Average Error: 18.5 → 18.5
Time: 2.6s
Precision: binary64
\[\frac{1}{\sqrt{\left(x - b\right) \cdot \left(x - b\right) + a \cdot a}} - \frac{1}{\sqrt{\left(x + b\right) \cdot \left(x + b\right) + a \cdot a}}\]
↓
\[\frac{1}{\sqrt{\left(x - b\right) \cdot \left(x - b\right) + a \cdot a}} - \frac{1}{\sqrt{\left(x + b\right) \cdot \left(x + b\right) + a \cdot a}}\]
\frac{1}{\sqrt{\left(x - b\right) \cdot \left(x - b\right) + a \cdot a}} - \frac{1}{\sqrt{\left(x + b\right) \cdot \left(x + b\right) + a \cdot a}}
↓
\frac{1}{\sqrt{\left(x - b\right) \cdot \left(x - b\right) + a \cdot a}} - \frac{1}{\sqrt{\left(x + b\right) \cdot \left(x + b\right) + a \cdot a}}
double code(double x, double b, double a) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) (((double) (((double) (x - b)) * ((double) (x - b)))) + ((double) (a * a)))))))) - ((double) (1.0 / ((double) sqrt(((double) (((double) (((double) (x + b)) * ((double) (x + b)))) + ((double) (a * a))))))))));
}
↓
double code(double x, double b, double a) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) (((double) (((double) (x - b)) * ((double) (x - b)))) + ((double) (a * a)))))))) - ((double) (1.0 / ((double) sqrt(((double) (((double) (((double) (x + b)) * ((double) (x + b)))) + ((double) (a * a))))))))));
}

Error

Bits error versus x

Bits error versus b

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.5

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

  2. Final simplification18.5

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

Reproduce

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