Average Error: 0.2 → 0.0
Time: 12.6s
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 r36361210 = 6.0;
        double r36361211 = x;
        double r36361212 = 1.0;
        double r36361213 = r36361211 - r36361212;
        double r36361214 = r36361210 * r36361213;
        double r36361215 = r36361211 + r36361212;
        double r36361216 = 4.0;
        double r36361217 = sqrt(r36361211);
        double r36361218 = r36361216 * r36361217;
        double r36361219 = r36361215 + r36361218;
        double r36361220 = r36361214 / r36361219;
        return r36361220;
}
↓
double f(double x) {
        double r36361221 = 6.0;
        double r36361222 = x;
        double r36361223 = 1.0;
        double r36361224 = r36361222 + r36361223;
        double r36361225 = 4.0;
        double r36361226 = sqrt(r36361222);
        double r36361227 = r36361225 * r36361226;
        double r36361228 = r36361224 + r36361227;
        double r36361229 = r36361222 - r36361223;
        double r36361230 = r36361228 / r36361229;
        double r36361231 = r36361221 / r36361230;
        return r36361231;
}

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

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*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(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)))))