Average Error: 0.0 → 0.1
Time: 7.9s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\cos x \cdot \sinh y}{y}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\frac{\cos x \cdot \sinh y}{y}
double f(double x, double y) {
        double r94811 = x;
        double r94812 = cos(r94811);
        double r94813 = y;
        double r94814 = sinh(r94813);
        double r94815 = r94814 / r94813;
        double r94816 = r94812 * r94815;
        return r94816;
}
↓
double f(double x, double y) {
        double r94817 = x;
        double r94818 = cos(r94817);
        double r94819 = y;
        double r94820 = sinh(r94819);
        double r94821 = r94818 * r94820;
        double r94822 = r94821 / r94819;
        return r94822;
}

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-cube-cbrt0.0

    \[\leadsto \cos x \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)}\]
  4. Using strategy rm

  5. Applied pow1/30.0

    \[\leadsto \cos x \cdot \left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \color{blue}{{\left(\frac{\sinh y}{y}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\]

  6. Applied pow1/30.0

    \[\leadsto \cos x \cdot \left(\left(\color{blue}{{\left(\frac{\sinh y}{y}\right)}^{\frac{1}{3}}} \cdot {\left(\frac{\sinh y}{y}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\]

  7. Applied pow-prod-up0.0

    \[\leadsto \cos x \cdot \left(\color{blue}{{\left(\frac{\sinh y}{y}\right)}^{\left(\frac{1}{3} + \frac{1}{3}\right)}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\]

  8. Simplified0.0

    \[\leadsto \cos x \cdot \left({\left(\frac{\sinh y}{y}\right)}^{\color{blue}{\frac{2}{3}}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\]

  9. Final simplification0.1

    \[\leadsto \frac{\cos x \cdot \sinh y}{y}\]

Reproduce

herbie shell --seed 2019308 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))