Average Error: 31.6 → 0
Time: 4.3s
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 r3083136 = x;
        double r3083137 = r3083136 / r3083136;
        double r3083138 = 1.0;
        double r3083139 = r3083138 / r3083136;
        double r3083140 = r3083136 * r3083136;
        double r3083141 = sqrt(r3083140);
        double r3083142 = r3083139 * r3083141;
        double r3083143 = r3083137 - r3083142;
        return r3083143;
}
↓
double f(double x) {
        double r3083144 = 1.0;
        double r3083145 = x;
        double r3083146 = fabs(r3083145);
        double r3083147 = r3083146 / r3083145;
        double r3083148 = r3083144 - r3083147;
        return r3083148;
}

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 2019132 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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