Average Error: 0.3 → 0.0
Time: 3.7s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
double f(double x) {
        double r801723 = 6.0;
        double r801724 = x;
        double r801725 = 1.0;
        double r801726 = r801724 - r801725;
        double r801727 = r801723 * r801726;
        double r801728 = r801724 + r801725;
        double r801729 = 4.0;
        double r801730 = sqrt(r801724);
        double r801731 = r801729 * r801730;
        double r801732 = r801728 + r801731;
        double r801733 = r801727 / r801732;
        return r801733;
}
↓
double f(double x) {
        double r801734 = 6.0;
        double r801735 = x;
        double r801736 = 1.0;
        double r801737 = r801735 - r801736;
        double r801738 = r801735 + r801736;
        double r801739 = 4.0;
        double r801740 = sqrt(r801735);
        double r801741 = r801739 * r801740;
        double r801742 = r801738 + r801741;
        double r801743 = r801737 / r801742;
        double r801744 = r801734 * r801743;
        return r801744;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.0
Herbie0.0
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Derivation

  1. Initial program 0.3

    \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.3

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

  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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 
(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)))))