Average Error: 32.1 → 0
Time: 4.0s
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 r1778117 = x;
        double r1778118 = r1778117 / r1778117;
        double r1778119 = 1.0;
        double r1778120 = r1778119 / r1778117;
        double r1778121 = r1778117 * r1778117;
        double r1778122 = sqrt(r1778121);
        double r1778123 = r1778120 * r1778122;
        double r1778124 = r1778118 - r1778123;
        return r1778124;
}
↓
double f(double x) {
        double r1778125 = 1.0;
        double r1778126 = x;
        double r1778127 = fabs(r1778126);
        double r1778128 = r1778127 / r1778126;
        double r1778129 = r1778125 - r1778128;
        return r1778129;
}

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)))))