Average Error: 20.1 → 0.1
Time: 21.3s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -172446901772025375848918711117734366674900:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \mathbf{elif}\;z \le 38319471531.16735076904296875:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) + 0.2791953179185249767080279070796677842736}{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}
↓
\begin{array}{l}
\mathbf{if}\;z \le -172446901772025375848918711117734366674900:\\
\;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\

\mathbf{elif}\;z \le 38319471531.16735076904296875:\\
\;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) + 0.2791953179185249767080279070796677842736}{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\

\end{array}
double f(double x, double y, double z) {
        double r19480513 = x;
        double r19480514 = y;
        double r19480515 = z;
        double r19480516 = 0.0692910599291889;
        double r19480517 = r19480515 * r19480516;
        double r19480518 = 0.4917317610505968;
        double r19480519 = r19480517 + r19480518;
        double r19480520 = r19480519 * r19480515;
        double r19480521 = 0.279195317918525;
        double r19480522 = r19480520 + r19480521;
        double r19480523 = r19480514 * r19480522;
        double r19480524 = 6.012459259764103;
        double r19480525 = r19480515 + r19480524;
        double r19480526 = r19480525 * r19480515;
        double r19480527 = 3.350343815022304;
        double r19480528 = r19480526 + r19480527;
        double r19480529 = r19480523 / r19480528;
        double r19480530 = r19480513 + r19480529;
        return r19480530;
}
↓
double f(double x, double y, double z) {
        double r19480531 = z;
        double r19480532 = -1.7244690177202538e+41;
        bool r19480533 = r19480531 <= r19480532;
        double r19480534 = 0.0692910599291889;
        double r19480535 = y;
        double r19480536 = r19480534 * r19480535;
        double r19480537 = r19480535 / r19480531;
        double r19480538 = 0.07512208616047561;
        double r19480539 = r19480537 * r19480538;
        double r19480540 = r19480536 + r19480539;
        double r19480541 = x;
        double r19480542 = r19480540 + r19480541;
        double r19480543 = 38319471531.16735;
        bool r19480544 = r19480531 <= r19480543;
        double r19480545 = r19480531 * r19480534;
        double r19480546 = 0.4917317610505968;
        double r19480547 = r19480545 + r19480546;
        double r19480548 = r19480531 * r19480547;
        double r19480549 = 0.279195317918525;
        double r19480550 = r19480548 + r19480549;
        double r19480551 = 3.350343815022304;
        double r19480552 = 6.012459259764103;
        double r19480553 = r19480552 + r19480531;
        double r19480554 = r19480553 * r19480531;
        double r19480555 = r19480551 + r19480554;
        double r19480556 = r19480550 / r19480555;
        double r19480557 = r19480535 * r19480556;
        double r19480558 = r19480541 + r19480557;
        double r19480559 = r19480544 ? r19480558 : r19480542;
        double r19480560 = r19480533 ? r19480542 : r19480559;
        return r19480560;
}

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

Original20.1
Target0.2
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.6524566747248172760009765625:\\ \;\;\;\;\left(\frac{0.07512208616047560960637952121032867580652}{z} + 0.06929105992918889456166908757950295694172\right) \cdot y - \left(\frac{0.4046220386999212492717958866705885156989 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 657611897278737678336:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047560960637952121032867580652}{z} + 0.06929105992918889456166908757950295694172\right) \cdot y - \left(\frac{0.4046220386999212492717958866705885156989 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.7244690177202538e+41 or 38319471531.16735 < z

    1. Initial program 43.0

      \[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]

    2. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{x + \left(0.07512208616047560960637952121032867580652 \cdot \frac{y}{z} + 0.06929105992918889456166908757950295694172 \cdot y\right)}\]

    if -1.7244690177202538e+41 < z < 38319471531.16735

    1. Initial program 0.3

      \[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity0.3

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\color{blue}{1 \cdot \left(\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084\right)}}\]

    4. Applied times-frac0.1

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}}\]

    5. Simplified0.1

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -172446901772025375848918711117734366674900:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \mathbf{elif}\;z \le 38319471531.16735076904296875:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) + 0.2791953179185249767080279070796677842736}{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 
(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)) (/ 1.0 (+ (* (+ 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))))