Average Error: 0.2 → 0.1
Time: 5.0s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \log \left(e^{\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}}\right)\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \log \left(e^{\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}}\right)
double f(double x) {
        double r837565 = 6.0;
        double r837566 = x;
        double r837567 = 1.0;
        double r837568 = r837566 - r837567;
        double r837569 = r837565 * r837568;
        double r837570 = r837566 + r837567;
        double r837571 = 4.0;
        double r837572 = sqrt(r837566);
        double r837573 = r837571 * r837572;
        double r837574 = r837570 + r837573;
        double r837575 = r837569 / r837574;
        return r837575;
}
↓
double f(double x) {
        double r837576 = 6.0;
        double r837577 = x;
        double r837578 = 1.0;
        double r837579 = r837577 - r837578;
        double r837580 = r837577 + r837578;
        double r837581 = 4.0;
        double r837582 = sqrt(r837577);
        double r837583 = r837581 * r837582;
        double r837584 = r837580 + r837583;
        double r837585 = r837579 / r837584;
        double r837586 = exp(r837585);
        double r837587 = log(r837586);
        double r837588 = r837576 * r837587;
        return r837588;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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 *-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. Using strategy rm

  7. Applied add-log-exp0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(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)))))