Average Error: 0.0 → 0.1
Time: 32.9s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \left(\sqrt{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sinh y}{y}\right)\right)} \cdot \sqrt{\frac{\sinh y}{y}}\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \left(\sqrt{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sinh y}{y}\right)\right)} \cdot \sqrt{\frac{\sinh y}{y}}\right)
double f(double x, double y) {
        double r98410 = x;
        double r98411 = sin(r98410);
        double r98412 = y;
        double r98413 = sinh(r98412);
        double r98414 = r98413 / r98412;
        double r98415 = r98411 * r98414;
        return r98415;
}
↓
double f(double x, double y) {
        double r98416 = x;
        double r98417 = sin(r98416);
        double r98418 = y;
        double r98419 = sinh(r98418);
        double r98420 = r98419 / r98418;
        double r98421 = log1p(r98420);
        double r98422 = expm1(r98421);
        double r98423 = sqrt(r98422);
        double r98424 = sqrt(r98420);
        double r98425 = r98423 * r98424;
        double r98426 = r98417 * r98425;
        return r98426;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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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. Using strategy rm

  5. Applied expm1-log1p-u0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))