Average Error: 0.2 → 0.1
Time: 14.6s
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 r614549 = 6.0;
        double r614550 = x;
        double r614551 = 1.0;
        double r614552 = r614550 - r614551;
        double r614553 = r614549 * r614552;
        double r614554 = r614550 + r614551;
        double r614555 = 4.0;
        double r614556 = sqrt(r614550);
        double r614557 = r614555 * r614556;
        double r614558 = r614554 + r614557;
        double r614559 = r614553 / r614558;
        return r614559;
}
↓
double f(double x) {
        double r614560 = 6.0;
        double r614561 = x;
        double r614562 = 1.0;
        double r614563 = r614561 + r614562;
        double r614564 = 4.0;
        double r614565 = sqrt(r614561);
        double r614566 = r614564 * r614565;
        double r614567 = r614563 + r614566;
        double r614568 = r614561 - r614562;
        double r614569 = r614567 / r614568;
        double r614570 = cbrt(r614569);
        double r614571 = r614570 * r614570;
        double r614572 = r614560 / r614571;
        double r614573 = r614572 / r614570;
        return r614573;
}

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-cbrt0.2

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

  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 2019325 
(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)))))