Average Error: 31.5 → 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 r16628656 = x;
        double r16628657 = r16628656 / r16628656;
        double r16628658 = 1.0;
        double r16628659 = r16628658 / r16628656;
        double r16628660 = r16628656 * r16628656;
        double r16628661 = sqrt(r16628660);
        double r16628662 = r16628659 * r16628661;
        double r16628663 = r16628657 - r16628662;
        return r16628663;
}
↓
double f(double x) {
        double r16628664 = 1.0;
        double r16628665 = x;
        double r16628666 = fabs(r16628665);
        double r16628667 = r16628666 / r16628665;
        double r16628668 = r16628664 - r16628667;
        return r16628668;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.5
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.5

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

  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 2019107 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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