Average Error: 0.0 → 0.0
Time: 27.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sin x\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sin x\right)
double f(double x, double y) {
        double r7377487 = x;
        double r7377488 = sin(r7377487);
        double r7377489 = y;
        double r7377490 = sinh(r7377489);
        double r7377491 = r7377490 / r7377489;
        double r7377492 = r7377488 * r7377491;
        return r7377492;
}
↓
double f(double x, double y) {
        double r7377493 = y;
        double r7377494 = sinh(r7377493);
        double r7377495 = r7377494 / r7377493;
        double r7377496 = sqrt(r7377495);
        double r7377497 = x;
        double r7377498 = sin(r7377497);
        double r7377499 = r7377496 * r7377498;
        double r7377500 = r7377496 * r7377499;
        return r7377500;
}

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. 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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))