Average Error: 19.4 → 0.1
Time: 24.3s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -273974326636.0899:\\ \;\;\;\;\left(y \cdot 0.0692910599291889 + \left(\frac{y \cdot 0.07512208616047561}{z} - \frac{y \cdot 0.40462203869992125}{z \cdot z}\right)\right) + x\\ \mathbf{elif}\;z \le 727958.1035308853:\\ \;\;\;\;\frac{y \cdot \left(0.279195317918525 + \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right) \cdot z\right)}{3.350343815022304 + \left(z + 6.012459259764103\right) \cdot z} + x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.0692910599291889 + \left(\frac{y \cdot 0.07512208616047561}{z} - \frac{y \cdot 0.40462203869992125}{z \cdot z}\right)\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}
↓
\begin{array}{l}
\mathbf{if}\;z \le -273974326636.0899:\\
\;\;\;\;\left(y \cdot 0.0692910599291889 + \left(\frac{y \cdot 0.07512208616047561}{z} - \frac{y \cdot 0.40462203869992125}{z \cdot z}\right)\right) + x\\

\mathbf{elif}\;z \le 727958.1035308853:\\
\;\;\;\;\frac{y \cdot \left(0.279195317918525 + \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right) \cdot z\right)}{3.350343815022304 + \left(z + 6.012459259764103\right) \cdot z} + x\\

\mathbf{else}:\\
\;\;\;\;\left(y \cdot 0.0692910599291889 + \left(\frac{y \cdot 0.07512208616047561}{z} - \frac{y \cdot 0.40462203869992125}{z \cdot z}\right)\right) + x\\

\end{array}
double f(double x, double y, double z) {
        double r21989413 = x;
        double r21989414 = y;
        double r21989415 = z;
        double r21989416 = 0.0692910599291889;
        double r21989417 = r21989415 * r21989416;
        double r21989418 = 0.4917317610505968;
        double r21989419 = r21989417 + r21989418;
        double r21989420 = r21989419 * r21989415;
        double r21989421 = 0.279195317918525;
        double r21989422 = r21989420 + r21989421;
        double r21989423 = r21989414 * r21989422;
        double r21989424 = 6.012459259764103;
        double r21989425 = r21989415 + r21989424;
        double r21989426 = r21989425 * r21989415;
        double r21989427 = 3.350343815022304;
        double r21989428 = r21989426 + r21989427;
        double r21989429 = r21989423 / r21989428;
        double r21989430 = r21989413 + r21989429;
        return r21989430;
}
↓
double f(double x, double y, double z) {
        double r21989431 = z;
        double r21989432 = -273974326636.0899;
        bool r21989433 = r21989431 <= r21989432;
        double r21989434 = y;
        double r21989435 = 0.0692910599291889;
        double r21989436 = r21989434 * r21989435;
        double r21989437 = 0.07512208616047561;
        double r21989438 = r21989434 * r21989437;
        double r21989439 = r21989438 / r21989431;
        double r21989440 = 0.40462203869992125;
        double r21989441 = r21989434 * r21989440;
        double r21989442 = r21989431 * r21989431;
        double r21989443 = r21989441 / r21989442;
        double r21989444 = r21989439 - r21989443;
        double r21989445 = r21989436 + r21989444;
        double r21989446 = x;
        double r21989447 = r21989445 + r21989446;
        double r21989448 = 727958.1035308853;
        bool r21989449 = r21989431 <= r21989448;
        double r21989450 = 0.279195317918525;
        double r21989451 = 0.4917317610505968;
        double r21989452 = r21989435 * r21989431;
        double r21989453 = r21989451 + r21989452;
        double r21989454 = r21989453 * r21989431;
        double r21989455 = r21989450 + r21989454;
        double r21989456 = r21989434 * r21989455;
        double r21989457 = 3.350343815022304;
        double r21989458 = 6.012459259764103;
        double r21989459 = r21989431 + r21989458;
        double r21989460 = r21989459 * r21989431;
        double r21989461 = r21989457 + r21989460;
        double r21989462 = r21989456 / r21989461;
        double r21989463 = r21989462 + r21989446;
        double r21989464 = r21989449 ? r21989463 : r21989447;
        double r21989465 = r21989433 ? r21989447 : r21989464;
        return r21989465;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original19.4
Target0.2
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.652456675:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -273974326636.0899 or 727958.1035308853 < z

    1. Initial program 40.3

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt40.3

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\color{blue}{\sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \cdot \sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}}\]

    4. Applied times-frac33.4

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}}\]

    5. Taylor expanded around inf 0.0

      \[\leadsto x + \color{blue}{\left(\left(0.0692910599291889 \cdot y + 0.07512208616047561 \cdot \frac{y}{z}\right) - 0.40462203869992125 \cdot \frac{y}{{z}^{2}}\right)}\]

    6. Simplified0.0

      \[\leadsto x + \color{blue}{\left(\left(\frac{y \cdot 0.07512208616047561}{z} - \frac{y \cdot 0.40462203869992125}{z \cdot z}\right) + y \cdot 0.0692910599291889\right)}\]

    if -273974326636.0899 < z < 727958.1035308853

    1. Initial program 0.2

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -273974326636.0899:\\ \;\;\;\;\left(y \cdot 0.0692910599291889 + \left(\frac{y \cdot 0.07512208616047561}{z} - \frac{y \cdot 0.40462203869992125}{z \cdot z}\right)\right) + x\\ \mathbf{elif}\;z \le 727958.1035308853:\\ \;\;\;\;\frac{y \cdot \left(0.279195317918525 + \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right) \cdot z\right)}{3.350343815022304 + \left(z + 6.012459259764103\right) \cdot z} + x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.0692910599291889 + \left(\frac{y \cdot 0.07512208616047561}{z} - \frac{y \cdot 0.40462203869992125}{z \cdot z}\right)\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 6.576118972787377e+20) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))