Average Error: 0.2 → 0.0
Time: 15.8s
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 r565310 = 6.0;
        double r565311 = x;
        double r565312 = 1.0;
        double r565313 = r565311 - r565312;
        double r565314 = r565310 * r565313;
        double r565315 = r565311 + r565312;
        double r565316 = 4.0;
        double r565317 = sqrt(r565311);
        double r565318 = r565316 * r565317;
        double r565319 = r565315 + r565318;
        double r565320 = r565314 / r565319;
        return r565320;
}
↓
double f(double x) {
        double r565321 = 6.0;
        double r565322 = x;
        double r565323 = 1.0;
        double r565324 = r565322 - r565323;
        double r565325 = r565322 + r565323;
        double r565326 = 4.0;
        double r565327 = sqrt(r565322);
        double r565328 = r565326 * r565327;
        double r565329 = r565325 + r565328;
        double r565330 = r565324 / r565329;
        double r565331 = r565321 * r565330;
        return r565331;
}

Error

Bits error versus x

Try it out

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 *-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 2019323 
(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)))))