Average Error: 29.1 → 29.2
Time: 29.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + y \cdot \left(230661.5106160000141244381666183471679688 + \left(\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}} \cdot \left(\sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}} \cdot \sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}}\right)\right)\right)}{i + \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) \cdot y}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{t + y \cdot \left(230661.5106160000141244381666183471679688 + \left(\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}} \cdot \left(\sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}} \cdot \sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}}\right)\right)\right)}{i + \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) \cdot y}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r84540 = x;
        double r84541 = y;
        double r84542 = r84540 * r84541;
        double r84543 = z;
        double r84544 = r84542 + r84543;
        double r84545 = r84544 * r84541;
        double r84546 = 27464.7644705;
        double r84547 = r84545 + r84546;
        double r84548 = r84547 * r84541;
        double r84549 = 230661.510616;
        double r84550 = r84548 + r84549;
        double r84551 = r84550 * r84541;
        double r84552 = t;
        double r84553 = r84551 + r84552;
        double r84554 = a;
        double r84555 = r84541 + r84554;
        double r84556 = r84555 * r84541;
        double r84557 = b;
        double r84558 = r84556 + r84557;
        double r84559 = r84558 * r84541;
        double r84560 = c;
        double r84561 = r84559 + r84560;
        double r84562 = r84561 * r84541;
        double r84563 = i;
        double r84564 = r84562 + r84563;
        double r84565 = r84553 / r84564;
        return r84565;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r84566 = t;
        double r84567 = y;
        double r84568 = 230661.510616;
        double r84569 = 27464.7644705;
        double r84570 = z;
        double r84571 = x;
        double r84572 = r84567 * r84571;
        double r84573 = r84570 + r84572;
        double r84574 = r84573 * r84567;
        double r84575 = r84569 + r84574;
        double r84576 = r84575 * r84567;
        double r84577 = cbrt(r84576);
        double r84578 = r84577 * r84577;
        double r84579 = cbrt(r84577);
        double r84580 = r84579 * r84579;
        double r84581 = r84579 * r84580;
        double r84582 = r84578 * r84581;
        double r84583 = r84568 + r84582;
        double r84584 = r84567 * r84583;
        double r84585 = r84566 + r84584;
        double r84586 = i;
        double r84587 = b;
        double r84588 = a;
        double r84589 = r84588 + r84567;
        double r84590 = r84567 * r84589;
        double r84591 = r84587 + r84590;
        double r84592 = r84567 * r84591;
        double r84593 = c;
        double r84594 = r84592 + r84593;
        double r84595 = r84594 * r84567;
        double r84596 = r84586 + r84595;
        double r84597 = r84585 / r84596;
        return r84597;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.1

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt29.2

    \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Simplified29.2

    \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y}\right)} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  5. Simplified29.2

    \[\leadsto \frac{\left(\left(\sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \color{blue}{\sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y}} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt29.2

    \[\leadsto \frac{\left(\left(\sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y}} \cdot \sqrt[3]{\sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y}}\right) \cdot \sqrt[3]{\sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y}}\right)} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  8. Simplified29.2

    \[\leadsto \frac{\left(\left(\sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \left(\color{blue}{\left(\sqrt[3]{\sqrt[3]{\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}} \cdot \sqrt[3]{\sqrt[3]{\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}}\right)} \cdot \sqrt[3]{\sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y}}\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  9. Simplified29.2

    \[\leadsto \frac{\left(\left(\sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(y \cdot \left(z + y \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}} \cdot \sqrt[3]{\sqrt[3]{\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}}\right) \cdot \color{blue}{\sqrt[3]{\sqrt[3]{\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}}}\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  10. Final simplification29.2

    \[\leadsto \frac{t + y \cdot \left(230661.5106160000141244381666183471679688 + \left(\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}} \cdot \left(\sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}} \cdot \sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}}\right)\right)\right)}{i + \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) \cdot y}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))