Average Error: 32.4 → 0
Time: 8.6s
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 r3919554 = x;
        double r3919555 = r3919554 / r3919554;
        double r3919556 = 1.0;
        double r3919557 = r3919556 / r3919554;
        double r3919558 = r3919554 * r3919554;
        double r3919559 = sqrt(r3919558);
        double r3919560 = r3919557 * r3919559;
        double r3919561 = r3919555 - r3919560;
        return r3919561;
}
↓
double f(double x) {
        double r3919562 = 1.0;
        double r3919563 = x;
        double r3919564 = fabs(r3919563);
        double r3919565 = r3919564 / r3919563;
        double r3919566 = r3919562 - r3919565;
        return r3919566;
}

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 2019163 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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