Average Error: 0.2 → 0.0
Time: 27.2s
Precision: 64
\[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
↓
\[\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]
\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}
↓
\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}
double f(double x) {
        double r43780017 = 6.0;
        double r43780018 = x;
        double r43780019 = 1.0;
        double r43780020 = r43780018 - r43780019;
        double r43780021 = r43780017 * r43780020;
        double r43780022 = r43780018 + r43780019;
        double r43780023 = 4.0;
        double r43780024 = sqrt(r43780018);
        double r43780025 = r43780023 * r43780024;
        double r43780026 = r43780022 + r43780025;
        double r43780027 = r43780021 / r43780026;
        return r43780027;
}
↓
double f(double x) {
        double r43780028 = 6.0;
        double r43780029 = x;
        double r43780030 = 1.0;
        double r43780031 = r43780029 + r43780030;
        double r43780032 = 4.0;
        double r43780033 = sqrt(r43780029);
        double r43780034 = r43780032 * r43780033;
        double r43780035 = r43780031 + r43780034;
        double r43780036 = r43780029 - r43780030;
        double r43780037 = r43780035 / r43780036;
        double r43780038 = r43780028 / r43780037;
        return r43780038;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/l*0.0

    \[\leadsto \color{blue}{\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}}\]

  4. Final simplification0.0

    \[\leadsto \frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]

Reproduce

herbie shell --seed 2019165 
(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)))))