Average Error: 0.5 → 0.5
Time: 12.4s
Precision: 64
\[\sin x \cdot \cos x + \sin x\]
\[e^{\log \left(\cos x + 1\right)} \cdot \sin x\]
\sin x \cdot \cos x + \sin x
e^{\log \left(\cos x + 1\right)} \cdot \sin x
double f(double x) {
        double r952470 = x;
        double r952471 = sin(r952470);
        double r952472 = cos(r952470);
        double r952473 = r952471 * r952472;
        double r952474 = r952473 + r952471;
        return r952474;
}

double f(double x) {
        double r952475 = x;
        double r952476 = cos(r952475);
        double r952477 = 1.0;
        double r952478 = r952476 + r952477;
        double r952479 = log(r952478);
        double r952480 = exp(r952479);
        double r952481 = sin(r952475);
        double r952482 = r952480 * r952481;
        return r952482;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\sin x \cdot \cos x + \sin x\]
  2. Simplified0.5

    \[\leadsto \color{blue}{\left(\cos x + 1\right) \cdot \sin x}\]
  3. Using strategy rm
  4. Applied add-exp-log0.5

    \[\leadsto \color{blue}{e^{\log \left(\cos x + 1\right)}} \cdot \sin x\]
  5. Final simplification0.5

    \[\leadsto e^{\log \left(\cos x + 1\right)} \cdot \sin x\]

Reproduce

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