Average Error: 31.8 → 0
Time: 4.2s
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 r2651936 = x;
        double r2651937 = r2651936 / r2651936;
        double r2651938 = 1.0;
        double r2651939 = r2651938 / r2651936;
        double r2651940 = r2651936 * r2651936;
        double r2651941 = sqrt(r2651940);
        double r2651942 = r2651939 * r2651941;
        double r2651943 = r2651937 - r2651942;
        return r2651943;
}
↓
double f(double x) {
        double r2651944 = 1.0;
        double r2651945 = x;
        double r2651946 = fabs(r2651945);
        double r2651947 = r2651946 / r2651945;
        double r2651948 = r2651944 - r2651947;
        return r2651948;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.8
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.8

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

  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 2019152 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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