Average Error: 0.2 → 0.0
Time: 7.3s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \cdot 6\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \cdot 6
double f(double x) {
        double r767438 = 6.0;
        double r767439 = x;
        double r767440 = 1.0;
        double r767441 = r767439 - r767440;
        double r767442 = r767438 * r767441;
        double r767443 = r767439 + r767440;
        double r767444 = 4.0;
        double r767445 = sqrt(r767439);
        double r767446 = r767444 * r767445;
        double r767447 = r767443 + r767446;
        double r767448 = r767442 / r767447;
        return r767448;
}
↓
double f(double x) {
        double r767449 = x;
        double r767450 = 1.0;
        double r767451 = r767449 - r767450;
        double r767452 = r767449 + r767450;
        double r767453 = 4.0;
        double r767454 = sqrt(r767449);
        double r767455 = r767453 * r767454;
        double r767456 = r767452 + r767455;
        double r767457 = r767451 / r767456;
        double r767458 = 6.0;
        double r767459 = r767457 * r767458;
        return r767459;
}

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

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-cbrt-cube21.2

    \[\leadsto 6 \cdot \frac{x - 1}{\color{blue}{\sqrt[3]{\left(\left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right) \cdot \left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right)\right) \cdot \left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right)}}}\]

  8. Applied add-cbrt-cube21.8

    \[\leadsto 6 \cdot \frac{\color{blue}{\sqrt[3]{\left(\left(x - 1\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 1\right)}}}{\sqrt[3]{\left(\left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right) \cdot \left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right)\right) \cdot \left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right)}}\]

  9. Applied cbrt-undiv21.8

    \[\leadsto 6 \cdot \color{blue}{\sqrt[3]{\frac{\left(\left(x - 1\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 1\right)}{\left(\left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right) \cdot \left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right)\right) \cdot \left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right)}}}\]

  10. Simplified0.1

    \[\leadsto 6 \cdot \sqrt[3]{\color{blue}{{\left(\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\right)}^{3}}}\]

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 1978988140 
(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)))))