Average Error: 14.7 → 0.3
Time: 13.5s
Precision: 64
\[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]
↓
\[\tan^{-1}_* \frac{1}{1 + N \cdot \left(1 + N\right)}\]
\tan^{-1} \left(N + 1\right) - \tan^{-1} N
↓
\tan^{-1}_* \frac{1}{1 + N \cdot \left(1 + N\right)}
double f(double N) {
        double r5680474 = N;
        double r5680475 = 1.0;
        double r5680476 = r5680474 + r5680475;
        double r5680477 = atan(r5680476);
        double r5680478 = atan(r5680474);
        double r5680479 = r5680477 - r5680478;
        return r5680479;
}
↓
double f(double N) {
        double r5680480 = 1.0;
        double r5680481 = 1.0;
        double r5680482 = N;
        double r5680483 = r5680480 + r5680482;
        double r5680484 = r5680482 * r5680483;
        double r5680485 = r5680481 + r5680484;
        double r5680486 = atan2(r5680480, r5680485);
        return r5680486;
}

Error

Bits error versus N

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.7
Target0.3
Herbie0.3
\[\tan^{-1} \left(\frac{1}{1 + N \cdot \left(N + 1\right)}\right)\]

Derivation

  1. Initial program 14.7

    \[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]
  2. Using strategy rm

  3. Applied diff-atan13.7

    \[\leadsto \color{blue}{\tan^{-1}_* \frac{\left(N + 1\right) - N}{1 + \left(N + 1\right) \cdot N}}\]

  4. Simplified0.3

    \[\leadsto \tan^{-1}_* \frac{\color{blue}{1}}{1 + \left(N + 1\right) \cdot N}\]

  5. Final simplification0.3

    \[\leadsto \tan^{-1}_* \frac{1}{1 + N \cdot \left(1 + N\right)}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (N)
  :name "2atan (example 3.5)"

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

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