Average Error: 0.2 → 0.0
Time: 13.4s
Precision: 64
\[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1.0}{4.0 \cdot \sqrt{x} + \left(x + 1.0\right)} \cdot 6.0\]
\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}
↓
\frac{x - 1.0}{4.0 \cdot \sqrt{x} + \left(x + 1.0\right)} \cdot 6.0
double f(double x) {
        double r44030027 = 6.0;
        double r44030028 = x;
        double r44030029 = 1.0;
        double r44030030 = r44030028 - r44030029;
        double r44030031 = r44030027 * r44030030;
        double r44030032 = r44030028 + r44030029;
        double r44030033 = 4.0;
        double r44030034 = sqrt(r44030028);
        double r44030035 = r44030033 * r44030034;
        double r44030036 = r44030032 + r44030035;
        double r44030037 = r44030031 / r44030036;
        return r44030037;
}
↓
double f(double x) {
        double r44030038 = x;
        double r44030039 = 1.0;
        double r44030040 = r44030038 - r44030039;
        double r44030041 = 4.0;
        double r44030042 = sqrt(r44030038);
        double r44030043 = r44030041 * r44030042;
        double r44030044 = r44030038 + r44030039;
        double r44030045 = r44030043 + r44030044;
        double r44030046 = r44030040 / r44030045;
        double r44030047 = 6.0;
        double r44030048 = r44030046 * r44030047;
        return r44030048;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.0
\[\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]

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 *-un-lft-identity0.2

    \[\leadsto \frac{6.0 \cdot \left(x - 1.0\right)}{\color{blue}{1 \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)}}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{6.0}{1} \cdot \frac{x - 1.0}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}}\]

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(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)))))