Average Error: 32.6 → 0
Time: 1.8s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 + \left(-\frac{1 \cdot \left|x\right|}{x}\right)\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 + \left(-\frac{1 \cdot \left|x\right|}{x}\right)
double f(double x) {
        double r268432 = x;
        double r268433 = r268432 / r268432;
        double r268434 = 1.0;
        double r268435 = r268434 / r268432;
        double r268436 = r268432 * r268432;
        double r268437 = sqrt(r268436);
        double r268438 = r268435 * r268437;
        double r268439 = r268433 - r268438;
        return r268439;
}
↓
double f(double x) {
        double r268440 = 1.0;
        double r268441 = 1.0;
        double r268442 = x;
        double r268443 = fabs(r268442);
        double r268444 = r268441 * r268443;
        double r268445 = r268444 / r268442;
        double r268446 = -r268445;
        double r268447 = r268440 + r268446;
        return r268447;
}

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. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

  :herbie-target
  (if (< x 0.0) 2 0.0)

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