Average Error: 32.6 → 0
Time: 4.2s
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 r3650105 = x;
        double r3650106 = r3650105 / r3650105;
        double r3650107 = 1.0;
        double r3650108 = r3650107 / r3650105;
        double r3650109 = r3650105 * r3650105;
        double r3650110 = sqrt(r3650109);
        double r3650111 = r3650108 * r3650110;
        double r3650112 = r3650106 - r3650111;
        return r3650112;
}
↓
double f(double x) {
        double r3650113 = 1.0;
        double r3650114 = x;
        double r3650115 = fabs(r3650114);
        double r3650116 = r3650115 / r3650114;
        double r3650117 = r3650113 - r3650116;
        return r3650117;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.6

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

  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 2019133 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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