Average Error: 32.1 → 0
Time: 4.1s
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 r34887971 = x;
        double r34887972 = r34887971 / r34887971;
        double r34887973 = 1.0;
        double r34887974 = r34887973 / r34887971;
        double r34887975 = r34887971 * r34887971;
        double r34887976 = sqrt(r34887975);
        double r34887977 = r34887974 * r34887976;
        double r34887978 = r34887972 - r34887977;
        return r34887978;
}
↓
double f(double x) {
        double r34887979 = 1.0;
        double r34887980 = x;
        double r34887981 = fabs(r34887980);
        double r34887982 = r34887981 / r34887980;
        double r34887983 = r34887979 - r34887982;
        return r34887983;
}

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 2019125 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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