Average Error: 32.8 → 0.0
Time: 11.9s
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 r99019 = x;
        double r99020 = r99019 / r99019;
        double r99021 = 1.0;
        double r99022 = r99021 / r99019;
        double r99023 = r99019 * r99019;
        double r99024 = sqrt(r99023);
        double r99025 = r99022 * r99024;
        double r99026 = r99020 - r99025;
        return r99026;
}
↓
double f(double x) {
        double r99027 = 1.0;
        double r99028 = x;
        double r99029 = fabs(r99028);
        double r99030 = 1.0;
        double r99031 = r99030 / r99028;
        double r99032 = r99029 * r99031;
        double r99033 = 3.0;
        double r99034 = pow(r99032, r99033);
        double r99035 = cbrt(r99034);
        double r99036 = r99027 - r99035;
        return r99036;
}

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-cbrt-cube45.5

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

  5. Applied add-cbrt-cube43.8

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

  6. Applied add-cbrt-cube43.8

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

  7. Applied cbrt-undiv49.5

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

  8. Applied cbrt-unprod42.9

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

  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 2019325 +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)))))