Average Error: 29.6 → 0.3
Time: 15.7s
Precision: 64
\[\sin x - \sin \left(x - 1\right)\]
\[\left(\sin x - \left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1}\right) + \sin 1 \cdot \cos x\]
\sin x - \sin \left(x - 1\right)
\left(\sin x - \left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1}\right) + \sin 1 \cdot \cos x
double f(double x) {
        double r21565078 = x;
        double r21565079 = sin(r21565078);
        double r21565080 = 1.0;
        double r21565081 = r21565078 - r21565080;
        double r21565082 = sin(r21565081);
        double r21565083 = r21565079 - r21565082;
        return r21565083;
}

double f(double x) {
        double r21565084 = x;
        double r21565085 = sin(r21565084);
        double r21565086 = 1.0;
        double r21565087 = cos(r21565086);
        double r21565088 = cbrt(r21565087);
        double r21565089 = r21565088 * r21565088;
        double r21565090 = r21565085 * r21565089;
        double r21565091 = r21565090 * r21565088;
        double r21565092 = r21565085 - r21565091;
        double r21565093 = sin(r21565086);
        double r21565094 = cos(r21565084);
        double r21565095 = r21565093 * r21565094;
        double r21565096 = r21565092 + r21565095;
        return r21565096;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.6

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

    \[\leadsto \sin x - \color{blue}{\left(\sin x \cdot \cos 1 - \cos x \cdot \sin 1\right)}\]
  4. Applied associate--r-0.4

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

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

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

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

Reproduce

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