Average Error: 31.6 → 0
Time: 5.3s
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 r3694340 = x;
        double r3694341 = r3694340 / r3694340;
        double r3694342 = 1.0;
        double r3694343 = r3694342 / r3694340;
        double r3694344 = r3694340 * r3694340;
        double r3694345 = sqrt(r3694344);
        double r3694346 = r3694343 * r3694345;
        double r3694347 = r3694341 - r3694346;
        return r3694347;
}
↓
double f(double x) {
        double r3694348 = 1.0;
        double r3694349 = x;
        double r3694350 = fabs(r3694349);
        double r3694351 = r3694350 / r3694349;
        double r3694352 = r3694348 - r3694351;
        return r3694352;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.6

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

  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 2019165 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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