Average Error: 29.6 → 0.4
Time: 13.6s
Precision: 64
\[\sin \left(x + 1\right) - \sin x\]
\[\left(\left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1} + \sin 1 \cdot \cos x\right) - \sin x\]
\sin \left(x + 1\right) - \sin x
\left(\left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1} + \sin 1 \cdot \cos x\right) - \sin x
double f(double x) {
        double r4890437 = x;
        double r4890438 = 1.0;
        double r4890439 = r4890437 + r4890438;
        double r4890440 = sin(r4890439);
        double r4890441 = sin(r4890437);
        double r4890442 = r4890440 - r4890441;
        return r4890442;
}

double f(double x) {
        double r4890443 = x;
        double r4890444 = sin(r4890443);
        double r4890445 = 1.0;
        double r4890446 = cos(r4890445);
        double r4890447 = cbrt(r4890446);
        double r4890448 = r4890447 * r4890447;
        double r4890449 = r4890444 * r4890448;
        double r4890450 = r4890449 * r4890447;
        double r4890451 = sin(r4890445);
        double r4890452 = cos(r4890443);
        double r4890453 = r4890451 * r4890452;
        double r4890454 = r4890450 + r4890453;
        double r4890455 = r4890454 - r4890444;
        return r4890455;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.6

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

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

    \[\leadsto \left(\sin x \cdot \color{blue}{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sqrt[3]{\cos 1}\right)} + \cos x \cdot \sin 1\right) - \sin x\]
  6. Applied associate-*r*0.4

    \[\leadsto \left(\color{blue}{\left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1}} + \cos x \cdot \sin 1\right) - \sin x\]
  7. Final simplification0.4

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

Reproduce

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