Average Error: 0.2 → 0.1
Time: 16.1s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \frac{1}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \frac{1}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}
double f(double x) {
        double r59517068 = 6.0;
        double r59517069 = x;
        double r59517070 = 1.0;
        double r59517071 = r59517069 - r59517070;
        double r59517072 = r59517068 * r59517071;
        double r59517073 = r59517069 + r59517070;
        double r59517074 = 4.0;
        double r59517075 = sqrt(r59517069);
        double r59517076 = r59517074 * r59517075;
        double r59517077 = r59517073 + r59517076;
        double r59517078 = r59517072 / r59517077;
        return r59517078;
}
↓
double f(double x) {
        double r59517079 = 6.0;
        double r59517080 = 1.0;
        double r59517081 = x;
        double r59517082 = 1.0;
        double r59517083 = r59517081 + r59517082;
        double r59517084 = 4.0;
        double r59517085 = sqrt(r59517081);
        double r59517086 = r59517084 * r59517085;
        double r59517087 = r59517083 + r59517086;
        double r59517088 = r59517081 - r59517082;
        double r59517089 = r59517087 / r59517088;
        double r59517090 = r59517080 / r59517089;
        double r59517091 = r59517079 * r59517090;
        return r59517091;
}

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

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

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)))))