Average Error: 0.2 → 0.1
Time: 4.0s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \log \left(e^{\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}}\right)\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \log \left(e^{\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}}\right)
double f(double x) {
        double r989857 = 6.0;
        double r989858 = x;
        double r989859 = 1.0;
        double r989860 = r989858 - r989859;
        double r989861 = r989857 * r989860;
        double r989862 = r989858 + r989859;
        double r989863 = 4.0;
        double r989864 = sqrt(r989858);
        double r989865 = r989863 * r989864;
        double r989866 = r989862 + r989865;
        double r989867 = r989861 / r989866;
        return r989867;
}
↓
double f(double x) {
        double r989868 = 6.0;
        double r989869 = x;
        double r989870 = 1.0;
        double r989871 = r989869 - r989870;
        double r989872 = r989869 + r989870;
        double r989873 = 4.0;
        double r989874 = sqrt(r989869);
        double r989875 = r989873 * r989874;
        double r989876 = r989872 + r989875;
        double r989877 = r989871 / r989876;
        double r989878 = exp(r989877);
        double r989879 = log(r989878);
        double r989880 = r989868 * r989879;
        return r989880;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.1
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

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. Using strategy rm

  7. Applied add-log-exp0.1

    \[\leadsto 6 \cdot \color{blue}{\log \left(e^{\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}}\right)}\]

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(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)))))