Average Error: 29.0 → 29.0
Time: 49.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(230661.5106160000141244381666183471679688 + \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right) \cdot y}{y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) + i}\]
\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 + \left(230661.5106160000141244381666183471679688 + \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right) \cdot y}{y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3786546 = x;
        double r3786547 = y;
        double r3786548 = r3786546 * r3786547;
        double r3786549 = z;
        double r3786550 = r3786548 + r3786549;
        double r3786551 = r3786550 * r3786547;
        double r3786552 = 27464.7644705;
        double r3786553 = r3786551 + r3786552;
        double r3786554 = r3786553 * r3786547;
        double r3786555 = 230661.510616;
        double r3786556 = r3786554 + r3786555;
        double r3786557 = r3786556 * r3786547;
        double r3786558 = t;
        double r3786559 = r3786557 + r3786558;
        double r3786560 = a;
        double r3786561 = r3786547 + r3786560;
        double r3786562 = r3786561 * r3786547;
        double r3786563 = b;
        double r3786564 = r3786562 + r3786563;
        double r3786565 = r3786564 * r3786547;
        double r3786566 = c;
        double r3786567 = r3786565 + r3786566;
        double r3786568 = r3786567 * r3786547;
        double r3786569 = i;
        double r3786570 = r3786568 + r3786569;
        double r3786571 = r3786559 / r3786570;
        return r3786571;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3786572 = t;
        double r3786573 = 230661.510616;
        double r3786574 = y;
        double r3786575 = x;
        double r3786576 = r3786574 * r3786575;
        double r3786577 = z;
        double r3786578 = r3786576 + r3786577;
        double r3786579 = r3786578 * r3786574;
        double r3786580 = 27464.7644705;
        double r3786581 = r3786579 + r3786580;
        double r3786582 = cbrt(r3786574);
        double r3786583 = r3786582 * r3786582;
        double r3786584 = r3786581 * r3786583;
        double r3786585 = r3786584 * r3786582;
        double r3786586 = r3786573 + r3786585;
        double r3786587 = r3786586 * r3786574;
        double r3786588 = r3786572 + r3786587;
        double r3786589 = b;
        double r3786590 = a;
        double r3786591 = r3786590 + r3786574;
        double r3786592 = r3786574 * r3786591;
        double r3786593 = r3786589 + r3786592;
        double r3786594 = r3786574 * r3786593;
        double r3786595 = c;
        double r3786596 = r3786594 + r3786595;
        double r3786597 = r3786574 * r3786596;
        double r3786598 = i;
        double r3786599 = r3786597 + r3786598;
        double r3786600 = r3786588 / r3786599;
        return r3786600;
}

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 29.0

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

  3. Applied add-cube-cbrt29.0

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

  4. Applied associate-*r*29.0

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

  5. Final simplification29.0

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

Reproduce

herbie shell --seed 2019200 
(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)))