Average Error: 29.1 → 29.4
Time: 25.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(\left(y \cdot 27464.7644704999984242022037506103515625 + \left({y}^{2} \cdot z + \left(y \cdot x\right) \cdot \left(y \cdot y\right)\right)\right) + 230661.5106160000141244381666183471679688\right) + t}{\left(\left(y \cdot y\right) \cdot \left(\left(a + y\right) \cdot y + b\right) + y \cdot c\right) + i}\]
\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{y \cdot \left(\left(y \cdot 27464.7644704999984242022037506103515625 + \left({y}^{2} \cdot z + \left(y \cdot x\right) \cdot \left(y \cdot y\right)\right)\right) + 230661.5106160000141244381666183471679688\right) + t}{\left(\left(y \cdot y\right) \cdot \left(\left(a + y\right) \cdot y + b\right) + y \cdot c\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r44640 = x;
        double r44641 = y;
        double r44642 = r44640 * r44641;
        double r44643 = z;
        double r44644 = r44642 + r44643;
        double r44645 = r44644 * r44641;
        double r44646 = 27464.7644705;
        double r44647 = r44645 + r44646;
        double r44648 = r44647 * r44641;
        double r44649 = 230661.510616;
        double r44650 = r44648 + r44649;
        double r44651 = r44650 * r44641;
        double r44652 = t;
        double r44653 = r44651 + r44652;
        double r44654 = a;
        double r44655 = r44641 + r44654;
        double r44656 = r44655 * r44641;
        double r44657 = b;
        double r44658 = r44656 + r44657;
        double r44659 = r44658 * r44641;
        double r44660 = c;
        double r44661 = r44659 + r44660;
        double r44662 = r44661 * r44641;
        double r44663 = i;
        double r44664 = r44662 + r44663;
        double r44665 = r44653 / r44664;
        return r44665;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r44666 = y;
        double r44667 = 27464.7644705;
        double r44668 = r44666 * r44667;
        double r44669 = 2.0;
        double r44670 = pow(r44666, r44669);
        double r44671 = z;
        double r44672 = r44670 * r44671;
        double r44673 = x;
        double r44674 = r44666 * r44673;
        double r44675 = r44666 * r44666;
        double r44676 = r44674 * r44675;
        double r44677 = r44672 + r44676;
        double r44678 = r44668 + r44677;
        double r44679 = 230661.510616;
        double r44680 = r44678 + r44679;
        double r44681 = r44666 * r44680;
        double r44682 = t;
        double r44683 = r44681 + r44682;
        double r44684 = a;
        double r44685 = r44684 + r44666;
        double r44686 = r44685 * r44666;
        double r44687 = b;
        double r44688 = r44686 + r44687;
        double r44689 = r44675 * r44688;
        double r44690 = c;
        double r44691 = r44666 * r44690;
        double r44692 = r44689 + r44691;
        double r44693 = i;
        double r44694 = r44692 + r44693;
        double r44695 = r44683 / r44694;
        return r44695;
}

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. Simplified29.1

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

  4. Applied distribute-lft-in29.1

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

  5. Simplified29.4

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

  6. Simplified29.4

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

  7. Taylor expanded around inf 29.5

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

  8. Simplified29.5

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

  10. Applied unpow329.5

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

  11. Applied associate-*l*29.4

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

  12. Simplified29.4

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

  13. Final simplification29.4

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

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)))