Average Error: 0.0 → 0.7
Time: 4.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sin x \cdot \left({\left(\frac{1}{6} \cdot {y}^{2}\right)}^{3} + {\left(\frac{1}{120} \cdot {y}^{4} + 1\right)}^{3}\right)}{\left(\frac{1}{6} \cdot {y}^{2}\right) \cdot \left(\frac{1}{6} \cdot {y}^{2}\right) + \left(\left(\frac{1}{120} \cdot {y}^{4} + 1\right) \cdot \left(\frac{1}{120} \cdot {y}^{4} + 1\right) - \left(\frac{1}{6} \cdot {y}^{2}\right) \cdot \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x \cdot \left({\left(\frac{1}{6} \cdot {y}^{2}\right)}^{3} + {\left(\frac{1}{120} \cdot {y}^{4} + 1\right)}^{3}\right)}{\left(\frac{1}{6} \cdot {y}^{2}\right) \cdot \left(\frac{1}{6} \cdot {y}^{2}\right) + \left(\left(\frac{1}{120} \cdot {y}^{4} + 1\right) \cdot \left(\frac{1}{120} \cdot {y}^{4} + 1\right) - \left(\frac{1}{6} \cdot {y}^{2}\right) \cdot \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)}
double f(double x, double y) {
        double r157338 = x;
        double r157339 = sin(r157338);
        double r157340 = y;
        double r157341 = sinh(r157340);
        double r157342 = r157341 / r157340;
        double r157343 = r157339 * r157342;
        return r157343;
}
↓
double f(double x, double y) {
        double r157344 = x;
        double r157345 = sin(r157344);
        double r157346 = 0.16666666666666666;
        double r157347 = y;
        double r157348 = 2.0;
        double r157349 = pow(r157347, r157348);
        double r157350 = r157346 * r157349;
        double r157351 = 3.0;
        double r157352 = pow(r157350, r157351);
        double r157353 = 0.008333333333333333;
        double r157354 = 4.0;
        double r157355 = pow(r157347, r157354);
        double r157356 = r157353 * r157355;
        double r157357 = 1.0;
        double r157358 = r157356 + r157357;
        double r157359 = pow(r157358, r157351);
        double r157360 = r157352 + r157359;
        double r157361 = r157345 * r157360;
        double r157362 = r157350 * r157350;
        double r157363 = r157358 * r157358;
        double r157364 = r157350 * r157358;
        double r157365 = r157363 - r157364;
        double r157366 = r157362 + r157365;
        double r157367 = r157361 / r157366;
        return r157367;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\sin x \cdot \frac{\sinh y}{y}\]

  2. Taylor expanded around 0 0.7

    \[\leadsto \sin x \cdot \color{blue}{\left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)}\]
  3. Using strategy rm

  4. Applied flip3-+0.7

    \[\leadsto \sin x \cdot \color{blue}{\frac{{\left(\frac{1}{6} \cdot {y}^{2}\right)}^{3} + {\left(\frac{1}{120} \cdot {y}^{4} + 1\right)}^{3}}{\left(\frac{1}{6} \cdot {y}^{2}\right) \cdot \left(\frac{1}{6} \cdot {y}^{2}\right) + \left(\left(\frac{1}{120} \cdot {y}^{4} + 1\right) \cdot \left(\frac{1}{120} \cdot {y}^{4} + 1\right) - \left(\frac{1}{6} \cdot {y}^{2}\right) \cdot \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)}}\]

  5. Applied associate-*r/0.7

    \[\leadsto \color{blue}{\frac{\sin x \cdot \left({\left(\frac{1}{6} \cdot {y}^{2}\right)}^{3} + {\left(\frac{1}{120} \cdot {y}^{4} + 1\right)}^{3}\right)}{\left(\frac{1}{6} \cdot {y}^{2}\right) \cdot \left(\frac{1}{6} \cdot {y}^{2}\right) + \left(\left(\frac{1}{120} \cdot {y}^{4} + 1\right) \cdot \left(\frac{1}{120} \cdot {y}^{4} + 1\right) - \left(\frac{1}{6} \cdot {y}^{2}\right) \cdot \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)}}\]

  6. Final simplification0.7

    \[\leadsto \frac{\sin x \cdot \left({\left(\frac{1}{6} \cdot {y}^{2}\right)}^{3} + {\left(\frac{1}{120} \cdot {y}^{4} + 1\right)}^{3}\right)}{\left(\frac{1}{6} \cdot {y}^{2}\right) \cdot \left(\frac{1}{6} \cdot {y}^{2}\right) + \left(\left(\frac{1}{120} \cdot {y}^{4} + 1\right) \cdot \left(\frac{1}{120} \cdot {y}^{4} + 1\right) - \left(\frac{1}{6} \cdot {y}^{2}\right) \cdot \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)}\]

Reproduce

herbie shell --seed 2020018 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))