Average Error: 0.2 → 0.0
Time: 14.8s
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 r1446280 = 6.0;
        double r1446281 = x;
        double r1446282 = 1.0;
        double r1446283 = r1446281 - r1446282;
        double r1446284 = r1446280 * r1446283;
        double r1446285 = r1446281 + r1446282;
        double r1446286 = 4.0;
        double r1446287 = sqrt(r1446281);
        double r1446288 = r1446286 * r1446287;
        double r1446289 = r1446285 + r1446288;
        double r1446290 = r1446284 / r1446289;
        return r1446290;
}
↓
double f(double x) {
        double r1446291 = 6.0;
        double r1446292 = x;
        double r1446293 = 1.0;
        double r1446294 = r1446292 - r1446293;
        double r1446295 = r1446292 + r1446293;
        double r1446296 = 4.0;
        double r1446297 = sqrt(r1446292);
        double r1446298 = r1446296 * r1446297;
        double r1446299 = r1446295 + r1446298;
        double r1446300 = r1446294 / r1446299;
        double r1446301 = r1446291 * r1446300;
        return r1446301;
}

Error

Bits error versus x

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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 2019303 
(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)))))