Average Error: 28.6 → 28.7
Time: 31.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}\right) \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}} \cdot \sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}}\right) \cdot y\right) + t}{i + y \cdot \left(y \cdot \left(b + \left(a + y\right) \cdot y\right) + c\right)}\]
\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}
↓
\frac{\left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}\right) \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}} \cdot \sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}}\right) \cdot y\right) + t}{i + y \cdot \left(y \cdot \left(b + \left(a + y\right) \cdot y\right) + c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5104508 = x;
        double r5104509 = y;
        double r5104510 = r5104508 * r5104509;
        double r5104511 = z;
        double r5104512 = r5104510 + r5104511;
        double r5104513 = r5104512 * r5104509;
        double r5104514 = 27464.7644705;
        double r5104515 = r5104513 + r5104514;
        double r5104516 = r5104515 * r5104509;
        double r5104517 = 230661.510616;
        double r5104518 = r5104516 + r5104517;
        double r5104519 = r5104518 * r5104509;
        double r5104520 = t;
        double r5104521 = r5104519 + r5104520;
        double r5104522 = a;
        double r5104523 = r5104509 + r5104522;
        double r5104524 = r5104523 * r5104509;
        double r5104525 = b;
        double r5104526 = r5104524 + r5104525;
        double r5104527 = r5104526 * r5104509;
        double r5104528 = c;
        double r5104529 = r5104527 + r5104528;
        double r5104530 = r5104529 * r5104509;
        double r5104531 = i;
        double r5104532 = r5104530 + r5104531;
        double r5104533 = r5104521 / r5104532;
        return r5104533;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5104534 = y;
        double r5104535 = z;
        double r5104536 = x;
        double r5104537 = r5104536 * r5104534;
        double r5104538 = r5104535 + r5104537;
        double r5104539 = r5104534 * r5104538;
        double r5104540 = 27464.7644705;
        double r5104541 = r5104539 + r5104540;
        double r5104542 = r5104534 * r5104541;
        double r5104543 = 230661.510616;
        double r5104544 = r5104542 + r5104543;
        double r5104545 = cbrt(r5104544);
        double r5104546 = r5104545 * r5104545;
        double r5104547 = cbrt(r5104545);
        double r5104548 = r5104547 * r5104547;
        double r5104549 = r5104548 * r5104547;
        double r5104550 = r5104549 * r5104534;
        double r5104551 = r5104546 * r5104550;
        double r5104552 = t;
        double r5104553 = r5104551 + r5104552;
        double r5104554 = i;
        double r5104555 = b;
        double r5104556 = a;
        double r5104557 = r5104556 + r5104534;
        double r5104558 = r5104557 * r5104534;
        double r5104559 = r5104555 + r5104558;
        double r5104560 = r5104534 * r5104559;
        double r5104561 = c;
        double r5104562 = r5104560 + r5104561;
        double r5104563 = r5104534 * r5104562;
        double r5104564 = r5104554 + r5104563;
        double r5104565 = r5104553 / r5104564;
        return r5104565;
}

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 28.6

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

  3. Applied add-cube-cbrt28.7

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

  4. Applied associate-*l*28.7

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

  6. Applied add-cube-cbrt28.7

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

  7. Final simplification28.7

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

Reproduce

herbie shell --seed 2019163 
(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)))