Average Error: 29.2 → 29.2
Time: 24.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{-\left(t + 230661.5106160000141244381666183471679688 \cdot y\right)}{-\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)} - \frac{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(y \cdot y\right)}{-\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)}\]
\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(t + 230661.5106160000141244381666183471679688 \cdot y\right)}{-\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)} - \frac{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(y \cdot y\right)}{-\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r83434 = x;
        double r83435 = y;
        double r83436 = r83434 * r83435;
        double r83437 = z;
        double r83438 = r83436 + r83437;
        double r83439 = r83438 * r83435;
        double r83440 = 27464.7644705;
        double r83441 = r83439 + r83440;
        double r83442 = r83441 * r83435;
        double r83443 = 230661.510616;
        double r83444 = r83442 + r83443;
        double r83445 = r83444 * r83435;
        double r83446 = t;
        double r83447 = r83445 + r83446;
        double r83448 = a;
        double r83449 = r83435 + r83448;
        double r83450 = r83449 * r83435;
        double r83451 = b;
        double r83452 = r83450 + r83451;
        double r83453 = r83452 * r83435;
        double r83454 = c;
        double r83455 = r83453 + r83454;
        double r83456 = r83455 * r83435;
        double r83457 = i;
        double r83458 = r83456 + r83457;
        double r83459 = r83447 / r83458;
        return r83459;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r83460 = t;
        double r83461 = 230661.510616;
        double r83462 = y;
        double r83463 = r83461 * r83462;
        double r83464 = r83460 + r83463;
        double r83465 = -r83464;
        double r83466 = a;
        double r83467 = r83462 + r83466;
        double r83468 = r83467 * r83462;
        double r83469 = b;
        double r83470 = r83468 + r83469;
        double r83471 = r83470 * r83462;
        double r83472 = c;
        double r83473 = r83471 + r83472;
        double r83474 = r83473 * r83462;
        double r83475 = i;
        double r83476 = r83474 + r83475;
        double r83477 = -r83476;
        double r83478 = r83465 / r83477;
        double r83479 = x;
        double r83480 = r83479 * r83462;
        double r83481 = z;
        double r83482 = r83480 + r83481;
        double r83483 = r83482 * r83462;
        double r83484 = 27464.7644705;
        double r83485 = r83483 + r83484;
        double r83486 = r83462 * r83462;
        double r83487 = r83485 * r83486;
        double r83488 = r83487 / r83477;
        double r83489 = r83478 - r83488;
        return r83489;
}

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

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

  4. Applied associate-*r*29.3

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

  6. Applied frac-2neg29.3

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

  7. Simplified29.2

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

  9. Applied distribute-lft-neg-out29.2

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

  10. Applied unsub-neg29.2

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

  11. Applied div-sub29.2

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

  12. Final simplification29.2

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

Reproduce

herbie shell --seed 2019297 
(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)))