Average Error: 37.1 → 0.4
Time: 7.5s
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) (((double) (((double) sin(eps)) / ((double) cos(eps)))) * ((double) cos(x)))) + ((double) (((double) (((double) sin(eps)) / ((double) cos(eps)))) * ((double) (((double) pow(((double) sin(x)), 2.0)) / ((double) cos(x)))))))) / ((double) (((double) cos(x)) * ((double) (1.0 - ((double) (((double) tan(x)) * ((double) tan(eps))))))))));
}

Error
Bits error versus x
Bits error versus eps
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original37.1
Target14.9
Herbie0.4
\[\]
Derivation
  1. Initial program 37.1
    \[\]
  2. Using strategy rm
  3. Applied tan-quot37.1
    \[\leadsto \]
  4. Applied tan-sum22.2
    \[\leadsto \]
  5. Applied frac-sub22.2
    \[\leadsto \]
  6. Taylor expanded around inf 0.4
    \[\leadsto \]
  7. Simplified0.4
    \[\leadsto \]
  8. Using strategy rm
  9. Applied distribute-lft-in0.4
    \[\leadsto \]
  10. Final simplification0.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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)))