Average Error: 32.1 → 0
Time: 3.5s
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 r24201462 = x;
        double r24201463 = r24201462 / r24201462;
        double r24201464 = 1.0;
        double r24201465 = r24201464 / r24201462;
        double r24201466 = r24201462 * r24201462;
        double r24201467 = sqrt(r24201466);
        double r24201468 = r24201465 * r24201467;
        double r24201469 = r24201463 - r24201468;
        return r24201469;
}
↓
double f(double x) {
        double r24201470 = 1.0;
        double r24201471 = x;
        double r24201472 = fabs(r24201471);
        double r24201473 = r24201472 / r24201471;
        double r24201474 = r24201470 - r24201473;
        return r24201474;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.1
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.1

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

  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 2019128 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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