Average Error: 19.6 → 0.1
Time: 12.4s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -33431027.499201205:\\ \;\;\;\;x + y \cdot \left(\left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right) - \frac{0.40462203869992125}{z \cdot z}\right)\\ \mathbf{elif}\;z \le 6913926.788249764:\\ \;\;\;\;x + \frac{z \cdot \left(0.0692910599291889 \cdot z + 0.4917317610505968\right) + 0.279195317918525}{z \cdot \left(6.012459259764103 + z\right) + 3.350343815022304} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right) - \frac{0.40462203869992125}{z \cdot z}\right)\\ \end{array}\]
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 -33431027.499201205:\\
\;\;\;\;x + y \cdot \left(\left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right) - \frac{0.40462203869992125}{z \cdot z}\right)\\

\mathbf{elif}\;z \le 6913926.788249764:\\
\;\;\;\;x + \frac{z \cdot \left(0.0692910599291889 \cdot z + 0.4917317610505968\right) + 0.279195317918525}{z \cdot \left(6.012459259764103 + z\right) + 3.350343815022304} \cdot y\\

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

\end{array}
double f(double x, double y, double z) {
        double r6628451 = x;
        double r6628452 = y;
        double r6628453 = z;
        double r6628454 = 0.0692910599291889;
        double r6628455 = r6628453 * r6628454;
        double r6628456 = 0.4917317610505968;
        double r6628457 = r6628455 + r6628456;
        double r6628458 = r6628457 * r6628453;
        double r6628459 = 0.279195317918525;
        double r6628460 = r6628458 + r6628459;
        double r6628461 = r6628452 * r6628460;
        double r6628462 = 6.012459259764103;
        double r6628463 = r6628453 + r6628462;
        double r6628464 = r6628463 * r6628453;
        double r6628465 = 3.350343815022304;
        double r6628466 = r6628464 + r6628465;
        double r6628467 = r6628461 / r6628466;
        double r6628468 = r6628451 + r6628467;
        return r6628468;
}
↓
double f(double x, double y, double z) {
        double r6628469 = z;
        double r6628470 = -33431027.499201205;
        bool r6628471 = r6628469 <= r6628470;
        double r6628472 = x;
        double r6628473 = y;
        double r6628474 = 0.0692910599291889;
        double r6628475 = 0.07512208616047561;
        double r6628476 = r6628475 / r6628469;
        double r6628477 = r6628474 + r6628476;
        double r6628478 = 0.40462203869992125;
        double r6628479 = r6628469 * r6628469;
        double r6628480 = r6628478 / r6628479;
        double r6628481 = r6628477 - r6628480;
        double r6628482 = r6628473 * r6628481;
        double r6628483 = r6628472 + r6628482;
        double r6628484 = 6913926.788249764;
        bool r6628485 = r6628469 <= r6628484;
        double r6628486 = r6628474 * r6628469;
        double r6628487 = 0.4917317610505968;
        double r6628488 = r6628486 + r6628487;
        double r6628489 = r6628469 * r6628488;
        double r6628490 = 0.279195317918525;
        double r6628491 = r6628489 + r6628490;
        double r6628492 = 6.012459259764103;
        double r6628493 = r6628492 + r6628469;
        double r6628494 = r6628469 * r6628493;
        double r6628495 = 3.350343815022304;
        double r6628496 = r6628494 + r6628495;
        double r6628497 = r6628491 / r6628496;
        double r6628498 = r6628497 * r6628473;
        double r6628499 = r6628472 + r6628498;
        double r6628500 = r6628485 ? r6628499 : r6628483;
        double r6628501 = r6628471 ? r6628483 : r6628500;
        return r6628501;
}

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

Original19.6
Target0.1
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 < -33431027.499201205 or 6913926.788249764 < z

    1. Initial program 40.0

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

    3. Applied *-un-lft-identity40.0

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\color{blue}{1 \cdot \left(\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304\right)}}\]

    4. Applied times-frac32.2

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\]

    5. Simplified32.2

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

    6. Taylor expanded around inf 0.0

      \[\leadsto x + y \cdot \color{blue}{\left(\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}\right) - 0.40462203869992125 \cdot \frac{1}{{z}^{2}}\right)}\]

    7. Simplified0.0

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

    if -33431027.499201205 < z < 6913926.788249764

    1. Initial program 0.1

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

    3. Applied *-un-lft-identity0.1

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\color{blue}{1 \cdot \left(\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304\right)}}\]

    4. Applied times-frac0.1

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\]

    5. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -33431027.499201205:\\ \;\;\;\;x + y \cdot \left(\left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right) - \frac{0.40462203869992125}{z \cdot z}\right)\\ \mathbf{elif}\;z \le 6913926.788249764:\\ \;\;\;\;x + \frac{z \cdot \left(0.0692910599291889 \cdot z + 0.4917317610505968\right) + 0.279195317918525}{z \cdot \left(6.012459259764103 + z\right) + 3.350343815022304} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right) - \frac{0.40462203869992125}{z \cdot z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(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))))