Average Error: 0.0 → 0.0
Time: 12.2s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \cos x\right)\]
\cos x \cdot \frac{\sinh y}{y}
↓
\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \cos x\right)
double f(double x, double y) {
        double r111113 = x;
        double r111114 = cos(r111113);
        double r111115 = y;
        double r111116 = sinh(r111115);
        double r111117 = r111116 / r111115;
        double r111118 = r111114 * r111117;
        return r111118;
}
↓
double f(double x, double y) {
        double r111119 = y;
        double r111120 = sinh(r111119);
        double r111121 = r111120 / r111119;
        double r111122 = sqrt(r111121);
        double r111123 = x;
        double r111124 = cos(r111123);
        double r111125 = r111122 * r111124;
        double r111126 = r111122 * r111125;
        return r111126;
}

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

    \[\cos x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))