Average Error: 19.8 → 0.2
Time: 15.1s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.325087509950303175598374268610755021633 \cdot 10^{61} \lor \neg \left(z \le 7.619103618905890033200650757194694051577 \cdot 10^{-5}\right):\\ \;\;\;\;x + \left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047560960637952121032867580652 - \frac{0.4046220386999212492717958866705885156989}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \end{array}\]
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 -1.325087509950303175598374268610755021633 \cdot 10^{61} \lor \neg \left(z \le 7.619103618905890033200650757194694051577 \cdot 10^{-5}\right):\\
\;\;\;\;x + \left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047560960637952121032867580652 - \frac{0.4046220386999212492717958866705885156989}{z}\right)\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r201258 = x;
        double r201259 = y;
        double r201260 = z;
        double r201261 = 0.0692910599291889;
        double r201262 = r201260 * r201261;
        double r201263 = 0.4917317610505968;
        double r201264 = r201262 + r201263;
        double r201265 = r201264 * r201260;
        double r201266 = 0.279195317918525;
        double r201267 = r201265 + r201266;
        double r201268 = r201259 * r201267;
        double r201269 = 6.012459259764103;
        double r201270 = r201260 + r201269;
        double r201271 = r201270 * r201260;
        double r201272 = 3.350343815022304;
        double r201273 = r201271 + r201272;
        double r201274 = r201268 / r201273;
        double r201275 = r201258 + r201274;
        return r201275;
}
↓
double f(double x, double y, double z) {
        double r201276 = z;
        double r201277 = -1.3250875099503032e+61;
        bool r201278 = r201276 <= r201277;
        double r201279 = 7.61910361890589e-05;
        bool r201280 = r201276 <= r201279;
        double r201281 = !r201280;
        bool r201282 = r201278 || r201281;
        double r201283 = x;
        double r201284 = 0.0692910599291889;
        double r201285 = y;
        double r201286 = r201284 * r201285;
        double r201287 = r201285 / r201276;
        double r201288 = 0.07512208616047561;
        double r201289 = 0.40462203869992125;
        double r201290 = r201289 / r201276;
        double r201291 = r201288 - r201290;
        double r201292 = r201287 * r201291;
        double r201293 = r201286 + r201292;
        double r201294 = r201283 + r201293;
        double r201295 = r201276 * r201284;
        double r201296 = 0.4917317610505968;
        double r201297 = r201295 + r201296;
        double r201298 = r201297 * r201276;
        double r201299 = 0.279195317918525;
        double r201300 = r201298 + r201299;
        double r201301 = 6.012459259764103;
        double r201302 = r201276 + r201301;
        double r201303 = r201302 * r201276;
        double r201304 = 3.350343815022304;
        double r201305 = r201303 + r201304;
        double r201306 = r201300 / r201305;
        double r201307 = r201285 * r201306;
        double r201308 = r201283 + r201307;
        double r201309 = r201282 ? r201294 : r201308;
        return r201309;
}

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

Original19.8
Target0.2
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.6524566747248172760009765625:\\ \;\;\;\;\left(\frac{0.07512208616047560960637952121032867580652}{z} + 0.06929105992918889456166908757950295694172\right) \cdot y - \left(\frac{0.4046220386999212492717958866705885156989 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 657611897278737678336:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047560960637952121032867580652}{z} + 0.06929105992918889456166908757950295694172\right) \cdot y - \left(\frac{0.4046220386999212492717958866705885156989 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.3250875099503032e+61 or 7.61910361890589e-05 < z

    1. Initial program 43.1

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

    2. Taylor expanded around inf 0.3

      \[\leadsto x + \color{blue}{\left(\left(0.07512208616047560960637952121032867580652 \cdot \frac{y}{z} + 0.06929105992918889456166908757950295694172 \cdot y\right) - 0.4046220386999212492717958866705885156989 \cdot \frac{y}{{z}^{2}}\right)}\]

    3. Simplified0.3

      \[\leadsto x + \color{blue}{\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047560960637952121032867580652 - \frac{0.4046220386999212492717958866705885156989}{z}\right)\right)}\]

    if -1.3250875099503032e+61 < z < 7.61910361890589e-05

    1. Initial program 0.6

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

    3. Applied *-un-lft-identity0.6

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

    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 simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.325087509950303175598374268610755021633 \cdot 10^{61} \lor \neg \left(z \le 7.619103618905890033200650757194694051577 \cdot 10^{-5}\right):\\ \;\;\;\;x + \left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047560960637952121032867580652 - \frac{0.4046220386999212492717958866705885156989}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 657611897278737680000) (+ 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))))