Average Error: 26.1 → 0.3
Time: 12.3s
Precision: 64
\[\frac{\sin \left(x - 1\right)}{x + 1}\]
\[\frac{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sin x\right) \cdot \sqrt[3]{\cos 1} - \cos x \cdot \sin 1}{x + 1}\]
\frac{\sin \left(x - 1\right)}{x + 1}
\frac{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sin x\right) \cdot \sqrt[3]{\cos 1} - \cos x \cdot \sin 1}{x + 1}
double f(double x) {
        double r1503004 = x;
        double r1503005 = 1.0;
        double r1503006 = r1503004 - r1503005;
        double r1503007 = sin(r1503006);
        double r1503008 = r1503004 + r1503005;
        double r1503009 = r1503007 / r1503008;
        return r1503009;
}

double f(double x) {
        double r1503010 = 1.0;
        double r1503011 = cos(r1503010);
        double r1503012 = cbrt(r1503011);
        double r1503013 = r1503012 * r1503012;
        double r1503014 = x;
        double r1503015 = sin(r1503014);
        double r1503016 = r1503013 * r1503015;
        double r1503017 = r1503016 * r1503012;
        double r1503018 = cos(r1503014);
        double r1503019 = sin(r1503010);
        double r1503020 = r1503018 * r1503019;
        double r1503021 = r1503017 - r1503020;
        double r1503022 = r1503014 + r1503010;
        double r1503023 = r1503021 / r1503022;
        return r1503023;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 26.1

    \[\frac{\sin \left(x - 1\right)}{x + 1}\]
  2. Using strategy rm
  3. Applied sin-diff0.4

    \[\leadsto \frac{\color{blue}{\sin x \cdot \cos 1 - \cos x \cdot \sin 1}}{x + 1}\]
  4. Using strategy rm
  5. Applied add-cube-cbrt0.4

    \[\leadsto \frac{\sin x \cdot \color{blue}{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sqrt[3]{\cos 1}\right)} - \cos x \cdot \sin 1}{x + 1}\]
  6. Applied associate-*r*0.3

    \[\leadsto \frac{\color{blue}{\left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1}} - \cos x \cdot \sin 1}{x + 1}\]
  7. Simplified0.3

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

    \[\leadsto \frac{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sin x\right) \cdot \sqrt[3]{\cos 1} - \cos x \cdot \sin 1}{x + 1}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sin(x-1)/(x+1)"
  :precision binary64
  (/ (sin (- x 1)) (+ x 1)))