Average Error: 29.2 → 29.3
Time: 14.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\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{\left(\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62503 = x;
        double r62504 = y;
        double r62505 = r62503 * r62504;
        double r62506 = z;
        double r62507 = r62505 + r62506;
        double r62508 = r62507 * r62504;
        double r62509 = 27464.7644705;
        double r62510 = r62508 + r62509;
        double r62511 = r62510 * r62504;
        double r62512 = 230661.510616;
        double r62513 = r62511 + r62512;
        double r62514 = r62513 * r62504;
        double r62515 = t;
        double r62516 = r62514 + r62515;
        double r62517 = a;
        double r62518 = r62504 + r62517;
        double r62519 = r62518 * r62504;
        double r62520 = b;
        double r62521 = r62519 + r62520;
        double r62522 = r62521 * r62504;
        double r62523 = c;
        double r62524 = r62522 + r62523;
        double r62525 = r62524 * r62504;
        double r62526 = i;
        double r62527 = r62525 + r62526;
        double r62528 = r62516 / r62527;
        return r62528;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62529 = x;
        double r62530 = y;
        double r62531 = r62529 * r62530;
        double r62532 = z;
        double r62533 = r62531 + r62532;
        double r62534 = cbrt(r62533);
        double r62535 = r62534 * r62534;
        double r62536 = r62534 * r62530;
        double r62537 = r62535 * r62536;
        double r62538 = 27464.7644705;
        double r62539 = r62537 + r62538;
        double r62540 = r62539 * r62530;
        double r62541 = 230661.510616;
        double r62542 = r62540 + r62541;
        double r62543 = r62542 * r62530;
        double r62544 = t;
        double r62545 = r62543 + r62544;
        double r62546 = a;
        double r62547 = r62530 + r62546;
        double r62548 = r62547 * r62530;
        double r62549 = b;
        double r62550 = r62548 + r62549;
        double r62551 = r62550 * r62530;
        double r62552 = c;
        double r62553 = r62551 + r62552;
        double r62554 = r62553 * r62530;
        double r62555 = i;
        double r62556 = r62554 + r62555;
        double r62557 = r62545 / r62556;
        return r62557;
}

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. Using strategy rm

  3. Applied add-cube-cbrt29.3

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

  4. Applied associate-*l*29.3

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

  5. Final simplification29.3

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

Reproduce

herbie shell --seed 2019308 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))