Average Error: 32.6 → 0
Time: 4.2s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right|}{x}
double f(double x) {
        double r3042783 = x;
        double r3042784 = r3042783 / r3042783;
        double r3042785 = 1.0;
        double r3042786 = r3042785 / r3042783;
        double r3042787 = r3042783 * r3042783;
        double r3042788 = sqrt(r3042787);
        double r3042789 = r3042786 * r3042788;
        double r3042790 = r3042784 - r3042789;
        return r3042790;
}
↓
double f(double x) {
        double r3042791 = 1.0;
        double r3042792 = x;
        double r3042793 = fabs(r3042792);
        double r3042794 = r3042793 / r3042792;
        double r3042795 = r3042791 - r3042794;
        return r3042795;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.6

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

  2. Simplified0

    \[\leadsto \color{blue}{1 - \frac{\left|x\right|}{x}}\]

  3. Final simplification0

    \[\leadsto 1 - \frac{\left|x\right|}{x}\]

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0) 2 0)

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