Average Error: 0.2 → 0.0
Time: 12.6s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
double f(double x) {
        double r658274 = 6.0;
        double r658275 = x;
        double r658276 = 1.0;
        double r658277 = r658275 - r658276;
        double r658278 = r658274 * r658277;
        double r658279 = r658275 + r658276;
        double r658280 = 4.0;
        double r658281 = sqrt(r658275);
        double r658282 = r658280 * r658281;
        double r658283 = r658279 + r658282;
        double r658284 = r658278 / r658283;
        return r658284;
}
↓
double f(double x) {
        double r658285 = 6.0;
        double r658286 = x;
        double r658287 = 1.0;
        double r658288 = r658286 - r658287;
        double r658289 = r658286 + r658287;
        double r658290 = 4.0;
        double r658291 = sqrt(r658286);
        double r658292 = r658290 * r658291;
        double r658293 = r658289 + r658292;
        double r658294 = r658288 / r658293;
        double r658295 = r658285 * r658294;
        return r658295;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019235 
(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)))))