Average Error: 37.2 → 0.7
Time: 7.9s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double eps) {
	return ((double) (((double) tan(((double) (x + eps)))) - ((double) tan(x))));
}

↓
double code(double x, double eps) {
	return ((double) (((double) (((double) (1.0 + ((double) (((double) pow(((double) sin(x)), 2.0)) / ((double) pow(((double) cos(x)), 2.0)))))) * ((double) (((double) sin(eps)) / ((double) (((double) cos(eps)) * ((double) (1.0 - ((double) (((double) (((double) pow(((double) sin(x)), 2.0)) / ((double) pow(((double) cos(x)), 2.0)))) * ((double) (((double) pow(((double) sin(eps)), 2.0)) / ((double) pow(((double) cos(eps)), 2.0)))))))))))))) + ((double) log(((double) exp(((double) (((double) (((double) (1.0 + ((double) (((double) pow(((double) sin(eps)), 2.0)) / ((double) pow(((double) cos(eps)), 2.0)))))) * ((double) (((double) sin(x)) / ((double) (((double) cos(x)) * ((double) (1.0 - ((double) (((double) (((double) pow(((double) sin(x)), 2.0)) / ((double) pow(((double) cos(x)), 2.0)))) * ((double) (((double) pow(((double) sin(eps)), 2.0)) / ((double) pow(((double) cos(eps)), 2.0)))))))))))))) - ((double) (((double) sin(x)) / ((double) cos(x))))))))))));
}

Error
Bits error versus x
Bits error versus eps
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original37.2
Target14.9
Herbie0.7
\[\]
Derivation
  1. Initial program 37.2
    \[\]
  2. Using strategy rm
  3. Applied tan-sum22.2
    \[\leadsto \]
  4. Using strategy rm
  5. Applied flip--22.2
    \[\leadsto \]
  6. Simplified22.2
    \[\leadsto \]
  7. Taylor expanded around inf 22.4
    \[\leadsto \]
  8. Simplified0.6
    \[\leadsto \]
  9. Using strategy rm
  10. Applied add-log-exp13.0
    \[\leadsto \]
  11. Applied add-log-exp0.7
    \[\leadsto \]
  12. Applied diff-log0.7
    \[\leadsto \]
  13. Simplified0.7
    \[\leadsto \]
  14. Final simplification0.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(FPCore (x eps)
  :name "2tan (problem 3.3.2)"
  :precision binary64

  :herbie-target
  (/ (sin eps) (* (cos x) (cos (+ x eps))))

  (- (tan (+ x eps)) (tan x)))