Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\left(\sin x \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\left(\sin x \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r141981 = x;
        double r141982 = sin(r141981);
        double r141983 = y;
        double r141984 = sinh(r141983);
        double r141985 = r141984 / r141983;
        double r141986 = r141982 * r141985;
        return r141986;
}
↓
double f(double x, double y) {
        double r141987 = x;
        double r141988 = sin(r141987);
        double r141989 = y;
        double r141990 = sinh(r141989);
        double r141991 = r141990 / r141989;
        double r141992 = sqrt(r141991);
        double r141993 = sqrt(r141992);
        double r141994 = r141988 * r141993;
        double r141995 = r141994 * r141993;
        double r141996 = r141995 * r141992;
        return r141996;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

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

  6. Applied add-sqr-sqrt0.0

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

  7. Applied sqrt-prod0.0

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

  8. Applied associate-*r*0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))