Average Error: 31.6 → 0
Time: 4.3s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[\sqrt[3]{{\left(1 - \frac{\left|x\right|}{\frac{x}{1}}\right)}^{3}}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
\sqrt[3]{{\left(1 - \frac{\left|x\right|}{\frac{x}{1}}\right)}^{3}}
double f(double x) {
        double r83897 = x;
        double r83898 = r83897 / r83897;
        double r83899 = 1.0;
        double r83900 = r83899 / r83897;
        double r83901 = r83897 * r83897;
        double r83902 = sqrt(r83901);
        double r83903 = r83900 * r83902;
        double r83904 = r83898 - r83903;
        return r83904;
}
↓
double f(double x) {
        double r83905 = 1.0;
        double r83906 = x;
        double r83907 = fabs(r83906);
        double r83908 = 1.0;
        double r83909 = r83906 / r83908;
        double r83910 = r83907 / r83909;
        double r83911 = r83905 - r83910;
        double r83912 = 3.0;
        double r83913 = pow(r83911, r83912);
        double r83914 = cbrt(r83913);
        return r83914;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 31.6

    \[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]

  2. Simplified5.0

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  3. Using strategy rm

  4. Applied add-cbrt-cube5.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(1 - \frac{1}{x} \cdot \left|x\right|\right) \cdot \left(1 - \frac{1}{x} \cdot \left|x\right|\right)\right) \cdot \left(1 - \frac{1}{x} \cdot \left|x\right|\right)}}\]

  5. Simplified0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(1 - \frac{\left|x\right|}{\frac{x}{1}}\right)}^{3}}}\]

  6. Final simplification0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0.0) 2.0 0.0)

  (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))