Average Error: 32.7 → 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 r3474963 = x;
        double r3474964 = r3474963 / r3474963;
        double r3474965 = 1.0;
        double r3474966 = r3474965 / r3474963;
        double r3474967 = r3474963 * r3474963;
        double r3474968 = sqrt(r3474967);
        double r3474969 = r3474966 * r3474968;
        double r3474970 = r3474964 - r3474969;
        return r3474970;
}
↓
double f(double x) {
        double r3474971 = 1.0;
        double r3474972 = x;
        double r3474973 = fabs(r3474972);
        double r3474974 = r3474973 / r3474972;
        double r3474975 = r3474971 - r3474974;
        return r3474975;
}

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 2019135 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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