Average Error: 29.2 → 29.3
Time: 38.5s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{i + y \cdot \left(c + \left(y \cdot b + \sqrt[3]{y + a} \cdot \left(\left(\left(y \cdot \sqrt[3]{y + a}\right) \cdot y\right) \cdot \sqrt[3]{y + a}\right)\right)\right)}\]
\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(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{i + y \cdot \left(c + \left(y \cdot b + \sqrt[3]{y + a} \cdot \left(\left(\left(y \cdot \sqrt[3]{y + a}\right) \cdot y\right) \cdot \sqrt[3]{y + a}\right)\right)\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r143545 = x;
        double r143546 = y;
        double r143547 = r143545 * r143546;
        double r143548 = z;
        double r143549 = r143547 + r143548;
        double r143550 = r143549 * r143546;
        double r143551 = 27464.7644705;
        double r143552 = r143550 + r143551;
        double r143553 = r143552 * r143546;
        double r143554 = 230661.510616;
        double r143555 = r143553 + r143554;
        double r143556 = r143555 * r143546;
        double r143557 = t;
        double r143558 = r143556 + r143557;
        double r143559 = a;
        double r143560 = r143546 + r143559;
        double r143561 = r143560 * r143546;
        double r143562 = b;
        double r143563 = r143561 + r143562;
        double r143564 = r143563 * r143546;
        double r143565 = c;
        double r143566 = r143564 + r143565;
        double r143567 = r143566 * r143546;
        double r143568 = i;
        double r143569 = r143567 + r143568;
        double r143570 = r143558 / r143569;
        return r143570;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r143571 = t;
        double r143572 = y;
        double r143573 = z;
        double r143574 = x;
        double r143575 = r143574 * r143572;
        double r143576 = r143573 + r143575;
        double r143577 = r143572 * r143576;
        double r143578 = 27464.7644705;
        double r143579 = r143577 + r143578;
        double r143580 = r143572 * r143579;
        double r143581 = 230661.510616;
        double r143582 = r143580 + r143581;
        double r143583 = r143582 * r143572;
        double r143584 = r143571 + r143583;
        double r143585 = i;
        double r143586 = c;
        double r143587 = b;
        double r143588 = r143572 * r143587;
        double r143589 = a;
        double r143590 = r143572 + r143589;
        double r143591 = cbrt(r143590);
        double r143592 = r143572 * r143591;
        double r143593 = r143592 * r143572;
        double r143594 = r143593 * r143591;
        double r143595 = r143591 * r143594;
        double r143596 = r143588 + r143595;
        double r143597 = r143586 + r143596;
        double r143598 = r143572 * r143597;
        double r143599 = r143585 + r143598;
        double r143600 = r143584 / r143599;
        return r143600;
}

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 29.2

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

  2. Taylor expanded around inf 29.3

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\color{blue}{\left(a \cdot {y}^{2} + \left({y}^{3} + y \cdot b\right)\right)} + c\right) \cdot y + i}\]

  3. Simplified29.3

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

  5. Applied add-cube-cbrt29.3

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

  6. Applied associate-*r*29.3

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

  7. Simplified29.3

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

  8. Final simplification29.3

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

Reproduce

herbie shell --seed 2019174 
(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)))