Average Error: 2.2 → 2.1
Time: 41.7s
Precision: 64
\[\left(0.5\right) \cdot \left(\sqrt{\left(\left(2.0\right) \cdot \left(\frac{\left(\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}\right)}{re}\right)\right)}\right)\]
↓
\[\left(0.5\right) \cdot \left(\sqrt{\left(\left(2.0\right) \cdot \left(\frac{\left(\sqrt{\left(\left(\mathsf{qma}\left(\left(\left(re \cdot re\right)\right), im, im\right)\right)\right)}\right)}{re}\right)\right)}\right)\]
\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)
↓
\left(0.5\right) \cdot \left(\sqrt{\left(\left(2.0\right) \cdot \left(\frac{\left(\sqrt{\left(\left(\mathsf{qma}\left(\left(\left(re \cdot re\right)\right), im, im\right)\right)\right)}\right)}{re}\right)\right)}\right)
double f(double re, double im) {
        double r938377 = 0.5;
        double r938378 = /* ERROR: no posit support in C */;
        double r938379 = 2.0;
        double r938380 = /* ERROR: no posit support in C */;
        double r938381 = re;
        double r938382 = r938381 * r938381;
        double r938383 = im;
        double r938384 = r938383 * r938383;
        double r938385 = r938382 + r938384;
        double r938386 = sqrt(r938385);
        double r938387 = r938386 + r938381;
        double r938388 = r938380 * r938387;
        double r938389 = sqrt(r938388);
        double r938390 = r938378 * r938389;
        return r938390;
}
↓
double f(double re, double im) {
        double r938391 = 0.5;
        double r938392 = /* ERROR: no posit support in C */;
        double r938393 = 2.0;
        double r938394 = /* ERROR: no posit support in C */;
        double r938395 = re;
        double r938396 = r938395 * r938395;
        double r938397 = /*Error: no posit support in C */;
        double r938398 = im;
        double r938399 = /*Error: no posit support in C */;
        double r938400 = /*Error: no posit support in C */;
        double r938401 = sqrt(r938400);
        double r938402 = r938401 + r938395;
        double r938403 = r938394 * r938402;
        double r938404 = sqrt(r938403);
        double r938405 = r938392 * r938404;
        return r938405;
}

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 2.2

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

  3. Applied introduce-quire2.2

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

  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

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

Reproduce

herbie shell --seed 2019168 
(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)))))