Average Error: 0.0 → 0.0
Time: 22.3s
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 r6612684 = x;
        double r6612685 = cos(r6612684);
        double r6612686 = y;
        double r6612687 = sinh(r6612686);
        double r6612688 = r6612687 / r6612686;
        double r6612689 = r6612685 * r6612688;
        return r6612689;
}
↓
double f(double x, double y) {
        double r6612690 = y;
        double r6612691 = sinh(r6612690);
        double r6612692 = r6612691 / r6612690;
        double r6612693 = sqrt(r6612692);
        double r6612694 = sqrt(r6612693);
        double r6612695 = r6612693 * r6612694;
        double r6612696 = r6612695 * r6612694;
        double r6612697 = x;
        double r6612698 = cos(r6612697);
        double r6612699 = r6612696 * r6612698;
        return r6612699;
}

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 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))