Average Error: 32.7 → 0
Time: 4.5s
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 r3291236 = x;
        double r3291237 = r3291236 / r3291236;
        double r3291238 = 1.0;
        double r3291239 = r3291238 / r3291236;
        double r3291240 = r3291236 * r3291236;
        double r3291241 = sqrt(r3291240);
        double r3291242 = r3291239 * r3291241;
        double r3291243 = r3291237 - r3291242;
        return r3291243;
}
↓
double f(double x) {
        double r3291244 = 1.0;
        double r3291245 = x;
        double r3291246 = fabs(r3291245);
        double r3291247 = r3291246 / r3291245;
        double r3291248 = r3291244 - r3291247;
        return r3291248;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.7
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.7

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

  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 2019134 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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