Average Error: 19.9 → 0.3
Time: 3.1s
Precision: binary64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.7704488784677663 \cdot 10^{57} \lor \neg \left(z \le 104230107.00093396\right):\\ \;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z\right) + y \cdot 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]
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 -1.7704488784677663 \cdot 10^{57} \lor \neg \left(z \le 104230107.00093396\right):\\
\;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{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}\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (x + ((double) (((double) (y * ((double) (((double) (((double) (((double) (z * 0.0692910599291889)) + 0.4917317610505968)) * z)) + 0.279195317918525)))) / ((double) (((double) (((double) (z + 6.012459259764103)) * z)) + 3.350343815022304))))));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -1.7704488784677663e+57) || !(z <= 104230107.00093396))) {
		VAR = ((double) (x + ((double) (((double) (((double) (0.07512208616047561 * ((double) (y / z)))) + ((double) (0.0692910599291889 * y)))) - ((double) (0.40462203869992125 * ((double) (y / ((double) pow(z, 2.0))))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (((double) (y * ((double) (((double) (((double) (z * 0.0692910599291889)) + 0.4917317610505968)) * z)))) + ((double) (y * 0.279195317918525)))) / ((double) (((double) (((double) (z + 6.012459259764103)) * z)) + 3.350343815022304))))));
	}
	return VAR;
}

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

Original19.9
Target0.1
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.6524566747:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291888946\right) \cdot y - \left(\frac{0.404622038699921249 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 657611897278737680000:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)\right) \cdot \frac{1}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291888946\right) \cdot y - \left(\frac{0.404622038699921249 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.7704488784677663e57 or 104230107.00093396 < z

    1. Initial program 43.8

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

    2. Taylor expanded around inf 0.0

      \[\leadsto x + \color{blue}{\left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)}\]

    if -1.7704488784677663e57 < z < 104230107.00093396

    1. Initial program 0.6

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

    3. Applied distribute-lft-in0.6

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.7704488784677663 \cdot 10^{57} \lor \neg \left(z \le 104230107.00093396\right):\\ \;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z\right) + y \cdot 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(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 6.576118972787377e+20) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1.0 (+ (* (+ 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))))