Average Error: 32.6 → 0
Time: 13.0s
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 r66200 = x;
        double r66201 = r66200 / r66200;
        double r66202 = 1.0;
        double r66203 = r66202 / r66200;
        double r66204 = r66200 * r66200;
        double r66205 = sqrt(r66204);
        double r66206 = r66203 * r66205;
        double r66207 = r66201 - r66206;
        return r66207;
}
↓
double f(double x) {
        double r66208 = 1.0;
        double r66209 = 1.0;
        double r66210 = x;
        double r66211 = r66209 / r66210;
        double r66212 = fabs(r66210);
        double r66213 = r66211 * r66212;
        double r66214 = cbrt(r66213);
        double r66215 = r66214 * r66214;
        double r66216 = r66215 * r66214;
        double r66217 = r66208 - r66216;
        return r66217;
}

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)))))