Average Error: 14.4 → 0.3
Time: 3.5s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double a, double b) {
	return ((double) (((double) (((double) (((double) M_PI) / 2.0)) * ((double) (1.0 / ((double) (((double) (b * b)) - ((double) (a * a)))))))) * ((double) (((double) (1.0 / a)) - ((double) (1.0 / b))))));
}

↓
double code(double a, double b) {
	return ((double) (((double) (((double) (((double) M_PI) / ((double) (a + b)))) * ((double) (1.0 * ((double) (((double) (1.0 / a)) - ((double) (1.0 / b)))))))) / ((double) (((double) (b - a)) * 2.0))));
}

Error
Bits error versus a
Bits error versus b
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 14.4
    \[\]
  2. Simplified14.4
    \[\leadsto \]
  3. Using strategy rm
  4. Applied associate-*r/14.4
    \[\leadsto \]
  5. Applied associate-*r/14.4
    \[\leadsto \]
  6. Simplified14.4
    \[\leadsto \]
  7. Using strategy rm
  8. Applied times-frac14.4
    \[\leadsto \]
  9. Simplified0.3
    \[\leadsto \]
  10. Using strategy rm
  11. Applied associate-*r/0.3
    \[\leadsto \]
  12. Applied frac-times0.3
    \[\leadsto \]
  13. Simplified0.3
    \[\leadsto \]
  14. Simplified0.3
    \[\leadsto \]
  15. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  :precision binary64
  (* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b))))