Average Error: 0.2 → 0.0
Time: 3.5s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
double f(double x) {
        double r954636 = 6.0;
        double r954637 = x;
        double r954638 = 1.0;
        double r954639 = r954637 - r954638;
        double r954640 = r954636 * r954639;
        double r954641 = r954637 + r954638;
        double r954642 = 4.0;
        double r954643 = sqrt(r954637);
        double r954644 = r954642 * r954643;
        double r954645 = r954641 + r954644;
        double r954646 = r954640 / r954645;
        return r954646;
}
↓
double f(double x) {
        double r954647 = 6.0;
        double r954648 = x;
        double r954649 = 1.0;
        double r954650 = r954648 - r954649;
        double r954651 = r954648 + r954649;
        double r954652 = 4.0;
        double r954653 = sqrt(r954648);
        double r954654 = r954652 * r954653;
        double r954655 = r954651 + r954654;
        double r954656 = r954650 / r954655;
        double r954657 = r954647 * r954656;
        return r954657;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.0
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

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

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

  4. Applied times-frac0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"
  :precision binary64

  :herbie-target
  (/ 6 (/ (+ (+ x 1) (* 4 (sqrt x))) (- x 1)))

  (/ (* 6 (- x 1)) (+ (+ x 1) (* 4 (sqrt x)))))