Average Error: 18.7 → 18.7
Time: 3.5s
Precision: binary64
\[\frac{1}{\sqrt{{\left(x - b\right)}^{2} + a \cdot a}} - \frac{1}{\sqrt{{\left(x + b\right)}^{2} + a \cdot a}}\]
↓
\[\frac{1}{\sqrt{{\left(x - b\right)}^{2} + a \cdot a}} - \frac{1}{\sqrt{{\left(x + b\right)}^{2} + a \cdot a}}\]
\frac{1}{\sqrt{{\left(x - b\right)}^{2} + a \cdot a}} - \frac{1}{\sqrt{{\left(x + b\right)}^{2} + a \cdot a}}
↓
\frac{1}{\sqrt{{\left(x - b\right)}^{2} + a \cdot a}} - \frac{1}{\sqrt{{\left(x + b\right)}^{2} + a \cdot a}}
double code(double x, double b, double a) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) (((double) pow(((double) (x - b)), 2.0)) + ((double) (a * a)))))))) - ((double) (1.0 / ((double) sqrt(((double) (((double) pow(((double) (x + b)), 2.0)) + ((double) (a * a))))))))));
}
↓
double code(double x, double b, double a) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) (((double) pow(((double) (x - b)), 2.0)) + ((double) (a * a)))))))) - ((double) (1.0 / ((double) sqrt(((double) (((double) pow(((double) (x + b)), 2.0)) + ((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 18.7

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

  2. Final simplification18.7

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

Reproduce

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