Average Error: 0.2 → 0.0
Time: 4.1s
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 r712420 = 6.0;
        double r712421 = x;
        double r712422 = 1.0;
        double r712423 = r712421 - r712422;
        double r712424 = r712420 * r712423;
        double r712425 = r712421 + r712422;
        double r712426 = 4.0;
        double r712427 = sqrt(r712421);
        double r712428 = r712426 * r712427;
        double r712429 = r712425 + r712428;
        double r712430 = r712424 / r712429;
        return r712430;
}
↓
double f(double x) {
        double r712431 = 6.0;
        double r712432 = x;
        double r712433 = 1.0;
        double r712434 = r712432 - r712433;
        double r712435 = r712432 + r712433;
        double r712436 = 4.0;
        double r712437 = sqrt(r712432);
        double r712438 = r712436 * r712437;
        double r712439 = r712435 + r712438;
        double r712440 = r712434 / r712439;
        double r712441 = r712431 * r712440;
        return r712441;
}

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 2020035 
(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)))))