Average Error: 0.3 → 0.1
Time: 10.8s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}
double f(double x) {
        double r42717537 = 6.0;
        double r42717538 = x;
        double r42717539 = 1.0;
        double r42717540 = r42717538 - r42717539;
        double r42717541 = r42717537 * r42717540;
        double r42717542 = r42717538 + r42717539;
        double r42717543 = 4.0;
        double r42717544 = sqrt(r42717538);
        double r42717545 = r42717543 * r42717544;
        double r42717546 = r42717542 + r42717545;
        double r42717547 = r42717541 / r42717546;
        return r42717547;
}
↓
double f(double x) {
        double r42717548 = 6.0;
        double r42717549 = x;
        double r42717550 = 1.0;
        double r42717551 = r42717549 + r42717550;
        double r42717552 = 4.0;
        double r42717553 = sqrt(r42717549);
        double r42717554 = r42717552 * r42717553;
        double r42717555 = r42717551 + r42717554;
        double r42717556 = r42717549 - r42717550;
        double r42717557 = r42717555 / r42717556;
        double r42717558 = r42717548 / r42717557;
        return r42717558;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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 associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(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)))))