Average Error: 0.0 → 0.1
Time: 17.6s
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 r3226157 = x;
        double r3226158 = sin(r3226157);
        double r3226159 = y;
        double r3226160 = sinh(r3226159);
        double r3226161 = r3226160 / r3226159;
        double r3226162 = r3226158 * r3226161;
        return r3226162;
}
↓
double f(double x, double y) {
        double r3226163 = y;
        double r3226164 = sinh(r3226163);
        double r3226165 = r3226164 / r3226163;
        double r3226166 = sqrt(r3226165);
        double r3226167 = x;
        double r3226168 = sin(r3226167);
        double r3226169 = r3226166 * r3226168;
        double r3226170 = r3226166 * r3226169;
        return r3226170;
}

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*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))