Average Error: 20.3 → 0.2
Time: 7.7s
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 r468286 = x;
        double r468287 = y;
        double r468288 = z;
        double r468289 = 0.0692910599291889;
        double r468290 = r468288 * r468289;
        double r468291 = 0.4917317610505968;
        double r468292 = r468290 + r468291;
        double r468293 = r468292 * r468288;
        double r468294 = 0.279195317918525;
        double r468295 = r468293 + r468294;
        double r468296 = r468287 * r468295;
        double r468297 = 6.012459259764103;
        double r468298 = r468288 + r468297;
        double r468299 = r468298 * r468288;
        double r468300 = 3.350343815022304;
        double r468301 = r468299 + r468300;
        double r468302 = r468296 / r468301;
        double r468303 = r468286 + r468302;
        return r468303;
}
↓
double f(double x, double y, double z) {
        double r468304 = z;
        double r468305 = -1.2730222216892933e+26;
        bool r468306 = r468304 <= r468305;
        double r468307 = 72489.24391222252;
        bool r468308 = r468304 <= r468307;
        double r468309 = !r468308;
        bool r468310 = r468306 || r468309;
        double r468311 = x;
        double r468312 = 0.07512208616047561;
        double r468313 = y;
        double r468314 = r468313 / r468304;
        double r468315 = r468312 * r468314;
        double r468316 = 0.0692910599291889;
        double r468317 = r468316 * r468313;
        double r468318 = r468315 + r468317;
        double r468319 = r468311 + r468318;
        double r468320 = r468304 * r468313;
        double r468321 = r468304 * r468316;
        double r468322 = 0.4917317610505968;
        double r468323 = r468321 + r468322;
        double r468324 = r468320 * r468323;
        double r468325 = 0.279195317918525;
        double r468326 = r468313 * r468325;
        double r468327 = r468324 + r468326;
        double r468328 = 6.012459259764103;
        double r468329 = r468304 + r468328;
        double r468330 = r468329 * r468304;
        double r468331 = 3.350343815022304;
        double r468332 = r468330 + r468331;
        double r468333 = r468327 / r468332;
        double r468334 = r468311 + r468333;
        double r468335 = r468310 ? r468319 : r468334;
        return r468335;
}

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))))