Average Error: 0.2 → 0.3
Time: 6.4s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{1}{\frac{y}{\sin y}}\right)\]
\cosh x \cdot \frac{\sin y}{y}
↓
\sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{1}{\frac{y}{\sin y}}\right)
double f(double x, double y) {
        double r402454 = x;
        double r402455 = cosh(r402454);
        double r402456 = y;
        double r402457 = sin(r402456);
        double r402458 = r402457 / r402456;
        double r402459 = r402455 * r402458;
        return r402459;
}
↓
double f(double x, double y) {
        double r402460 = x;
        double r402461 = cosh(r402460);
        double r402462 = sqrt(r402461);
        double r402463 = 1.0;
        double r402464 = y;
        double r402465 = sin(r402464);
        double r402466 = r402464 / r402465;
        double r402467 = r402463 / r402466;
        double r402468 = r402462 * r402467;
        double r402469 = r402462 * r402468;
        return r402469;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.3
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.2

    \[\cosh x \cdot \frac{\sin y}{y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.2

    \[\leadsto \color{blue}{\left(\sqrt{\cosh x} \cdot \sqrt{\cosh x}\right)} \cdot \frac{\sin y}{y}\]

  4. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{\sin y}{y}\right)}\]
  5. Using strategy rm

  6. Applied clear-num0.3

    \[\leadsto \sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\right)\]

  7. Final simplification0.3

    \[\leadsto \sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{1}{\frac{y}{\sin y}}\right)\]

Reproduce

herbie shell --seed 2020035 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))