Average Error: 31.7 → 0
Time: 3.7s
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 r6994017 = x;
        double r6994018 = r6994017 / r6994017;
        double r6994019 = 1.0;
        double r6994020 = r6994019 / r6994017;
        double r6994021 = r6994017 * r6994017;
        double r6994022 = sqrt(r6994021);
        double r6994023 = r6994020 * r6994022;
        double r6994024 = r6994018 - r6994023;
        return r6994024;
}
↓
double f(double x) {
        double r6994025 = 1.0;
        double r6994026 = x;
        double r6994027 = fabs(r6994026);
        double r6994028 = r6994027 / r6994026;
        double r6994029 = r6994025 - r6994028;
        return r6994029;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.7
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.7

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

  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 2019149 
(FPCore (x)
  :name "sqrt sqr"

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

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