Average Error: 14.4 → 0.3
Time: 3.4s
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) (1.0 * ((double) (1.0 / ((double) (b + a)))))) * ((double) (((double) M_PI) / ((double) (b * ((double) (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. Using strategy rm
  3. Applied difference-of-squares9.2
    \[\leadsto \]
  4. Applied *-un-lft-identity9.2
    \[\leadsto \]
  5. Applied times-frac8.8
    \[\leadsto \]
  6. Applied associate-*r*8.8
    \[\leadsto \]
  7. Simplified8.7
    \[\leadsto \]
  8. Using strategy rm
  9. Applied frac-sub8.7
    \[\leadsto \]
  10. Applied associate-*r/8.7
    \[\leadsto \]
  11. Simplified0.3
    \[\leadsto \]
  12. Using strategy rm
  13. Applied associate-/l*0.3
    \[\leadsto \]
  14. Simplified0.3
    \[\leadsto \]
  15. Using strategy rm
  16. Applied div-inv0.3
    \[\leadsto \]
  17. Applied *-un-lft-identity0.3
    \[\leadsto \]
  18. Applied times-frac0.3
    \[\leadsto \]
  19. Applied *-un-lft-identity0.3
    \[\leadsto \]
  20. Applied times-frac0.3
    \[\leadsto \]
  21. Applied times-frac0.3
    \[\leadsto \]
  22. Simplified0.3
    \[\leadsto \]
  23. Simplified0.3
    \[\leadsto \]
  24. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(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))))