Average Error: 26.4 → 0.5
Time: 13.2s
Precision: 64
\[\frac{\sin x}{\sin \left(1 + x\right)}\]
\[\frac{\sin x}{\frac{{\left(\sin 1 \cdot \cos x\right)}^{3} + {\left(\sin x \cdot \cos 1\right)}^{3}}{{\left(\sin 1\right)}^{2} \cdot \left(\cos x \cdot \cos x\right) + \left(\sin x \cdot \cos 1\right) \cdot \left(\sin x \cdot \cos 1 - \sin 1 \cdot \cos x\right)}}\]
\frac{\sin x}{\sin \left(1 + x\right)}
\frac{\sin x}{\frac{{\left(\sin 1 \cdot \cos x\right)}^{3} + {\left(\sin x \cdot \cos 1\right)}^{3}}{{\left(\sin 1\right)}^{2} \cdot \left(\cos x \cdot \cos x\right) + \left(\sin x \cdot \cos 1\right) \cdot \left(\sin x \cdot \cos 1 - \sin 1 \cdot \cos x\right)}}
double f(double x) {
        double r1952361 = x;
        double r1952362 = sin(r1952361);
        double r1952363 = 1.0;
        double r1952364 = r1952363 + r1952361;
        double r1952365 = sin(r1952364);
        double r1952366 = r1952362 / r1952365;
        return r1952366;
}

double f(double x) {
        double r1952367 = x;
        double r1952368 = sin(r1952367);
        double r1952369 = 1.0;
        double r1952370 = sin(r1952369);
        double r1952371 = cos(r1952367);
        double r1952372 = r1952370 * r1952371;
        double r1952373 = 3.0;
        double r1952374 = pow(r1952372, r1952373);
        double r1952375 = cos(r1952369);
        double r1952376 = r1952368 * r1952375;
        double r1952377 = pow(r1952376, r1952373);
        double r1952378 = r1952374 + r1952377;
        double r1952379 = 2.0;
        double r1952380 = pow(r1952370, r1952379);
        double r1952381 = r1952371 * r1952371;
        double r1952382 = r1952380 * r1952381;
        double r1952383 = r1952376 - r1952372;
        double r1952384 = r1952376 * r1952383;
        double r1952385 = r1952382 + r1952384;
        double r1952386 = r1952378 / r1952385;
        double r1952387 = r1952368 / r1952386;
        return r1952387;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 26.4

    \[\frac{\sin x}{\sin \left(1 + x\right)}\]
  2. Using strategy rm
  3. Applied sin-sum0.4

    \[\leadsto \frac{\sin x}{\color{blue}{\sin 1 \cdot \cos x + \cos 1 \cdot \sin x}}\]
  4. Simplified0.4

    \[\leadsto \frac{\sin x}{\sin 1 \cdot \cos x + \color{blue}{\sin x \cdot \cos 1}}\]
  5. Using strategy rm
  6. Applied flip3-+0.5

    \[\leadsto \frac{\sin x}{\color{blue}{\frac{{\left(\sin 1 \cdot \cos x\right)}^{3} + {\left(\sin x \cdot \cos 1\right)}^{3}}{\left(\sin 1 \cdot \cos x\right) \cdot \left(\sin 1 \cdot \cos x\right) + \left(\left(\sin x \cdot \cos 1\right) \cdot \left(\sin x \cdot \cos 1\right) - \left(\sin 1 \cdot \cos x\right) \cdot \left(\sin x \cdot \cos 1\right)\right)}}}\]
  7. Simplified0.5

    \[\leadsto \frac{\sin x}{\frac{{\left(\sin 1 \cdot \cos x\right)}^{3} + {\left(\sin x \cdot \cos 1\right)}^{3}}{\color{blue}{{\left(\sin 1\right)}^{2} \cdot \left(\cos x \cdot \cos x\right) + \left(\sin x \cdot \cos 1\right) \cdot \left(\sin x \cdot \cos 1 - \sin 1 \cdot \cos x\right)}}}\]
  8. Final simplification0.5

    \[\leadsto \frac{\sin x}{\frac{{\left(\sin 1 \cdot \cos x\right)}^{3} + {\left(\sin x \cdot \cos 1\right)}^{3}}{{\left(\sin 1\right)}^{2} \cdot \left(\cos x \cdot \cos x\right) + \left(\sin x \cdot \cos 1\right) \cdot \left(\sin x \cdot \cos 1 - \sin 1 \cdot \cos x\right)}}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sin(x) / sin(1+x)"
  :precision binary64
  (/ (sin x) (sin (+ 1 x))))