Average Error: 19.6 → 0.8
Time: 5.8s
Precision: binary64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -1.9035509329418147 \cdot 10^{+96} \lor \neg \left(z \leq 15564925946060844\right):\\ \;\;\;\;x + 0.0692910599291889 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(0.0692910599291889 \cdot {z}^{2} + \left(z \cdot 0.4917317610505968 + 0.279195317918525\right)\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \end{array}\]
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 \leq -1.9035509329418147 \cdot 10^{+96} \lor \neg \left(z \leq 15564925946060844\right):\\
\;\;\;\;x + 0.0692910599291889 \cdot y\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(0.0692910599291889 \cdot {z}^{2} + \left(z \cdot 0.4917317610505968 + 0.279195317918525\right)\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\

\end{array}
(FPCore (x y z)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+
     (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
     0.279195317918525))
   (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.9035509329418147e+96) (not (<= z 15564925946060844.0)))
   (+ x (* 0.0692910599291889 y))
   (+
    x
    (/
     (*
      y
      (+
       (* 0.0692910599291889 (pow z 2.0))
       (+ (* z 0.4917317610505968) 0.279195317918525)))
     (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))))
double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9035509329418147e+96) || !(z <= 15564925946060844.0)) {
		tmp = x + (0.0692910599291889 * y);
	} else {
		tmp = x + ((y * ((0.0692910599291889 * pow(z, 2.0)) + ((z * 0.4917317610505968) + 0.279195317918525))) / ((z * (z + 6.012459259764103)) + 3.350343815022304));
	}
	return tmp;
}

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
Target0.2
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z < -8120153.652456675:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z < 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.90355093294181469e96 or 15564925946060844 < z

    1. Initial program 46.7

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

    2. Taylor expanded around inf 0.0

      \[\leadsto x + \color{blue}{0.0692910599291889 \cdot y}\]

    if -1.90355093294181469e96 < z < 15564925946060844

    1. Initial program 1.3

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

    2. Taylor expanded around 0 1.3

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9035509329418147 \cdot 10^{+96} \lor \neg \left(z \leq 15564925946060844\right):\\ \;\;\;\;x + 0.0692910599291889 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(0.0692910599291889 \cdot {z}^{2} + \left(z \cdot 0.4917317610505968 + 0.279195317918525\right)\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \end{array}\]

Alternatives

Reproduce

herbie shell --seed 2021118 
(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))))