Average Error: 32.6 → 0
Time: 5.9s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right| \cdot 1}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right| \cdot 1}{x}
double f(double x) {
        double r4300676 = x;
        double r4300677 = r4300676 / r4300676;
        double r4300678 = 1.0;
        double r4300679 = r4300678 / r4300676;
        double r4300680 = r4300676 * r4300676;
        double r4300681 = sqrt(r4300680);
        double r4300682 = r4300679 * r4300681;
        double r4300683 = r4300677 - r4300682;
        return r4300683;
}
↓
double f(double x) {
        double r4300684 = 1.0;
        double r4300685 = x;
        double r4300686 = fabs(r4300685);
        double r4300687 = 1.0;
        double r4300688 = r4300686 * r4300687;
        double r4300689 = r4300688 / r4300685;
        double r4300690 = r4300684 - r4300689;
        return r4300690;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.6

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

  2. Simplified4.6

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  3. Using strategy rm

  4. Applied associate-*l/0

    \[\leadsto 1 - \color{blue}{\frac{1 \cdot \left|x\right|}{x}}\]

  5. Final simplification0

    \[\leadsto 1 - \frac{\left|x\right| \cdot 1}{x}\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0.0) 2.0 0.0)

  (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))