Average Error: 30.1 → 0.6
Time: 17.0s
Precision: 64
\[\cos \left(x + 1\right) - \cos x\]
\[\sqrt[3]{\left(\left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right) \cdot \left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right)\right) \cdot \left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right)}\]
\cos \left(x + 1\right) - \cos x
\sqrt[3]{\left(\left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right) \cdot \left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right)\right) \cdot \left(\cos 1 \cdot \cos x - \left(\sin x \cdot \sin 1 + \cos x\right)\right)}
double f(double x) {
        double r58843379 = x;
        double r58843380 = 1.0;
        double r58843381 = r58843379 + r58843380;
        double r58843382 = cos(r58843381);
        double r58843383 = cos(r58843379);
        double r58843384 = r58843382 - r58843383;
        return r58843384;
}

double f(double x) {
        double r58843385 = 1.0;
        double r58843386 = cos(r58843385);
        double r58843387 = x;
        double r58843388 = cos(r58843387);
        double r58843389 = r58843386 * r58843388;
        double r58843390 = sin(r58843387);
        double r58843391 = sin(r58843385);
        double r58843392 = r58843390 * r58843391;
        double r58843393 = r58843392 + r58843388;
        double r58843394 = r58843389 - r58843393;
        double r58843395 = r58843394 * r58843394;
        double r58843396 = r58843395 * r58843394;
        double r58843397 = cbrt(r58843396);
        return r58843397;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.1

    \[\cos \left(x + 1\right) - \cos x\]
  2. Using strategy rm
  3. Applied cos-sum0.9

    \[\leadsto \color{blue}{\left(\cos x \cdot \cos 1 - \sin x \cdot \sin 1\right)} - \cos x\]
  4. Applied associate--l-0.9

    \[\leadsto \color{blue}{\cos x \cdot \cos 1 - \left(\sin x \cdot \sin 1 + \cos x\right)}\]
  5. Using strategy rm
  6. Applied add-cbrt-cube0.6

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\cos x \cdot \cos 1 - \left(\sin x \cdot \sin 1 + \cos x\right)\right) \cdot \left(\cos x \cdot \cos 1 - \left(\sin x \cdot \sin 1 + \cos x\right)\right)\right) \cdot \left(\cos x \cdot \cos 1 - \left(\sin x \cdot \sin 1 + \cos x\right)\right)}}\]
  7. Final simplification0.6

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

Reproduce

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