Average Error: 0.0 → 0.0
Time: 52.0s
Precision: 64
\[\frac{1}{{\left(\cosh x\right)}^{2}}\]
\[\frac{1}{\cosh x} \cdot \frac{1}{\cosh x}\]
\frac{1}{{\left(\cosh x\right)}^{2}}
\frac{1}{\cosh x} \cdot \frac{1}{\cosh x}
double f(double x) {
        double r17124497 = 1.0;
        double r17124498 = x;
        double r17124499 = cosh(r17124498);
        double r17124500 = 2.0;
        double r17124501 = pow(r17124499, r17124500);
        double r17124502 = r17124497 / r17124501;
        return r17124502;
}

double f(double x) {
        double r17124503 = 1.0;
        double r17124504 = x;
        double r17124505 = cosh(r17124504);
        double r17124506 = r17124503 / r17124505;
        double r17124507 = r17124506 * r17124506;
        return r17124507;
}

Error

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Results

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Derivation

  1. Initial program 0.0

    \[\frac{1}{{\left(\cosh x\right)}^{2}}\]
  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{1}{\cosh x \cdot \cosh x}}\]
  3. Using strategy rm
  4. Applied add-cube-cbrt0.0

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\cosh x \cdot \cosh x}\]
  5. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\cosh x} \cdot \frac{\sqrt[3]{1}}{\cosh x}}\]
  6. Simplified0.0

    \[\leadsto \color{blue}{\frac{1}{\cosh x}} \cdot \frac{\sqrt[3]{1}}{\cosh x}\]
  7. Simplified0.0

    \[\leadsto \frac{1}{\cosh x} \cdot \color{blue}{\frac{1}{\cosh x}}\]
  8. Final simplification0.0

    \[\leadsto \frac{1}{\cosh x} \cdot \frac{1}{\cosh x}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "1/pow(cosh(x),2)"
  (/ 1 (pow (cosh x) 2)))