Average Error: 32.1 → 0
Time: 2.9s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{1 \cdot \left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{1 \cdot \left|x\right|}{x}
double f(double x) {
        double r31547 = x;
        double r31548 = r31547 / r31547;
        double r31549 = 1.0;
        double r31550 = r31549 / r31547;
        double r31551 = r31547 * r31547;
        double r31552 = sqrt(r31551);
        double r31553 = r31550 * r31552;
        double r31554 = r31548 - r31553;
        return r31554;
}
↓
double f(double x) {
        double r31555 = 1.0;
        double r31556 = 1.0;
        double r31557 = x;
        double r31558 = fabs(r31557);
        double r31559 = r31556 * r31558;
        double r31560 = r31559 / r31557;
        double r31561 = r31555 - r31560;
        return r31561;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.1
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.1

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

  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

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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