Average Error: 0.2 → 0.1
Time: 14.4s
Precision: 64
\[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
↓
\[\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]
\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}
↓
\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}
double f(double x) {
        double r39061503 = 6.0;
        double r39061504 = x;
        double r39061505 = 1.0;
        double r39061506 = r39061504 - r39061505;
        double r39061507 = r39061503 * r39061506;
        double r39061508 = r39061504 + r39061505;
        double r39061509 = 4.0;
        double r39061510 = sqrt(r39061504);
        double r39061511 = r39061509 * r39061510;
        double r39061512 = r39061508 + r39061511;
        double r39061513 = r39061507 / r39061512;
        return r39061513;
}
↓
double f(double x) {
        double r39061514 = 6.0;
        double r39061515 = x;
        double r39061516 = 1.0;
        double r39061517 = r39061515 + r39061516;
        double r39061518 = 4.0;
        double r39061519 = sqrt(r39061515);
        double r39061520 = r39061518 * r39061519;
        double r39061521 = r39061517 + r39061520;
        double r39061522 = r39061515 - r39061516;
        double r39061523 = r39061521 / r39061522;
        double r39061524 = r39061514 / r39061523;
        return r39061524;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.1
\[\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}}\]

  4. Final simplification0.1

    \[\leadsto \frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]

Reproduce

herbie shell --seed 2019162 
(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)))))