Average Error: 26.8 → 0.8
Time: 11.9s
Precision: 64
\[\sin \left(x + 1\right) - \cos \left(x + 1\right)\]
\[\left(\left(\sin x \cdot \cos 1 + \sin 1 \cdot \cos x\right) - \cos x \cdot \cos 1\right) + \sin x \cdot \sin 1\]
\sin \left(x + 1\right) - \cos \left(x + 1\right)
\left(\left(\sin x \cdot \cos 1 + \sin 1 \cdot \cos x\right) - \cos x \cdot \cos 1\right) + \sin x \cdot \sin 1
double f(double x) {
        double r1690450 = x;
        double r1690451 = 1.0;
        double r1690452 = r1690450 + r1690451;
        double r1690453 = sin(r1690452);
        double r1690454 = cos(r1690452);
        double r1690455 = r1690453 - r1690454;
        return r1690455;
}

double f(double x) {
        double r1690456 = x;
        double r1690457 = sin(r1690456);
        double r1690458 = 1.0;
        double r1690459 = cos(r1690458);
        double r1690460 = r1690457 * r1690459;
        double r1690461 = sin(r1690458);
        double r1690462 = cos(r1690456);
        double r1690463 = r1690461 * r1690462;
        double r1690464 = r1690460 + r1690463;
        double r1690465 = r1690462 * r1690459;
        double r1690466 = r1690464 - r1690465;
        double r1690467 = r1690457 * r1690461;
        double r1690468 = r1690466 + r1690467;
        return r1690468;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 26.8

    \[\sin \left(x + 1\right) - \cos \left(x + 1\right)\]
  2. Using strategy rm
  3. Applied cos-sum25.9

    \[\leadsto \sin \left(x + 1\right) - \color{blue}{\left(\cos x \cdot \cos 1 - \sin x \cdot \sin 1\right)}\]
  4. Applied associate--r-25.9

    \[\leadsto \color{blue}{\left(\sin \left(x + 1\right) - \cos x \cdot \cos 1\right) + \sin x \cdot \sin 1}\]
  5. Using strategy rm
  6. Applied sin-sum0.8

    \[\leadsto \left(\color{blue}{\left(\sin x \cdot \cos 1 + \cos x \cdot \sin 1\right)} - \cos x \cdot \cos 1\right) + \sin x \cdot \sin 1\]
  7. Simplified0.8

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

    \[\leadsto \left(\left(\sin x \cdot \cos 1 + \sin 1 \cdot \cos x\right) - \cos x \cdot \cos 1\right) + \sin x \cdot \sin 1\]

Reproduce

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