Average Error: 0.0 → 0.0
Time: 20.8s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \cos x\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \cos x
double f(double x, double y) {
        double r6176153 = x;
        double r6176154 = cos(r6176153);
        double r6176155 = y;
        double r6176156 = sinh(r6176155);
        double r6176157 = r6176156 / r6176155;
        double r6176158 = r6176154 * r6176157;
        return r6176158;
}
↓
double f(double x, double y) {
        double r6176159 = y;
        double r6176160 = sinh(r6176159);
        double r6176161 = r6176160 / r6176159;
        double r6176162 = sqrt(r6176161);
        double r6176163 = sqrt(r6176162);
        double r6176164 = r6176162 * r6176163;
        double r6176165 = r6176164 * r6176163;
        double r6176166 = x;
        double r6176167 = cos(r6176166);
        double r6176168 = r6176165 * r6176167;
        return r6176168;
}

Error

Bits error versus x

Bits error versus y

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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. Using strategy rm

  5. Applied add-sqr-sqrt0.0

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

  6. Applied sqrt-prod0.0

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

  7. Applied associate-*r*0.0

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

  8. Final simplification0.0

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

Reproduce

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