Average Error: 13.9 → 0.1
Time: 16.7s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sin x}{x} \cdot \sinh y\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sin x}{x} \cdot \sinh y
double f(double x, double y) {
        double r327657 = x;
        double r327658 = sin(r327657);
        double r327659 = y;
        double r327660 = sinh(r327659);
        double r327661 = r327658 * r327660;
        double r327662 = r327661 / r327657;
        return r327662;
}
↓
double f(double x, double y) {
        double r327663 = x;
        double r327664 = sin(r327663);
        double r327665 = r327664 / r327663;
        double r327666 = y;
        double r327667 = sinh(r327666);
        double r327668 = r327665 * r327667;
        return r327668;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original13.9
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.9

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

  3. Applied *-un-lft-identity13.9

    \[\leadsto \frac{\sin x \cdot \sinh y}{\color{blue}{1 \cdot x}}\]

  4. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{\sin x}{1} \cdot \frac{\sinh y}{x}}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{\sin x} \cdot \frac{\sinh y}{x}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity0.2

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

  8. Applied associate-*l*0.2

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

  9. Simplified0.9

    \[\leadsto 1 \cdot \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  10. Using strategy rm

  11. Applied associate-/r/0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

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

  (/ (* (sin x) (sinh y)) x))