Average Error: 32.3 → 0
Time: 2.7s
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 r103072 = x;
        double r103073 = r103072 / r103072;
        double r103074 = 1.0;
        double r103075 = r103074 / r103072;
        double r103076 = r103072 * r103072;
        double r103077 = sqrt(r103076);
        double r103078 = r103075 * r103077;
        double r103079 = r103073 - r103078;
        return r103079;
}
↓
double f(double x) {
        double r103080 = 1.0;
        double r103081 = 1.0;
        double r103082 = x;
        double r103083 = fabs(r103082);
        double r103084 = r103081 * r103083;
        double r103085 = r103084 / r103082;
        double r103086 = r103080 - r103085;
        return r103086;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.3
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.3

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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