Average Error: 29.1 → 29.2
Time: 9.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\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 + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64461 = x;
        double r64462 = y;
        double r64463 = r64461 * r64462;
        double r64464 = z;
        double r64465 = r64463 + r64464;
        double r64466 = r64465 * r64462;
        double r64467 = 27464.7644705;
        double r64468 = r64466 + r64467;
        double r64469 = r64468 * r64462;
        double r64470 = 230661.510616;
        double r64471 = r64469 + r64470;
        double r64472 = r64471 * r64462;
        double r64473 = t;
        double r64474 = r64472 + r64473;
        double r64475 = a;
        double r64476 = r64462 + r64475;
        double r64477 = r64476 * r64462;
        double r64478 = b;
        double r64479 = r64477 + r64478;
        double r64480 = r64479 * r64462;
        double r64481 = c;
        double r64482 = r64480 + r64481;
        double r64483 = r64482 * r64462;
        double r64484 = i;
        double r64485 = r64483 + r64484;
        double r64486 = r64474 / r64485;
        return r64486;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64487 = x;
        double r64488 = y;
        double r64489 = r64487 * r64488;
        double r64490 = z;
        double r64491 = r64489 + r64490;
        double r64492 = r64491 * r64488;
        double r64493 = 27464.7644705;
        double r64494 = r64492 + r64493;
        double r64495 = r64494 * r64488;
        double r64496 = 230661.510616;
        double r64497 = r64495 + r64496;
        double r64498 = r64497 * r64488;
        double r64499 = t;
        double r64500 = r64498 + r64499;
        double r64501 = a;
        double r64502 = r64488 + r64501;
        double r64503 = r64502 * r64488;
        double r64504 = b;
        double r64505 = r64503 + r64504;
        double r64506 = cbrt(r64505);
        double r64507 = r64506 * r64506;
        double r64508 = r64506 * r64488;
        double r64509 = r64507 * r64508;
        double r64510 = c;
        double r64511 = r64509 + r64510;
        double r64512 = r64511 * r64488;
        double r64513 = i;
        double r64514 = r64512 + r64513;
        double r64515 = r64500 / r64514;
        return r64515;
}

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 29.1

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right)} \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-*l*29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right)} + c\right) \cdot y + i}\]

  5. Final simplification29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(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) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))