Average Error: 31.5 → 0
Time: 8.3s
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 r3839731 = x;
        double r3839732 = r3839731 / r3839731;
        double r3839733 = 1.0;
        double r3839734 = r3839733 / r3839731;
        double r3839735 = r3839731 * r3839731;
        double r3839736 = sqrt(r3839735);
        double r3839737 = r3839734 * r3839736;
        double r3839738 = r3839732 - r3839737;
        return r3839738;
}
↓
double f(double x) {
        double r3839739 = 1.0;
        double r3839740 = x;
        double r3839741 = fabs(r3839740);
        double r3839742 = r3839741 / r3839740;
        double r3839743 = r3839739 - r3839742;
        return r3839743;
}

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 2019158 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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