Average Error: 32.8 → 0.0
Time: 14.1s
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 r102984 = x;
        double r102985 = r102984 / r102984;
        double r102986 = 1.0;
        double r102987 = r102986 / r102984;
        double r102988 = r102984 * r102984;
        double r102989 = sqrt(r102988);
        double r102990 = r102987 * r102989;
        double r102991 = r102985 - r102990;
        return r102991;
}
↓
double f(double x) {
        double r102992 = 1.0;
        double r102993 = 1.0;
        double r102994 = x;
        double r102995 = r102993 / r102994;
        double r102996 = fabs(r102994);
        double r102997 = r102995 * r102996;
        double r102998 = cbrt(r102997);
        double r102999 = r102998 * r102998;
        double r103000 = r102999 * r102998;
        double r103001 = r102992 - r103000;
        return r103001;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.8
Target0
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.8

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

  2. Simplified4.5

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

  4. Applied add-cube-cbrt0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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