Average Error: 9.5 → 9.5
Time: 2.2s
Precision: binary64
\[\frac{1}{{\left(\sqrt{\left(a - b\right) \cdot \left(a - b\right) + r \cdot r}\right)}^{3}} - \frac{1}{{\left(\sqrt{\left(a + b\right) \cdot \left(a + b\right) + r \cdot r}\right)}^{3}}\]
↓
\[\frac{1}{{\left(\sqrt{\left(a - b\right) \cdot \left(a - b\right) + r \cdot r}\right)}^{3}} - \frac{1}{{\left(\sqrt{\left(a + b\right) \cdot \left(a + b\right) + r \cdot r}\right)}^{3}}\]
\frac{1}{{\left(\sqrt{\left(a - b\right) \cdot \left(a - b\right) + r \cdot r}\right)}^{3}} - \frac{1}{{\left(\sqrt{\left(a + b\right) \cdot \left(a + b\right) + r \cdot r}\right)}^{3}}
↓
\frac{1}{{\left(\sqrt{\left(a - b\right) \cdot \left(a - b\right) + r \cdot r}\right)}^{3}} - \frac{1}{{\left(\sqrt{\left(a + b\right) \cdot \left(a + b\right) + r \cdot r}\right)}^{3}}
double code(double a, double b, double r) {
	return ((double) (((double) (1.0 / ((double) pow(((double) sqrt(((double) (((double) (((double) (a - b)) * ((double) (a - b)))) + ((double) (r * r)))))), 3.0)))) - ((double) (1.0 / ((double) pow(((double) sqrt(((double) (((double) (((double) (a + b)) * ((double) (a + b)))) + ((double) (r * r)))))), 3.0))))));
}
↓
double code(double a, double b, double r) {
	return ((double) (((double) (1.0 / ((double) pow(((double) sqrt(((double) (((double) (((double) (a - b)) * ((double) (a - b)))) + ((double) (r * r)))))), 3.0)))) - ((double) (1.0 / ((double) pow(((double) sqrt(((double) (((double) (((double) (a + b)) * ((double) (a + b)))) + ((double) (r * r)))))), 3.0))))));
}

Error

Bits error versus a

Bits error versus b

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 9.5

    \[\frac{1}{{\left(\sqrt{\left(a - b\right) \cdot \left(a - b\right) + r \cdot r}\right)}^{3}} - \frac{1}{{\left(\sqrt{\left(a + b\right) \cdot \left(a + b\right) + r \cdot r}\right)}^{3}}\]

  2. Final simplification9.5

    \[\leadsto \frac{1}{{\left(\sqrt{\left(a - b\right) \cdot \left(a - b\right) + r \cdot r}\right)}^{3}} - \frac{1}{{\left(\sqrt{\left(a + b\right) \cdot \left(a + b\right) + r \cdot r}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a b r)
  :name "(- (/ 1 (pow (sqrt (+ (* (- a b) (- a b)) (* r r))) 3)) (/ 1 (pow (sqrt (+ (* (+ a b) (+ a b)) (* r r))) 3)))"
  :precision binary64
  (- (/ 1.0 (pow (sqrt (+ (* (- a b) (- a b)) (* r r))) 3.0)) (/ 1.0 (pow (sqrt (+ (* (+ a b) (+ a b)) (* r r))) 3.0))))