Average Error: 0.2 → 0.1
Time: 12.6s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{\frac{6}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \cdot \sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{\frac{6}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \cdot \sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}
double f(double x) {
        double r596444 = 6.0;
        double r596445 = x;
        double r596446 = 1.0;
        double r596447 = r596445 - r596446;
        double r596448 = r596444 * r596447;
        double r596449 = r596445 + r596446;
        double r596450 = 4.0;
        double r596451 = sqrt(r596445);
        double r596452 = r596450 * r596451;
        double r596453 = r596449 + r596452;
        double r596454 = r596448 / r596453;
        return r596454;
}
↓
double f(double x) {
        double r596455 = 6.0;
        double r596456 = x;
        double r596457 = 1.0;
        double r596458 = r596456 + r596457;
        double r596459 = 4.0;
        double r596460 = sqrt(r596456);
        double r596461 = r596459 * r596460;
        double r596462 = r596458 + r596461;
        double r596463 = r596456 - r596457;
        double r596464 = r596462 / r596463;
        double r596465 = cbrt(r596464);
        double r596466 = r596465 * r596465;
        double r596467 = r596455 / r596466;
        double r596468 = r596467 / r596465;
        return r596468;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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 associate-/l*0.0

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

  5. Applied add-cube-cbrt0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

    \[\leadsto \frac{\frac{6}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \cdot \sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"
  :precision binary64

  :herbie-target
  (/ 6 (/ (+ (+ x 1) (* 4 (sqrt x))) (- x 1)))

  (/ (* 6 (- x 1)) (+ (+ x 1) (* 4 (sqrt x)))))