Average Error: 20.3 → 0.2
Time: 7.8s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.2730222216892933 \cdot 10^{26} \lor \neg \left(z \le 72489.2439122225187\right):\\ \;\;\;\;x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z \cdot y\right) \cdot \left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) + y \cdot 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.2730222216892933 \cdot 10^{26} \lor \neg \left(z \le 72489.2439122225187\right):\\
\;\;\;\;x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\left(z \cdot y\right) \cdot \left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) + y \cdot 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\

\end{array}
double f(double x, double y, double z) {
        double r419353 = x;
        double r419354 = y;
        double r419355 = z;
        double r419356 = 0.0692910599291889;
        double r419357 = r419355 * r419356;
        double r419358 = 0.4917317610505968;
        double r419359 = r419357 + r419358;
        double r419360 = r419359 * r419355;
        double r419361 = 0.279195317918525;
        double r419362 = r419360 + r419361;
        double r419363 = r419354 * r419362;
        double r419364 = 6.012459259764103;
        double r419365 = r419355 + r419364;
        double r419366 = r419365 * r419355;
        double r419367 = 3.350343815022304;
        double r419368 = r419366 + r419367;
        double r419369 = r419363 / r419368;
        double r419370 = r419353 + r419369;
        return r419370;
}
↓
double f(double x, double y, double z) {
        double r419371 = z;
        double r419372 = -1.2730222216892933e+26;
        bool r419373 = r419371 <= r419372;
        double r419374 = 72489.24391222252;
        bool r419375 = r419371 <= r419374;
        double r419376 = !r419375;
        bool r419377 = r419373 || r419376;
        double r419378 = x;
        double r419379 = 0.07512208616047561;
        double r419380 = y;
        double r419381 = r419380 / r419371;
        double r419382 = r419379 * r419381;
        double r419383 = 0.0692910599291889;
        double r419384 = r419383 * r419380;
        double r419385 = r419382 + r419384;
        double r419386 = r419378 + r419385;
        double r419387 = r419371 * r419380;
        double r419388 = r419371 * r419383;
        double r419389 = 0.4917317610505968;
        double r419390 = r419388 + r419389;
        double r419391 = r419387 * r419390;
        double r419392 = 0.279195317918525;
        double r419393 = r419380 * r419392;
        double r419394 = r419391 + r419393;
        double r419395 = 6.012459259764103;
        double r419396 = r419371 + r419395;
        double r419397 = r419396 * r419371;
        double r419398 = 3.350343815022304;
        double r419399 = r419397 + r419398;
        double r419400 = r419394 / r419399;
        double r419401 = r419378 + r419400;
        double r419402 = r419377 ? r419386 : r419401;
        return r419402;
}

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

Original20.3
Target0.1
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.6524566747:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291888946\right) \cdot y - \left(\frac{0.404622038699921249 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 657611897278737680000:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)\right) \cdot \frac{1}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291888946\right) \cdot y - \left(\frac{0.404622038699921249 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.2730222216892933e+26 or 72489.24391222252 < z

    1. Initial program 42.3

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]

    2. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)}\]

    if -1.2730222216892933e+26 < z < 72489.24391222252

    1. Initial program 0.3

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
    2. Using strategy rm

    3. Applied distribute-lft-in0.3

      \[\leadsto x + \frac{\color{blue}{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z\right) + y \cdot 0.279195317918524977}}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]

    4. Simplified0.3

      \[\leadsto x + \frac{\color{blue}{\left(z \cdot y\right) \cdot \left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right)} + y \cdot 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.2730222216892933 \cdot 10^{26} \lor \neg \left(z \le 72489.2439122225187\right):\\ \;\;\;\;x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z \cdot y\right) \cdot \left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) + y \cdot 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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))))