Average Error: 58.0 → 0.3
Time: 52.7s
Precision: 64
\[\cosh \left(x + 1\right) - \cosh 1\]
\[\left(\left(\sinh \left(\frac{x}{2}\right) \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right) \cdot \left(\sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)} \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right)\right) \cdot 2\]
\cosh \left(x + 1\right) - \cosh 1
\left(\left(\sinh \left(\frac{x}{2}\right) \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right) \cdot \left(\sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)} \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right)\right) \cdot 2
double f(double x) {
        double r33240509 = x;
        double r33240510 = 1.0;
        double r33240511 = r33240509 + r33240510;
        double r33240512 = cosh(r33240511);
        double r33240513 = cosh(r33240510);
        double r33240514 = r33240512 - r33240513;
        return r33240514;
}

double f(double x) {
        double r33240515 = x;
        double r33240516 = 2.0;
        double r33240517 = r33240515 / r33240516;
        double r33240518 = sinh(r33240517);
        double r33240519 = 1.0;
        double r33240520 = r33240519 + r33240515;
        double r33240521 = r33240519 + r33240520;
        double r33240522 = r33240521 / r33240516;
        double r33240523 = sinh(r33240522);
        double r33240524 = cbrt(r33240523);
        double r33240525 = r33240518 * r33240524;
        double r33240526 = r33240524 * r33240524;
        double r33240527 = r33240525 * r33240526;
        double r33240528 = r33240527 * r33240516;
        return r33240528;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.0

    \[\cosh \left(x + 1\right) - \cosh 1\]
  2. Using strategy rm
  3. Applied diff-cosh58.0

    \[\leadsto \color{blue}{2 \cdot \left(\sinh \left(\frac{\left(x + 1\right) + 1}{2}\right) \cdot \sinh \left(\frac{\left(x + 1\right) - 1}{2}\right)\right)}\]
  4. Simplified0.4

    \[\leadsto 2 \cdot \color{blue}{\left(\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right) \cdot \sinh \left(\frac{x}{2}\right)\right)}\]
  5. Using strategy rm
  6. Applied add-cube-cbrt0.5

    \[\leadsto 2 \cdot \left(\color{blue}{\left(\left(\sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)} \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)}\right) \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)}\right)} \cdot \sinh \left(\frac{x}{2}\right)\right)\]
  7. Applied associate-*l*0.3

    \[\leadsto 2 \cdot \color{blue}{\left(\left(\sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)} \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)}\right) \cdot \left(\sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)} \cdot \sinh \left(\frac{x}{2}\right)\right)\right)}\]
  8. Final simplification0.3

    \[\leadsto \left(\left(\sinh \left(\frac{x}{2}\right) \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right) \cdot \left(\sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)} \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "cosh(x+1)-cosh(1)"
  (- (cosh (+ x 1.0)) (cosh 1.0)))