Average Error: 26.4 → 0.3
Time: 9.0s
Precision: 64
\[\sin \left(x + 1\right)\]
\[\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sin x\right) \cdot \sqrt[3]{\cos 1} + \cos x \cdot \sin 1\]
\sin \left(x + 1\right)
\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
double f(double x) {
        double r1060687 = x;
        double r1060688 = 1.0;
        double r1060689 = r1060687 + r1060688;
        double r1060690 = sin(r1060689);
        return r1060690;
}

double f(double x) {
        double r1060691 = 1.0;
        double r1060692 = cos(r1060691);
        double r1060693 = cbrt(r1060692);
        double r1060694 = r1060693 * r1060693;
        double r1060695 = x;
        double r1060696 = sin(r1060695);
        double r1060697 = r1060694 * r1060696;
        double r1060698 = r1060697 * r1060693;
        double r1060699 = cos(r1060695);
        double r1060700 = sin(r1060691);
        double r1060701 = r1060699 * r1060700;
        double r1060702 = r1060698 + r1060701;
        return r1060702;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 26.4

    \[\sin \left(x + 1\right)\]
  2. Using strategy rm
  3. Applied sin-sum0.4

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

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

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

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

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

Reproduce

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