Average Error: 2.0 → 2.0
Time: 22.3s
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 r390127 = 0.5;
        double r390128 = /* ERROR: no posit support in C */;
        double r390129 = 2.0;
        double r390130 = /* ERROR: no posit support in C */;
        double r390131 = re;
        double r390132 = r390131 * r390131;
        double r390133 = im;
        double r390134 = r390133 * r390133;
        double r390135 = r390132 + r390134;
        double r390136 = sqrt(r390135);
        double r390137 = r390136 + r390131;
        double r390138 = r390130 * r390137;
        double r390139 = sqrt(r390138);
        double r390140 = r390128 * r390139;
        return r390140;
}
↓
double f(double re, double im) {
        double r390141 = 0.5;
        double r390142 = 2.0;
        double r390143 = re;
        double r390144 = r390143 * r390143;
        double r390145 = /*Error: no posit support in C */;
        double r390146 = im;
        double r390147 = /*Error: no posit support in C */;
        double r390148 = /*Error: no posit support in C */;
        double r390149 = sqrt(r390148);
        double r390150 = r390149 + r390143;
        double r390151 = r390142 * r390150;
        double r390152 = sqrt(r390151);
        double r390153 = r390141 * r390152;
        return r390153;
}

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 2.0

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

  3. Applied introduce-quire2.0

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

  4. Applied insert-quire-fdp-add2.0

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

  5. Final simplification2.0

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

Reproduce

herbie shell --seed 2019165 
(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)))))