Average Error: 10.8 → 10.8
Time: 3.7s
Precision: binary64
\[\frac{1}{\sqrt{1 + x} + \sqrt{1 + y}} - \frac{1}{\sqrt{1 + z} + \sqrt{1 + a}}\]
↓
\[\frac{1}{\sqrt{1 + x} + \sqrt{1 + y}} - \frac{1}{\sqrt{1 + z} + \sqrt{1 + a}}\]
\frac{1}{\sqrt{1 + x} + \sqrt{1 + y}} - \frac{1}{\sqrt{1 + z} + \sqrt{1 + a}}
↓
\frac{1}{\sqrt{1 + x} + \sqrt{1 + y}} - \frac{1}{\sqrt{1 + z} + \sqrt{1 + a}}
double code(double x, double y, double z, double a) {
	return ((double) (((double) (1.0 / ((double) (((double) sqrt(((double) (1.0 + x)))) + ((double) sqrt(((double) (1.0 + y)))))))) - ((double) (1.0 / ((double) (((double) sqrt(((double) (1.0 + z)))) + ((double) sqrt(((double) (1.0 + a))))))))));
}
↓
double code(double x, double y, double z, double a) {
	return ((double) (((double) (1.0 / ((double) (((double) sqrt(((double) (1.0 + x)))) + ((double) sqrt(((double) (1.0 + y)))))))) - ((double) (1.0 / ((double) (((double) sqrt(((double) (1.0 + z)))) + ((double) sqrt(((double) (1.0 + a))))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 10.8

    \[\frac{1}{\sqrt{1 + x} + \sqrt{1 + y}} - \frac{1}{\sqrt{1 + z} + \sqrt{1 + a}}\]

  2. Final simplification10.8

    \[\leadsto \frac{1}{\sqrt{1 + x} + \sqrt{1 + y}} - \frac{1}{\sqrt{1 + z} + \sqrt{1 + a}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y z a)
  :name "(- (/ 1 (+ (sqrt (+ 1 x)) (sqrt (+ 1 y)))) (/ 1 (+ (sqrt (+ 1 z)) (sqrt (+ 1 a)))))"
  :precision binary64
  (- (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt (+ 1.0 y)))) (/ 1.0 (+ (sqrt (+ 1.0 z)) (sqrt (+ 1.0 a))))))