Average Error: 16.3 → 8.1
Time: 48.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double F, double l) {
	return ((double) (((double) (((double) M_PI) * l)) - ((double) (((double) (1.0 / ((double) (F * F)))) * ((double) tan(((double) (((double) M_PI) * l))))))));
}

↓
double code(double F, double l) {
	return ((double) (((double) (((double) M_PI) * l)) + ((double) (1.0 * ((double) (-1.0 / ((double) (F * ((double) (((double) (F / ((double) (((double) M_PI) * l)))) + ((double) (((double) M_PI) * ((double) (l * ((double) (((double) (((double) cbrt(F)) * ((double) cbrt(F)))) * ((double) (((double) cbrt(F)) * -0.3333333333333333))))))))))))))))));
}

Error
Bits error versus F
Bits error versus l
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Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 16.3
    \[\]
  2. Simplified16.1
    \[\leadsto \]
  3. Using strategy rm
  4. Applied clear-num16.1
    \[\leadsto \]
  5. Simplified12.3
    \[\leadsto \]
  6. Taylor expanded around 0 8.1
    \[\leadsto \]
  7. Simplified8.1
    \[\leadsto \]
  8. Using strategy rm
  9. Applied add-cube-cbrt8.1
    \[\leadsto \]
  10. Applied associate-*l*8.1
    \[\leadsto \]
  11. Simplified8.1
    \[\leadsto \]
  12. Final simplification8.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))