Average Error: 0.2 → 0.0
Time: 10.2s
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 r619383 = 6.0;
        double r619384 = x;
        double r619385 = 1.0;
        double r619386 = r619384 - r619385;
        double r619387 = r619383 * r619386;
        double r619388 = r619384 + r619385;
        double r619389 = 4.0;
        double r619390 = sqrt(r619384);
        double r619391 = r619389 * r619390;
        double r619392 = r619388 + r619391;
        double r619393 = r619387 / r619392;
        return r619393;
}
↓
double f(double x) {
        double r619394 = 6.0;
        double r619395 = x;
        double r619396 = 1.0;
        double r619397 = r619395 - r619396;
        double r619398 = r619395 + r619396;
        double r619399 = 4.0;
        double r619400 = sqrt(r619395);
        double r619401 = r619399 * r619400;
        double r619402 = r619398 + r619401;
        double r619403 = r619397 / r619402;
        double r619404 = r619394 * r619403;
        return r619404;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 
(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)))))