Average Error: 32.8 → 0.0
Time: 8.5s
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 r156672 = x;
        double r156673 = r156672 / r156672;
        double r156674 = 1.0;
        double r156675 = r156674 / r156672;
        double r156676 = r156672 * r156672;
        double r156677 = sqrt(r156676);
        double r156678 = r156675 * r156677;
        double r156679 = r156673 - r156678;
        return r156679;
}
↓
double f(double x) {
        double r156680 = 1.0;
        double r156681 = 1.0;
        double r156682 = x;
        double r156683 = r156681 / r156682;
        double r156684 = fabs(r156682);
        double r156685 = r156683 * r156684;
        double r156686 = cbrt(r156685);
        double r156687 = r156686 * r156686;
        double r156688 = r156687 * r156686;
        double r156689 = r156680 - r156688;
        return r156689;
}

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-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 2019350 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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