Average Error: 32.1 → 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 r32764 = x;
        double r32765 = r32764 / r32764;
        double r32766 = 1.0;
        double r32767 = r32766 / r32764;
        double r32768 = r32764 * r32764;
        double r32769 = sqrt(r32768);
        double r32770 = r32767 * r32769;
        double r32771 = r32765 - r32770;
        return r32771;
}
↓
double f(double x) {
        double r32772 = 1.0;
        double r32773 = 1.0;
        double r32774 = x;
        double r32775 = fabs(r32774);
        double r32776 = r32773 * r32775;
        double r32777 = r32776 / r32774;
        double r32778 = r32772 - r32777;
        return r32778;
}

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)))))