Average Error: 39.0 → 39.0
Time: 1.1s
Precision: binary64
\[\sqrt{2 \cdot \left(\sqrt{xre \cdot xre + xim \cdot xim} + xre\right)}\]
↓
\[\sqrt{2 \cdot \left(\sqrt{xre \cdot xre + xim \cdot xim} + xre\right)}\]
\sqrt{2 \cdot \left(\sqrt{xre \cdot xre + xim \cdot xim} + xre\right)}
↓
\sqrt{2 \cdot \left(\sqrt{xre \cdot xre + xim \cdot xim} + xre\right)}
double code(double xre, double xim) {
	return ((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (((double) (xre * xre)) + ((double) (xim * xim)))))) + xre))))));
}
↓
double code(double xre, double xim) {
	return ((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (((double) (xre * xre)) + ((double) (xim * xim)))))) + xre))))));
}

Error

Bits error versus xre

Bits error versus xim

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.0

    \[\sqrt{2 \cdot \left(\sqrt{xre \cdot xre + xim \cdot xim} + xre\right)}\]

  2. Final simplification39.0

    \[\leadsto \sqrt{2 \cdot \left(\sqrt{xre \cdot xre + xim \cdot xim} + xre\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (xre xim)
  :name "(sqrt (* 2.0 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))"
  :precision binary64
  (sqrt (* 2.0 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))))