Average Error: 29.0 → 29.0
Time: 33.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{y \cdot \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{y \cdot \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2745540 = x;
        double r2745541 = y;
        double r2745542 = r2745540 * r2745541;
        double r2745543 = z;
        double r2745544 = r2745542 + r2745543;
        double r2745545 = r2745544 * r2745541;
        double r2745546 = 27464.7644705;
        double r2745547 = r2745545 + r2745546;
        double r2745548 = r2745547 * r2745541;
        double r2745549 = 230661.510616;
        double r2745550 = r2745548 + r2745549;
        double r2745551 = r2745550 * r2745541;
        double r2745552 = t;
        double r2745553 = r2745551 + r2745552;
        double r2745554 = a;
        double r2745555 = r2745541 + r2745554;
        double r2745556 = r2745555 * r2745541;
        double r2745557 = b;
        double r2745558 = r2745556 + r2745557;
        double r2745559 = r2745558 * r2745541;
        double r2745560 = c;
        double r2745561 = r2745559 + r2745560;
        double r2745562 = r2745561 * r2745541;
        double r2745563 = i;
        double r2745564 = r2745562 + r2745563;
        double r2745565 = r2745553 / r2745564;
        return r2745565;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2745566 = t;
        double r2745567 = y;
        double r2745568 = z;
        double r2745569 = x;
        double r2745570 = r2745569 * r2745567;
        double r2745571 = r2745568 + r2745570;
        double r2745572 = r2745567 * r2745571;
        double r2745573 = 27464.7644705;
        double r2745574 = r2745572 + r2745573;
        double r2745575 = r2745567 * r2745574;
        double r2745576 = 230661.510616;
        double r2745577 = r2745575 + r2745576;
        double r2745578 = r2745577 * r2745567;
        double r2745579 = r2745566 + r2745578;
        double r2745580 = 1.0;
        double r2745581 = c;
        double r2745582 = b;
        double r2745583 = a;
        double r2745584 = r2745567 + r2745583;
        double r2745585 = r2745584 * r2745567;
        double r2745586 = r2745582 + r2745585;
        double r2745587 = r2745567 * r2745586;
        double r2745588 = r2745581 + r2745587;
        double r2745589 = r2745567 * r2745588;
        double r2745590 = i;
        double r2745591 = r2745589 + r2745590;
        double r2745592 = r2745580 / r2745591;
        double r2745593 = r2745579 * r2745592;
        return r2745593;
}

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

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\left(\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c}\right) \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c}\right)} \cdot y + i}\]

  4. Applied associate-*l*29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c}\right) \cdot \left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c} \cdot y\right)} + i}\]
  5. Using strategy rm

  6. Applied div-inv29.2

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right) \cdot \frac{1}{\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c}\right) \cdot \left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c} \cdot y\right) + i}}\]

  7. Simplified29.0

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right) \cdot \color{blue}{\frac{1}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}}\]

  8. Final simplification29.0

    \[\leadsto \left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{y \cdot \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) + i}\]

Reproduce

herbie shell --seed 2019168 
(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)))