Average Error: 1.0 → 0.1
Time: 13.5s
Precision: 64
\[\sinh \left(x + 1\right) - \sinh 2\]
\[\frac{\sqrt[3]{\left(\left(\frac{-1}{e^{1 + x}} + e^{1 + x}\right) - \frac{-1}{e^{2}}\right) \cdot \left(\left(\left(\frac{-1}{e^{1 + x}} + e^{1 + x}\right) - \frac{-1}{e^{2}}\right) \cdot \left(\left(\frac{-1}{e^{1 + x}} + e^{1 + x}\right) - \frac{-1}{e^{2}}\right)\right)} - e^{2}}{2}\]
\sinh \left(x + 1\right) - \sinh 2
\frac{\sqrt[3]{\left(\left(\frac{-1}{e^{1 + x}} + e^{1 + x}\right) - \frac{-1}{e^{2}}\right) \cdot \left(\left(\left(\frac{-1}{e^{1 + x}} + e^{1 + x}\right) - \frac{-1}{e^{2}}\right) \cdot \left(\left(\frac{-1}{e^{1 + x}} + e^{1 + x}\right) - \frac{-1}{e^{2}}\right)\right)} - e^{2}}{2}
double f(double x) {
        double r10487516 = x;
        double r10487517 = 1.0;
        double r10487518 = r10487516 + r10487517;
        double r10487519 = sinh(r10487518);
        double r10487520 = 2.0;
        double r10487521 = sinh(r10487520);
        double r10487522 = r10487519 - r10487521;
        return r10487522;
}

double f(double x) {
        double r10487523 = -1.0;
        double r10487524 = 1.0;
        double r10487525 = x;
        double r10487526 = r10487524 + r10487525;
        double r10487527 = exp(r10487526);
        double r10487528 = r10487523 / r10487527;
        double r10487529 = r10487528 + r10487527;
        double r10487530 = 2.0;
        double r10487531 = exp(r10487530);
        double r10487532 = r10487523 / r10487531;
        double r10487533 = r10487529 - r10487532;
        double r10487534 = r10487533 * r10487533;
        double r10487535 = r10487533 * r10487534;
        double r10487536 = cbrt(r10487535);
        double r10487537 = r10487536 - r10487531;
        double r10487538 = 2.0;
        double r10487539 = r10487537 / r10487538;
        return r10487539;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[\sinh \left(x + 1\right) - \sinh 2\]
  2. Using strategy rm
  3. Applied sinh-def1.0

    \[\leadsto \sinh \left(x + 1\right) - \color{blue}{\frac{e^{2} - e^{-2}}{2}}\]
  4. Applied sinh-def1.0

    \[\leadsto \color{blue}{\frac{e^{x + 1} - e^{-\left(x + 1\right)}}{2}} - \frac{e^{2} - e^{-2}}{2}\]
  5. Applied sub-div1.0

    \[\leadsto \color{blue}{\frac{\left(e^{x + 1} - e^{-\left(x + 1\right)}\right) - \left(e^{2} - e^{-2}\right)}{2}}\]
  6. Simplified0.0

    \[\leadsto \frac{\color{blue}{\left(\left(\frac{-1}{e^{1 + x}} + e^{1 + x}\right) - \frac{-1}{e^{2}}\right) - e^{2}}}{2}\]
  7. Using strategy rm
  8. Applied add-cbrt-cube0.1

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(\left(\frac{-1}{e^{1 + x}} + e^{1 + x}\right) - \frac{-1}{e^{2}}\right) \cdot \left(\left(\frac{-1}{e^{1 + x}} + e^{1 + x}\right) - \frac{-1}{e^{2}}\right)\right) \cdot \left(\left(\frac{-1}{e^{1 + x}} + e^{1 + x}\right) - \frac{-1}{e^{2}}\right)}} - e^{2}}{2}\]
  9. Final simplification0.1

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

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sinh(x+1)-sinh(2)"
  (- (sinh (+ x 1.0)) (sinh 2.0)))