Average Error: 0.1 → 0.1
Time: 5.5s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sin y}{y}\right)\right)\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sin y}{y}\right)\right)
double f(double x, double y) {
        double r477460 = x;
        double r477461 = cosh(r477460);
        double r477462 = y;
        double r477463 = sin(r477462);
        double r477464 = r477463 / r477462;
        double r477465 = r477461 * r477464;
        return r477465;
}
↓
double f(double x, double y) {
        double r477466 = x;
        double r477467 = cosh(r477466);
        double r477468 = y;
        double r477469 = sin(r477468);
        double r477470 = r477469 / r477468;
        double r477471 = log1p(r477470);
        double r477472 = expm1(r477471);
        double r477473 = r477467 * r477472;
        return r477473;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

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

  3. Applied expm1-log1p-u0.1

    \[\leadsto \cosh x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sin y}{y}\right)\right)}\]

  4. Final simplification0.1

    \[\leadsto \cosh x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sin y}{y}\right)\right)\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(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)))