Average Error: 32.5 → 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 r107504 = x;
        double r107505 = r107504 / r107504;
        double r107506 = 1.0;
        double r107507 = r107506 / r107504;
        double r107508 = r107504 * r107504;
        double r107509 = sqrt(r107508);
        double r107510 = r107507 * r107509;
        double r107511 = r107505 - r107510;
        return r107511;
}
↓
double f(double x) {
        double r107512 = 1.0;
        double r107513 = 1.0;
        double r107514 = x;
        double r107515 = r107513 / r107514;
        double r107516 = fabs(r107514);
        double r107517 = r107515 * r107516;
        double r107518 = cbrt(r107517);
        double r107519 = r107518 * r107518;
        double r107520 = r107519 * r107518;
        double r107521 = r107512 - r107520;
        return r107521;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.5
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.5

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

  2. Simplified4.8

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  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 2019322 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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