Average Error: 27.9 → 28.0
Time: 2.2m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)}\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\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}
↓
\frac{y \cdot \left(230661.510616 + \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)}\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4581508 = x;
        double r4581509 = y;
        double r4581510 = r4581508 * r4581509;
        double r4581511 = z;
        double r4581512 = r4581510 + r4581511;
        double r4581513 = r4581512 * r4581509;
        double r4581514 = 27464.7644705;
        double r4581515 = r4581513 + r4581514;
        double r4581516 = r4581515 * r4581509;
        double r4581517 = 230661.510616;
        double r4581518 = r4581516 + r4581517;
        double r4581519 = r4581518 * r4581509;
        double r4581520 = t;
        double r4581521 = r4581519 + r4581520;
        double r4581522 = a;
        double r4581523 = r4581509 + r4581522;
        double r4581524 = r4581523 * r4581509;
        double r4581525 = b;
        double r4581526 = r4581524 + r4581525;
        double r4581527 = r4581526 * r4581509;
        double r4581528 = c;
        double r4581529 = r4581527 + r4581528;
        double r4581530 = r4581529 * r4581509;
        double r4581531 = i;
        double r4581532 = r4581530 + r4581531;
        double r4581533 = r4581521 / r4581532;
        return r4581533;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4581534 = y;
        double r4581535 = 230661.510616;
        double r4581536 = z;
        double r4581537 = x;
        double r4581538 = r4581537 * r4581534;
        double r4581539 = r4581536 + r4581538;
        double r4581540 = r4581534 * r4581539;
        double r4581541 = 27464.7644705;
        double r4581542 = r4581540 + r4581541;
        double r4581543 = r4581534 * r4581542;
        double r4581544 = cbrt(r4581543);
        double r4581545 = r4581544 * r4581544;
        double r4581546 = r4581544 * r4581545;
        double r4581547 = r4581535 + r4581546;
        double r4581548 = r4581534 * r4581547;
        double r4581549 = t;
        double r4581550 = r4581548 + r4581549;
        double r4581551 = c;
        double r4581552 = b;
        double r4581553 = a;
        double r4581554 = r4581534 + r4581553;
        double r4581555 = r4581534 * r4581554;
        double r4581556 = r4581552 + r4581555;
        double r4581557 = r4581556 * r4581534;
        double r4581558 = r4581551 + r4581557;
        double r4581559 = r4581534 * r4581558;
        double r4581560 = i;
        double r4581561 = r4581559 + r4581560;
        double r4581562 = r4581550 / r4581561;
        return r4581562;
}

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 27.9

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

  3. Applied add-cube-cbrt28.0

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

  4. Final simplification28.0

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

Reproduce

herbie shell --seed 2019158 
(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)))