Average Error: 13.5 → 0.2
Time: 11.5s
Precision: 64
\[{cos}^{2} \cdot x + {sin}^{2} \cdot x\]
\[{cos}^{\left(\frac{2}{2}\right)} \cdot \left({cos}^{\left(\frac{2}{2}\right)} \cdot x\right) + {sin}^{\left(\frac{2}{2}\right)} \cdot \left({sin}^{\left(\frac{2}{2}\right)} \cdot x\right)\]
{cos}^{2} \cdot x + {sin}^{2} \cdot x
{cos}^{\left(\frac{2}{2}\right)} \cdot \left({cos}^{\left(\frac{2}{2}\right)} \cdot x\right) + {sin}^{\left(\frac{2}{2}\right)} \cdot \left({sin}^{\left(\frac{2}{2}\right)} \cdot x\right)
double f(double cos, double x, double sin) {
        double r773101 = cos;
        double r773102 = 2.0;
        double r773103 = pow(r773101, r773102);
        double r773104 = x;
        double r773105 = r773103 * r773104;
        double r773106 = sin;
        double r773107 = pow(r773106, r773102);
        double r773108 = r773107 * r773104;
        double r773109 = r773105 + r773108;
        return r773109;
}

double f(double cos, double x, double sin) {
        double r773110 = cos;
        double r773111 = 2.0;
        double r773112 = 2.0;
        double r773113 = r773111 / r773112;
        double r773114 = pow(r773110, r773113);
        double r773115 = x;
        double r773116 = r773114 * r773115;
        double r773117 = r773114 * r773116;
        double r773118 = sin;
        double r773119 = pow(r773118, r773113);
        double r773120 = r773119 * r773115;
        double r773121 = r773119 * r773120;
        double r773122 = r773117 + r773121;
        return r773122;
}

Error

Bits error versus cos

Bits error versus x

Bits error versus sin

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.5

    \[{cos}^{2} \cdot x + {sin}^{2} \cdot x\]
  2. Using strategy rm
  3. Applied sqr-pow13.5

    \[\leadsto {cos}^{2} \cdot x + \color{blue}{\left({sin}^{\left(\frac{2}{2}\right)} \cdot {sin}^{\left(\frac{2}{2}\right)}\right)} \cdot x\]
  4. Applied associate-*l*7.4

    \[\leadsto {cos}^{2} \cdot x + \color{blue}{{sin}^{\left(\frac{2}{2}\right)} \cdot \left({sin}^{\left(\frac{2}{2}\right)} \cdot x\right)}\]
  5. Using strategy rm
  6. Applied sqr-pow7.4

    \[\leadsto \color{blue}{\left({cos}^{\left(\frac{2}{2}\right)} \cdot {cos}^{\left(\frac{2}{2}\right)}\right)} \cdot x + {sin}^{\left(\frac{2}{2}\right)} \cdot \left({sin}^{\left(\frac{2}{2}\right)} \cdot x\right)\]
  7. Applied associate-*l*0.2

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

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

Reproduce

herbie shell --seed 1 
(FPCore (cos x sin)
  :name "cos^2(x) + sin^2(x)"
  :precision binary64
  (+ (* (pow cos 2) x) (* (pow sin 2) x)))