Average Error: 32.4 → 0
Time: 4.0s
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 r3677825 = x;
        double r3677826 = r3677825 / r3677825;
        double r3677827 = 1.0;
        double r3677828 = r3677827 / r3677825;
        double r3677829 = r3677825 * r3677825;
        double r3677830 = sqrt(r3677829);
        double r3677831 = r3677828 * r3677830;
        double r3677832 = r3677826 - r3677831;
        return r3677832;
}
↓
double f(double x) {
        double r3677833 = 1.0;
        double r3677834 = x;
        double r3677835 = fabs(r3677834);
        double r3677836 = r3677835 / r3677834;
        double r3677837 = r3677833 - r3677836;
        return r3677837;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.4
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.4

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

  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 2019141 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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