Average Error: 0.2 → 0.0
Time: 3.2s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \left(\frac{x}{\left(x + 1\right) + 4 \cdot \sqrt{x}} - \frac{1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\right)\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \left(\frac{x}{\left(x + 1\right) + 4 \cdot \sqrt{x}} - \frac{1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\right)
double f(double x) {
        double r1705454 = 6.0;
        double r1705455 = x;
        double r1705456 = 1.0;
        double r1705457 = r1705455 - r1705456;
        double r1705458 = r1705454 * r1705457;
        double r1705459 = r1705455 + r1705456;
        double r1705460 = 4.0;
        double r1705461 = sqrt(r1705455);
        double r1705462 = r1705460 * r1705461;
        double r1705463 = r1705459 + r1705462;
        double r1705464 = r1705458 / r1705463;
        return r1705464;
}
↓
double f(double x) {
        double r1705465 = 6.0;
        double r1705466 = x;
        double r1705467 = 1.0;
        double r1705468 = r1705466 + r1705467;
        double r1705469 = 4.0;
        double r1705470 = sqrt(r1705466);
        double r1705471 = r1705469 * r1705470;
        double r1705472 = r1705468 + r1705471;
        double r1705473 = r1705466 / r1705472;
        double r1705474 = r1705467 / r1705472;
        double r1705475 = r1705473 - r1705474;
        double r1705476 = r1705465 * r1705475;
        return r1705476;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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 div-sub0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(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)))))