Average Error: 0.2 → 0.0
Time: 11.2s
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 r52928239 = 6.0;
        double r52928240 = x;
        double r52928241 = 1.0;
        double r52928242 = r52928240 - r52928241;
        double r52928243 = r52928239 * r52928242;
        double r52928244 = r52928240 + r52928241;
        double r52928245 = 4.0;
        double r52928246 = sqrt(r52928240);
        double r52928247 = r52928245 * r52928246;
        double r52928248 = r52928244 + r52928247;
        double r52928249 = r52928243 / r52928248;
        return r52928249;
}
↓
double f(double x) {
        double r52928250 = 6.0;
        double r52928251 = x;
        double r52928252 = 1.0;
        double r52928253 = r52928251 + r52928252;
        double r52928254 = 4.0;
        double r52928255 = sqrt(r52928251);
        double r52928256 = r52928254 * r52928255;
        double r52928257 = r52928253 + r52928256;
        double r52928258 = r52928251 - r52928252;
        double r52928259 = r52928257 / r52928258;
        double r52928260 = r52928250 / r52928259;
        return r52928260;
}

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 2019171 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"

  :herbie-target
  (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

  (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))