Average Error: 32.2 → 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 r4539364 = x;
        double r4539365 = r4539364 / r4539364;
        double r4539366 = 1.0;
        double r4539367 = r4539366 / r4539364;
        double r4539368 = r4539364 * r4539364;
        double r4539369 = sqrt(r4539368);
        double r4539370 = r4539367 * r4539369;
        double r4539371 = r4539365 - r4539370;
        return r4539371;
}
↓
double f(double x) {
        double r4539372 = 1.0;
        double r4539373 = x;
        double r4539374 = fabs(r4539373);
        double r4539375 = 1.0;
        double r4539376 = r4539374 * r4539375;
        double r4539377 = r4539376 / r4539373;
        double r4539378 = r4539372 - r4539377;
        return r4539378;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 32.2

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

  2. Simplified4.9

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  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 2019172 +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)))))