Average Error: 32.4 → 32.4
Time: 3.1s
Precision: binary64
\[\frac{\left(\sqrt{x \cdot x - 1} + x\right) + 1}{2 \cdot \sqrt{\sqrt{x \cdot x - 1} + x}}\]
↓
\[\frac{\left(\sqrt{x \cdot x - 1} + x\right) + 1}{2 \cdot \sqrt{\sqrt{x \cdot x - 1} + x}}\]
\frac{\left(\sqrt{x \cdot x - 1} + x\right) + 1}{2 \cdot \sqrt{\sqrt{x \cdot x - 1} + x}}
↓
\frac{\left(\sqrt{x \cdot x - 1} + x\right) + 1}{2 \cdot \sqrt{\sqrt{x \cdot x - 1} + x}}
double code(double x) {
	return ((double) (((double) (((double) (((double) sqrt(((double) (((double) (x * x)) - 1.0)))) + x)) + 1.0)) / ((double) (2.0 * ((double) sqrt(((double) (((double) sqrt(((double) (((double) (x * x)) - 1.0)))) + x))))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) sqrt(((double) (((double) (x * x)) - 1.0)))) + x)) + 1.0)) / ((double) (2.0 * ((double) sqrt(((double) (((double) sqrt(((double) (((double) (x * x)) - 1.0)))) + x))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 32.4

    \[\frac{\left(\sqrt{x \cdot x - 1} + x\right) + 1}{2 \cdot \sqrt{\sqrt{x \cdot x - 1} + x}}\]

  2. Final simplification32.4

    \[\leadsto \frac{\left(\sqrt{x \cdot x - 1} + x\right) + 1}{2 \cdot \sqrt{\sqrt{x \cdot x - 1} + x}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (+ (+ (sqrt (- (* x x) 1)) x) 1) (* 2 (sqrt (+ (sqrt (- (* x x) 1)) x))))"
  :precision binary64
  (/ (+ (+ (sqrt (- (* x x) 1.0)) x) 1.0) (* 2.0 (sqrt (+ (sqrt (- (* x x) 1.0)) x)))))