Average Error: 32.1 → 0
Time: 3.9s
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 r3241151 = x;
        double r3241152 = r3241151 / r3241151;
        double r3241153 = 1.0;
        double r3241154 = r3241153 / r3241151;
        double r3241155 = r3241151 * r3241151;
        double r3241156 = sqrt(r3241155);
        double r3241157 = r3241154 * r3241156;
        double r3241158 = r3241152 - r3241157;
        return r3241158;
}
↓
double f(double x) {
        double r3241159 = 1.0;
        double r3241160 = x;
        double r3241161 = fabs(r3241160);
        double r3241162 = r3241161 / r3241160;
        double r3241163 = r3241159 - r3241162;
        return r3241163;
}

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 2019151 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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