Average Error: 32.8 → 0.0
Time: 6.7s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \sqrt[3]{{\left(\left|x\right| \cdot \frac{1}{x}\right)}^{3}}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \sqrt[3]{{\left(\left|x\right| \cdot \frac{1}{x}\right)}^{3}}
double f(double x) {
        double r161610 = x;
        double r161611 = r161610 / r161610;
        double r161612 = 1.0;
        double r161613 = r161612 / r161610;
        double r161614 = r161610 * r161610;
        double r161615 = sqrt(r161614);
        double r161616 = r161613 * r161615;
        double r161617 = r161611 - r161616;
        return r161617;
}
↓
double f(double x) {
        double r161618 = 1.0;
        double r161619 = x;
        double r161620 = fabs(r161619);
        double r161621 = 1.0;
        double r161622 = r161621 / r161619;
        double r161623 = r161620 * r161622;
        double r161624 = 3.0;
        double r161625 = pow(r161623, r161624);
        double r161626 = cbrt(r161625);
        double r161627 = r161618 - r161626;
        return r161627;
}

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. Simplified4.9

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

  4. Applied add-cbrt-cube45.9

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

  5. Applied add-cbrt-cube44.2

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

  6. Applied add-cbrt-cube44.2

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

  7. Applied cbrt-undiv49.8

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

  8. Applied cbrt-unprod43.3

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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