Average Error: 32.6 → 0
Time: 4.1s
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 r29661206 = x;
        double r29661207 = r29661206 / r29661206;
        double r29661208 = 1.0;
        double r29661209 = r29661208 / r29661206;
        double r29661210 = r29661206 * r29661206;
        double r29661211 = sqrt(r29661210);
        double r29661212 = r29661209 * r29661211;
        double r29661213 = r29661207 - r29661212;
        return r29661213;
}
↓
double f(double x) {
        double r29661214 = 1.0;
        double r29661215 = x;
        double r29661216 = fabs(r29661215);
        double r29661217 = r29661216 / r29661215;
        double r29661218 = r29661214 - r29661217;
        return r29661218;
}

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 2019121 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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