Average Error: 20.1 → 0.1
Time: 7.0s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.344449140814709812702451729857916650488 \cdot 10^{51} \lor \neg \left(z \le 8549728.21505705825984477996826171875\right):\\ \;\;\;\;x + y \cdot \frac{1}{\left(14.43187621926893804413793986896052956581 - 15.64635683029203505611803848296403884888 \cdot \frac{1}{z}\right) + \frac{\frac{101.237333520038163214849191717803478241}{z}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \end{array}\]
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 -3.344449140814709812702451729857916650488 \cdot 10^{51} \lor \neg \left(z \le 8549728.21505705825984477996826171875\right):\\
\;\;\;\;x + y \cdot \frac{1}{\left(14.43187621926893804413793986896052956581 - 15.64635683029203505611803848296403884888 \cdot \frac{1}{z}\right) + \frac{\frac{101.237333520038163214849191717803478241}{z}}{z}}\\

\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 r256350 = x;
        double r256351 = y;
        double r256352 = z;
        double r256353 = 0.0692910599291889;
        double r256354 = r256352 * r256353;
        double r256355 = 0.4917317610505968;
        double r256356 = r256354 + r256355;
        double r256357 = r256356 * r256352;
        double r256358 = 0.279195317918525;
        double r256359 = r256357 + r256358;
        double r256360 = r256351 * r256359;
        double r256361 = 6.012459259764103;
        double r256362 = r256352 + r256361;
        double r256363 = r256362 * r256352;
        double r256364 = 3.350343815022304;
        double r256365 = r256363 + r256364;
        double r256366 = r256360 / r256365;
        double r256367 = r256350 + r256366;
        return r256367;
}
↓
double f(double x, double y, double z) {
        double r256368 = z;
        double r256369 = -3.34444914081471e+51;
        bool r256370 = r256368 <= r256369;
        double r256371 = 8549728.215057058;
        bool r256372 = r256368 <= r256371;
        double r256373 = !r256372;
        bool r256374 = r256370 || r256373;
        double r256375 = x;
        double r256376 = y;
        double r256377 = 1.0;
        double r256378 = 14.431876219268938;
        double r256379 = 15.646356830292035;
        double r256380 = r256377 / r256368;
        double r256381 = r256379 * r256380;
        double r256382 = r256378 - r256381;
        double r256383 = 101.23733352003816;
        double r256384 = r256383 / r256368;
        double r256385 = r256384 / r256368;
        double r256386 = r256382 + r256385;
        double r256387 = r256377 / r256386;
        double r256388 = r256376 * r256387;
        double r256389 = r256375 + r256388;
        double r256390 = 0.0692910599291889;
        double r256391 = r256368 * r256390;
        double r256392 = 0.4917317610505968;
        double r256393 = r256391 + r256392;
        double r256394 = r256393 * r256368;
        double r256395 = 0.279195317918525;
        double r256396 = r256394 + r256395;
        double r256397 = 6.012459259764103;
        double r256398 = r256368 + r256397;
        double r256399 = r256398 * r256368;
        double r256400 = 3.350343815022304;
        double r256401 = r256399 + r256400;
        double r256402 = r256396 / r256401;
        double r256403 = r256376 * r256402;
        double r256404 = r256375 + r256403;
        double r256405 = r256374 ? r256389 : r256404;
        return r256405;
}

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 < -3.34444914081471e+51 or 8549728.215057058 < z

    1. Initial program 43.7

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

    3. Applied associate-/l*34.9

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

    4. Taylor expanded around inf 0.1

      \[\leadsto x + \frac{y}{\color{blue}{\left(101.237333520038163214849191717803478241 \cdot \frac{1}{{z}^{2}} + 14.43187621926893804413793986896052956581\right) - 15.64635683029203505611803848296403884888 \cdot \frac{1}{z}}}\]

    5. Simplified0.1

      \[\leadsto x + \frac{y}{\color{blue}{\left(14.43187621926893804413793986896052956581 - 15.64635683029203505611803848296403884888 \cdot \frac{1}{z}\right) + \frac{\frac{101.237333520038163214849191717803478241}{z}}{z}}}\]
    6. Using strategy rm

    7. Applied div-inv0.0

      \[\leadsto x + \color{blue}{y \cdot \frac{1}{\left(14.43187621926893804413793986896052956581 - 15.64635683029203505611803848296403884888 \cdot \frac{1}{z}\right) + \frac{\frac{101.237333520038163214849191717803478241}{z}}{z}}}\]

    if -3.34444914081471e+51 < z < 8549728.215057058

    1. Initial program 0.5

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

    3. Applied *-un-lft-identity0.5

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

    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

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.344449140814709812702451729857916650488 \cdot 10^{51} \lor \neg \left(z \le 8549728.21505705825984477996826171875\right):\\ \;\;\;\;x + y \cdot \frac{1}{\left(14.43187621926893804413793986896052956581 - 15.64635683029203505611803848296403884888 \cdot \frac{1}{z}\right) + \frac{\frac{101.237333520038163214849191717803478241}{z}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \end{array}\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (if (< z -8120153.6524566747) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291888946) y) (- (/ (* 0.404622038699921249 y) (* z z)) x)) (if (< z 657611897278737680000) (+ x (* (* y (+ (* (+ (* z 0.0692910599291888946) 0.49173176105059679) z) 0.279195317918524977)) (/ 1 (+ (* (+ z 6.0124592597641033) z) 3.35034381502230394)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291888946) y) (- (/ (* 0.404622038699921249 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291888946) 0.49173176105059679) z) 0.279195317918524977)) (+ (* (+ z 6.0124592597641033) z) 3.35034381502230394))))