Average Error: 0.2 → 0.0
Time: 3.0s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}
double f(double x) {
        double r781368 = 6.0;
        double r781369 = x;
        double r781370 = 1.0;
        double r781371 = r781369 - r781370;
        double r781372 = r781368 * r781371;
        double r781373 = r781369 + r781370;
        double r781374 = 4.0;
        double r781375 = sqrt(r781369);
        double r781376 = r781374 * r781375;
        double r781377 = r781373 + r781376;
        double r781378 = r781372 / r781377;
        return r781378;
}
↓
double f(double x) {
        double r781379 = 6.0;
        double r781380 = x;
        double r781381 = 1.0;
        double r781382 = r781380 + r781381;
        double r781383 = 4.0;
        double r781384 = sqrt(r781380);
        double r781385 = r781383 * r781384;
        double r781386 = r781382 + r781385;
        double r781387 = r781380 - r781381;
        double r781388 = r781386 / r781387;
        double r781389 = r781379 / r781388;
        return r781389;
}

Error

Bits error versus x

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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 associate-/l*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020021 
(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)))))