Average Error: 32.3 → 0
Time: 6.5s
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 r3761183 = x;
        double r3761184 = r3761183 / r3761183;
        double r3761185 = 1.0;
        double r3761186 = r3761185 / r3761183;
        double r3761187 = r3761183 * r3761183;
        double r3761188 = sqrt(r3761187);
        double r3761189 = r3761186 * r3761188;
        double r3761190 = r3761184 - r3761189;
        return r3761190;
}
↓
double f(double x) {
        double r3761191 = 1.0;
        double r3761192 = x;
        double r3761193 = fabs(r3761192);
        double r3761194 = r3761193 / r3761192;
        double r3761195 = r3761191 - r3761194;
        return r3761195;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.3
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.3

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

  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 2019168 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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