Average Error: 0.2 → 0.0
Time: 12.5s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1}{\left(1 + 4 \cdot \sqrt{x}\right) + x} \cdot 6\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{x - 1}{\left(1 + 4 \cdot \sqrt{x}\right) + x} \cdot 6
double f(double x) {
        double r43593804 = 6.0;
        double r43593805 = x;
        double r43593806 = 1.0;
        double r43593807 = r43593805 - r43593806;
        double r43593808 = r43593804 * r43593807;
        double r43593809 = r43593805 + r43593806;
        double r43593810 = 4.0;
        double r43593811 = sqrt(r43593805);
        double r43593812 = r43593810 * r43593811;
        double r43593813 = r43593809 + r43593812;
        double r43593814 = r43593808 / r43593813;
        return r43593814;
}
↓
double f(double x) {
        double r43593815 = x;
        double r43593816 = 1.0;
        double r43593817 = r43593815 - r43593816;
        double r43593818 = 4.0;
        double r43593819 = sqrt(r43593815);
        double r43593820 = r43593818 * r43593819;
        double r43593821 = r43593816 + r43593820;
        double r43593822 = r43593821 + r43593815;
        double r43593823 = r43593817 / r43593822;
        double r43593824 = 6.0;
        double r43593825 = r43593823 * r43593824;
        return r43593825;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.2

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

  4. Applied times-frac0.0

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

  5. Simplified0.0

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

  7. Applied associate-+l+0.0

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

  8. Final simplification0.0

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

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)))))