Average Error: 31.9 → 0
Time: 4.0s
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 r3721976 = x;
        double r3721977 = r3721976 / r3721976;
        double r3721978 = 1.0;
        double r3721979 = r3721978 / r3721976;
        double r3721980 = r3721976 * r3721976;
        double r3721981 = sqrt(r3721980);
        double r3721982 = r3721979 * r3721981;
        double r3721983 = r3721977 - r3721982;
        return r3721983;
}
↓
double f(double x) {
        double r3721984 = 1.0;
        double r3721985 = x;
        double r3721986 = fabs(r3721985);
        double r3721987 = r3721986 / r3721985;
        double r3721988 = r3721984 - r3721987;
        return r3721988;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.9
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.9

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

  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 2019143 
(FPCore (x)
  :name "sqrt sqr"

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

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