Average Error: 0.2 → 0.2
Time: 16.3s
Precision: 64
\[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
↓
\[\left(\sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right)}} \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right)}}\]
\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}
↓
\left(\sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right)}} \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right)}}
double f(double x) {
        double r42524521 = 6.0;
        double r42524522 = x;
        double r42524523 = 1.0;
        double r42524524 = r42524522 - r42524523;
        double r42524525 = r42524521 * r42524524;
        double r42524526 = r42524522 + r42524523;
        double r42524527 = 4.0;
        double r42524528 = sqrt(r42524522);
        double r42524529 = r42524527 * r42524528;
        double r42524530 = r42524526 + r42524529;
        double r42524531 = r42524525 / r42524530;
        return r42524531;
}
↓
double f(double x) {
        double r42524532 = x;
        double r42524533 = 1.0;
        double r42524534 = r42524532 - r42524533;
        double r42524535 = 6.0;
        double r42524536 = r42524534 * r42524535;
        double r42524537 = sqrt(r42524532);
        double r42524538 = 4.0;
        double r42524539 = r42524537 * r42524538;
        double r42524540 = r42524539 + r42524533;
        double r42524541 = r42524532 + r42524540;
        double r42524542 = r42524536 / r42524541;
        double r42524543 = r42524542 * r42524542;
        double r42524544 = r42524542 * r42524543;
        double r42524545 = cbrt(r42524544);
        double r42524546 = cbrt(r42524545);
        double r42524547 = r42524546 * r42524546;
        double r42524548 = r42524547 * r42524546;
        return r42524548;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.2
\[\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube20.7

    \[\leadsto \frac{6.0 \cdot \left(x - 1.0\right)}{\color{blue}{\sqrt[3]{\left(\left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right) \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)\right) \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)}}}\]

  4. Applied add-cbrt-cube20.6

    \[\leadsto \frac{6.0 \cdot \color{blue}{\sqrt[3]{\left(\left(x - 1.0\right) \cdot \left(x - 1.0\right)\right) \cdot \left(x - 1.0\right)}}}{\sqrt[3]{\left(\left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right) \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)\right) \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)}}\]

  5. Applied add-cbrt-cube21.2

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(6.0 \cdot 6.0\right) \cdot 6.0}} \cdot \sqrt[3]{\left(\left(x - 1.0\right) \cdot \left(x - 1.0\right)\right) \cdot \left(x - 1.0\right)}}{\sqrt[3]{\left(\left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right) \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)\right) \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)}}\]

  6. Applied cbrt-unprod21.2

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(6.0 \cdot 6.0\right) \cdot 6.0\right) \cdot \left(\left(\left(x - 1.0\right) \cdot \left(x - 1.0\right)\right) \cdot \left(x - 1.0\right)\right)}}}{\sqrt[3]{\left(\left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right) \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)\right) \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)}}\]

  7. Applied cbrt-undiv21.2

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\left(6.0 \cdot 6.0\right) \cdot 6.0\right) \cdot \left(\left(\left(x - 1.0\right) \cdot \left(x - 1.0\right)\right) \cdot \left(x - 1.0\right)\right)}{\left(\left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right) \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)\right) \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)}}}\]

  8. Simplified1.1

    \[\leadsto \sqrt[3]{\color{blue}{\left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right) \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}}}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt0.2

    \[\leadsto \color{blue}{\left(\sqrt[3]{\sqrt[3]{\left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right) \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}}} \cdot \sqrt[3]{\sqrt[3]{\left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right) \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}}}\right) \cdot \sqrt[3]{\sqrt[3]{\left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right) \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}}}}\]

  11. Final simplification0.2

    \[\leadsto \left(\sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right)}} \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{x + \left(\sqrt{x} \cdot 4.0 + 1.0\right)}\right)}}\]

Reproduce

herbie shell --seed 2019163 
(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)))))