right) \cdot \left(\sqrt{\left(\left(2.0\right) \cdot \left(\frac{\left(\sqrt{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(re \cdot re\right)\right), im, im\right)\right)\right)}}\right)}{re}\right)\right)}\right)\]

  5. Final simplification2.1

    \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{\left(\mathsf{qma}\left(\left(\left(re \cdot re\right)\right), im, im\right)\right)} + re\right)}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (re im)
  :name "math.sqrt on complex, real part"
  (*.p16 (real->posit16 0.5) (sqrt.p16 (*.p16 (real->posit16 2.0) (+.p16 (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))) re)))))