Average Error: 15.6 → 15.6
Time: 1.4s
Precision: binary64
\[\sqrt{x \cdot \left(expt \cdot 2\right) + y \cdot \left(expt \cdot 2\right)}\]
↓
\[\sqrt{x \cdot \left(expt \cdot 2\right) + y \cdot \left(expt \cdot 2\right)}\]
\sqrt{x \cdot \left(expt \cdot 2\right) + y \cdot \left(expt \cdot 2\right)}
↓
\sqrt{x \cdot \left(expt \cdot 2\right) + y \cdot \left(expt \cdot 2\right)}
double code(double x, double expt, double y) {
	return ((double) sqrt(((double) (((double) (x * ((double) (expt * 2.0)))) + ((double) (y * ((double) (expt * 2.0))))))));
}
↓
double code(double x, double expt, double y) {
	return ((double) sqrt(((double) (((double) (x * ((double) (expt * 2.0)))) + ((double) (y * ((double) (expt * 2.0))))))));
}

Error

Bits error versus x

Bits error versus expt

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.6

    \[\sqrt{x \cdot \left(expt \cdot 2\right) + y \cdot \left(expt \cdot 2\right)}\]

  2. Final simplification15.6

    \[\leadsto \sqrt{x \cdot \left(expt \cdot 2\right) + y \cdot \left(expt \cdot 2\right)}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x expt y)
  :name "(sqrt (+ (* x (* expt 2)) (* y (* expt 2))))"
  :precision binary64
  (sqrt (+ (* x (* expt 2.0)) (* y (* expt 2.0)))))