Average Error: 31.7 → 0
Time: 4.3s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right|}{x}
double f(double x) {
        double r8907560 = x;
        double r8907561 = r8907560 / r8907560;
        double r8907562 = 1.0;
        double r8907563 = r8907562 / r8907560;
        double r8907564 = r8907560 * r8907560;
        double r8907565 = sqrt(r8907564);
        double r8907566 = r8907563 * r8907565;
        double r8907567 = r8907561 - r8907566;
        return r8907567;
}
↓
double f(double x) {
        double r8907568 = 1.0;
        double r8907569 = x;
        double r8907570 = fabs(r8907569);
        double r8907571 = r8907570 / r8907569;
        double r8907572 = r8907568 - r8907571;
        return r8907572;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.7
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 31.7

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019124 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0) 2 0)

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