Average Error: 32.5 → 0
Time: 6.1s
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 r4388602 = x;
        double r4388603 = r4388602 / r4388602;
        double r4388604 = 1.0;
        double r4388605 = r4388604 / r4388602;
        double r4388606 = r4388602 * r4388602;
        double r4388607 = sqrt(r4388606);
        double r4388608 = r4388605 * r4388607;
        double r4388609 = r4388603 - r4388608;
        return r4388609;
}
↓
double f(double x) {
        double r4388610 = 1.0;
        double r4388611 = x;
        double r4388612 = fabs(r4388611);
        double r4388613 = 1.0;
        double r4388614 = r4388612 * r4388613;
        double r4388615 = r4388614 / r4388611;
        double r4388616 = r4388610 - r4388615;
        return r4388616;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.5
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.5

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

  2. Simplified4.7

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  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 2019169 +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)))))