Average Error: 33.1 → 0
Time: 3.0s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - 1 \cdot \frac{\left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - 1 \cdot \frac{\left|x\right|}{x}
double f(double x) {
        double r139867 = x;
        double r139868 = r139867 / r139867;
        double r139869 = 1.0;
        double r139870 = r139869 / r139867;
        double r139871 = r139867 * r139867;
        double r139872 = sqrt(r139871);
        double r139873 = r139870 * r139872;
        double r139874 = r139868 - r139873;
        return r139874;
}
↓
double f(double x) {
        double r139875 = 1.0;
        double r139876 = 1.0;
        double r139877 = x;
        double r139878 = fabs(r139877);
        double r139879 = r139878 / r139877;
        double r139880 = r139876 * r139879;
        double r139881 = r139875 - r139880;
        return r139881;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original33.1
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 33.1

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

  2. Simplified4.9

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity4.9

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

  5. Applied *-un-lft-identity4.9

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

  6. Applied times-frac4.9

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

  7. Applied associate-*l*4.9

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

  8. Simplified0

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

  9. Final simplification0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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