Average Error: 14.2 → 0.3
Time: 4.4s
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) (((double) M_PI) / 2.0)) * ((double) (((double) (1.0 * ((double) (((double) (((double) (1.0 / a)) - ((double) (1.0 / b)))) / ((double) (a + b)))))) / ((double) (b - a))))));
}

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 14.2
    \[\]
  2. Simplified14.2
    \[\leadsto \]
  3. Using strategy rm
  4. Applied difference-of-squares9.5
    \[\leadsto \]
  5. Applied *-un-lft-identity9.5
    \[\leadsto \]
  6. Applied times-frac9.0
    \[\leadsto \]
  7. Applied associate-*l*0.4
    \[\leadsto \]
  8. Simplified0.4
    \[\leadsto \]
  9. Using strategy rm
  10. Applied associate-*r/0.3
    \[\leadsto \]
  11. Applied associate-*r/0.3
    \[\leadsto \]
  12. Simplified0.3
    \[\leadsto \]
  13. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(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))))