Average Error: 32.5 → 0
Time: 5.7s
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 r1866537 = x;
        double r1866538 = r1866537 / r1866537;
        double r1866539 = 1.0;
        double r1866540 = r1866539 / r1866537;
        double r1866541 = r1866537 * r1866537;
        double r1866542 = sqrt(r1866541);
        double r1866543 = r1866540 * r1866542;
        double r1866544 = r1866538 - r1866543;
        return r1866544;
}
↓
double f(double x) {
        double r1866545 = 1.0;
        double r1866546 = x;
        double r1866547 = fabs(r1866546);
        double r1866548 = r1866547 / r1866546;
        double r1866549 = r1866545 - r1866548;
        return r1866549;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.5
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.5

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

  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 2019153 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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