Average Error: 32.6 → 0
Time: 13.6s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \left(\sqrt[3]{\frac{1}{x} \cdot \left|x\right|} \cdot \sqrt[3]{\frac{1}{x} \cdot \left|x\right|}\right) \cdot \sqrt[3]{\frac{1}{x} \cdot \left|x\right|}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \left(\sqrt[3]{\frac{1}{x} \cdot \left|x\right|} \cdot \sqrt[3]{\frac{1}{x} \cdot \left|x\right|}\right) \cdot \sqrt[3]{\frac{1}{x} \cdot \left|x\right|}
double f(double x) {
        double r91428 = x;
        double r91429 = r91428 / r91428;
        double r91430 = 1.0;
        double r91431 = r91430 / r91428;
        double r91432 = r91428 * r91428;
        double r91433 = sqrt(r91432);
        double r91434 = r91431 * r91433;
        double r91435 = r91429 - r91434;
        return r91435;
}
↓
double f(double x) {
        double r91436 = 1.0;
        double r91437 = 1.0;
        double r91438 = x;
        double r91439 = r91437 / r91438;
        double r91440 = fabs(r91438);
        double r91441 = r91439 * r91440;
        double r91442 = cbrt(r91441);
        double r91443 = r91442 * r91442;
        double r91444 = r91443 * r91442;
        double r91445 = r91436 - r91444;
        return r91445;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.6

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

  2. Simplified4.7

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

  4. Applied add-cube-cbrt0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

  :herbie-target
  (if (< x 0.0) 2 0.0)

  (- (/ x x) (* (/ 1 x) (sqrt (* x x)))))