Average Error: 0.2 → 0.0
Time: 11.2s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1}{-\left(\left(4 \cdot \sqrt{x} + x\right) + 1\right)} \cdot \left(-6\right)\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{x - 1}{-\left(\left(4 \cdot \sqrt{x} + x\right) + 1\right)} \cdot \left(-6\right)
double f(double x) {
        double r759826 = 6.0;
        double r759827 = x;
        double r759828 = 1.0;
        double r759829 = r759827 - r759828;
        double r759830 = r759826 * r759829;
        double r759831 = r759827 + r759828;
        double r759832 = 4.0;
        double r759833 = sqrt(r759827);
        double r759834 = r759832 * r759833;
        double r759835 = r759831 + r759834;
        double r759836 = r759830 / r759835;
        return r759836;
}
↓
double f(double x) {
        double r759837 = x;
        double r759838 = 1.0;
        double r759839 = r759837 - r759838;
        double r759840 = 4.0;
        double r759841 = sqrt(r759837);
        double r759842 = r759840 * r759841;
        double r759843 = r759842 + r759837;
        double r759844 = r759843 + r759838;
        double r759845 = -r759844;
        double r759846 = r759839 / r759845;
        double r759847 = 6.0;
        double r759848 = -r759847;
        double r759849 = r759846 * r759848;
        return r759849;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.0
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{6 \cdot \frac{x - 1}{\left(x + 1\right) + \sqrt{x} \cdot 4}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.0

    \[\leadsto 6 \cdot \frac{x - 1}{\color{blue}{1 \cdot \left(\left(x + 1\right) + \sqrt{x} \cdot 4\right)}}\]
  5. Using strategy rm

  6. Applied frac-2neg0.0

    \[\leadsto 6 \cdot \color{blue}{\frac{-\left(x - 1\right)}{-1 \cdot \left(\left(x + 1\right) + \sqrt{x} \cdot 4\right)}}\]

  7. Simplified0.0

    \[\leadsto 6 \cdot \frac{-\left(x - 1\right)}{\color{blue}{-\left(\left(x + 4 \cdot \sqrt{x}\right) + 1\right)}}\]

  8. Final simplification0.0

    \[\leadsto \frac{x - 1}{-\left(\left(4 \cdot \sqrt{x} + x\right) + 1\right)} \cdot \left(-6\right)\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"

  :herbie-target
  (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

  (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))