Average Error: 0.2 → 0.2
Time: 12.4s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{\left(x - 1\right) \cdot 6}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{\left(x - 1\right) \cdot 6}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
double f(double x) {
        double r637925 = 6.0;
        double r637926 = x;
        double r637927 = 1.0;
        double r637928 = r637926 - r637927;
        double r637929 = r637925 * r637928;
        double r637930 = r637926 + r637927;
        double r637931 = 4.0;
        double r637932 = sqrt(r637926);
        double r637933 = r637931 * r637932;
        double r637934 = r637930 + r637933;
        double r637935 = r637929 / r637934;
        return r637935;
}
↓
double f(double x) {
        double r637936 = x;
        double r637937 = 1.0;
        double r637938 = r637936 - r637937;
        double r637939 = 6.0;
        double r637940 = r637938 * r637939;
        double r637941 = r637936 + r637937;
        double r637942 = 4.0;
        double r637943 = sqrt(r637936);
        double r637944 = r637942 * r637943;
        double r637945 = r637941 + r637944;
        double r637946 = r637940 / r637945;
        return r637946;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

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

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019198 
(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)))))