Average Error: 0.0 → 0.0
Time: 15.8s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sin x\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sin x
double f(double x, double y) {
        double r180143 = x;
        double r180144 = sin(r180143);
        double r180145 = y;
        double r180146 = sinh(r180145);
        double r180147 = r180146 / r180145;
        double r180148 = r180144 * r180147;
        return r180148;
}
↓
double f(double x, double y) {
        double r180149 = y;
        double r180150 = sinh(r180149);
        double r180151 = r180150 / r180149;
        double r180152 = sqrt(r180151);
        double r180153 = r180152 * r180152;
        double r180154 = x;
        double r180155 = sin(r180154);
        double r180156 = r180153 * r180155;
        return r180156;
}

Error

Bits error versus x

Bits error versus y

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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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))