Average Error: 16.4 → 16.4
Time: 13.3s
Precision: 64
\[\sin \left({x}^{2}\right) - \left|x\right|\]
\[\sin \left(\sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}} \cdot \left(\sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}} \cdot \sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}}\right)\right) - \left|x\right|\]
\sin \left({x}^{2}\right) - \left|x\right|
\sin \left(\sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}} \cdot \left(\sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}} \cdot \sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}}\right)\right) - \left|x\right|
double f(double x) {
        double r4360955 = x;
        double r4360956 = 2.0;
        double r4360957 = pow(r4360955, r4360956);
        double r4360958 = sin(r4360957);
        double r4360959 = fabs(r4360955);
        double r4360960 = r4360958 - r4360959;
        return r4360960;
}

double f(double x) {
        double r4360961 = 1.0;
        double r4360962 = x;
        double r4360963 = r4360961 / r4360962;
        double r4360964 = -2.0;
        double r4360965 = pow(r4360963, r4360964);
        double r4360966 = cbrt(r4360965);
        double r4360967 = r4360966 * r4360966;
        double r4360968 = r4360966 * r4360967;
        double r4360969 = sin(r4360968);
        double r4360970 = fabs(r4360962);
        double r4360971 = r4360969 - r4360970;
        return r4360971;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.4

    \[\sin \left({x}^{2}\right) - \left|x\right|\]
  2. Taylor expanded around inf 16.4

    \[\leadsto \color{blue}{\sin \left({\left(\frac{1}{x}\right)}^{-2}\right)} - \left|x\right|\]
  3. Using strategy rm
  4. Applied add-cube-cbrt16.4

    \[\leadsto \sin \color{blue}{\left(\left(\sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}} \cdot \sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}}\right) \cdot \sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}}\right)} - \left|x\right|\]
  5. Final simplification16.4

    \[\leadsto \sin \left(\sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}} \cdot \left(\sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}} \cdot \sqrt[3]{{\left(\frac{1}{x}\right)}^{-2}}\right)\right) - \left|x\right|\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sin(x^2) - abs(x)"
  (- (sin (pow x 2.0)) (fabs x)))