Average Error: 0.0 → 0.1
Time: 34.7s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sinh y}{y}\right)\right)} \cdot \sin x\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sinh y}{y}\right)\right)} \cdot \sin x\right)
double f(double x, double y) {
        double r137408 = x;
        double r137409 = sin(r137408);
        double r137410 = y;
        double r137411 = sinh(r137410);
        double r137412 = r137411 / r137410;
        double r137413 = r137409 * r137412;
        return r137413;
}
↓
double f(double x, double y) {
        double r137414 = y;
        double r137415 = sinh(r137414);
        double r137416 = r137415 / r137414;
        double r137417 = sqrt(r137416);
        double r137418 = log1p(r137416);
        double r137419 = expm1(r137418);
        double r137420 = sqrt(r137419);
        double r137421 = x;
        double r137422 = sin(r137421);
        double r137423 = r137420 * r137422;
        double r137424 = r137417 * r137423;
        return r137424;
}

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 *-commutative0.0

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

  5. Applied add-sqr-sqrt0.0

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

  6. Applied associate-*l*0.0

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

  8. Applied expm1-log1p-u0.1

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

  9. Final simplification0.1

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

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)))