Average Error: 15.3 → 15.3
Time: 2.0s
Precision: binary64
Cost: 13120
\[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]
↓
\[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]
\tan^{-1} \left(N + 1\right) - \tan^{-1} N
↓
\tan^{-1} \left(N + 1\right) - \tan^{-1} N
(FPCore (N) :precision binary64 (- (atan (+ N 1.0)) (atan N)))
↓
(FPCore (N) :precision binary64 (- (atan (+ N 1.0)) (atan N)))
double code(double N) {
	return atan(N + 1.0) - atan(N);
}
↓
double code(double N) {
	return atan(N + 1.0) - atan(N);
}

Error

Bits error versus N

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.3
Target0.4
Herbie15.3
\[\tan^{-1} \left(\frac{1}{1 + N \cdot \left(N + 1\right)}\right)\]

Derivation

  1. Initial program 15.3

    \[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]

Reproduce

herbie shell --seed 2021027 
(FPCore (N)
  :name "2atan (example 3.5)"
  :precision binary64

  :herbie-target
  (atan (/ 1.0 (+ 1.0 (* N (+ N 1.0)))))

  (- (atan (+ N 1.0)) (atan N)))