Average Error: 32.5 → 0
Time: 1.7s
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 r502 = x;
        double r503 = r502 / r502;
        double r504 = 1.0;
        double r505 = r504 / r502;
        double r506 = r502 * r502;
        double r507 = sqrt(r506);
        double r508 = r505 * r507;
        double r509 = r503 - r508;
        return r509;
}
↓
double f(double x) {
        double r510 = 1.0;
        double r511 = 1.0;
        double r512 = x;
        double r513 = fabs(r512);
        double r514 = r511 * r513;
        double r515 = r514 / r512;
        double r516 = -r515;
        double r517 = r510 + r516;
        return r517;
}

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. 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 2020025 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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