Average Error: 0.2 → 0.2
Time: 8.6s
Precision: 64
\[\left(x \cdot \sin x\right) \cdot \cos x\]
\[x \cdot \frac{\sin \left(x + x\right)}{2}\]
\left(x \cdot \sin x\right) \cdot \cos x
x \cdot \frac{\sin \left(x + x\right)}{2}
double f(double x) {
        double r1198226 = x;
        double r1198227 = sin(r1198226);
        double r1198228 = r1198226 * r1198227;
        double r1198229 = cos(r1198226);
        double r1198230 = r1198228 * r1198229;
        return r1198230;
}

double f(double x) {
        double r1198231 = x;
        double r1198232 = r1198231 + r1198231;
        double r1198233 = sin(r1198232);
        double r1198234 = 2.0;
        double r1198235 = r1198233 / r1198234;
        double r1198236 = r1198231 * r1198235;
        return r1198236;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(x \cdot \sin x\right) \cdot \cos x\]
  2. Using strategy rm
  3. Applied associate-*l*0.2

    \[\leadsto \color{blue}{x \cdot \left(\sin x \cdot \cos x\right)}\]
  4. Using strategy rm
  5. Applied sin-cos-mult0.2

    \[\leadsto x \cdot \color{blue}{\frac{\sin \left(x - x\right) + \sin \left(x + x\right)}{2}}\]
  6. Simplified0.2

    \[\leadsto x \cdot \frac{\color{blue}{\sin \left(x + x\right)}}{2}\]
  7. Final simplification0.2

    \[\leadsto x \cdot \frac{\sin \left(x + x\right)}{2}\]

Reproduce

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