Average Error: 0.2 → 0.1
Time: 15.1s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{1}{\frac{4 \cdot \sqrt{x} + \left(1 + x\right)}{x - 1}} \cdot 6\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{1}{\frac{4 \cdot \sqrt{x} + \left(1 + x\right)}{x - 1}} \cdot 6
double f(double x) {
        double r43843011 = 6.0;
        double r43843012 = x;
        double r43843013 = 1.0;
        double r43843014 = r43843012 - r43843013;
        double r43843015 = r43843011 * r43843014;
        double r43843016 = r43843012 + r43843013;
        double r43843017 = 4.0;
        double r43843018 = sqrt(r43843012);
        double r43843019 = r43843017 * r43843018;
        double r43843020 = r43843016 + r43843019;
        double r43843021 = r43843015 / r43843020;
        return r43843021;
}
↓
double f(double x) {
        double r43843022 = 1.0;
        double r43843023 = 4.0;
        double r43843024 = x;
        double r43843025 = sqrt(r43843024);
        double r43843026 = r43843023 * r43843025;
        double r43843027 = 1.0;
        double r43843028 = r43843027 + r43843024;
        double r43843029 = r43843026 + r43843028;
        double r43843030 = r43843024 - r43843027;
        double r43843031 = r43843029 / r43843030;
        double r43843032 = r43843022 / r43843031;
        double r43843033 = 6.0;
        double r43843034 = r43843032 * r43843033;
        return r43843034;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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 associate-/l*0.1

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

  5. Applied div-inv0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(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)))))