Average Error: 0.2 → 0.2
Time: 5.6s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
double f(double x) {
        double r863449 = 6.0;
        double r863450 = x;
        double r863451 = 1.0;
        double r863452 = r863450 - r863451;
        double r863453 = r863449 * r863452;
        double r863454 = r863450 + r863451;
        double r863455 = 4.0;
        double r863456 = sqrt(r863450);
        double r863457 = r863455 * r863456;
        double r863458 = r863454 + r863457;
        double r863459 = r863453 / r863458;
        return r863459;
}
↓
double f(double x) {
        double r863460 = 6.0;
        double r863461 = x;
        double r863462 = 1.0;
        double r863463 = r863461 - r863462;
        double r863464 = r863460 * r863463;
        double r863465 = r863461 + r863462;
        double r863466 = 4.0;
        double r863467 = sqrt(r863461);
        double r863468 = r863466 * r863467;
        double r863469 = r863465 + r863468;
        double r863470 = r863464 / r863469;
        return r863470;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.2
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019362 
(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)))))