Average Error: 20.0 → 0.1
Time: 8.5s
Precision: binary64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -3.900244530557504 \cdot 10^{+73}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{elif}\;z \leq 12837.105356225598:\\ \;\;\;\;x + y \cdot \frac{0.279195317918525 + z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right)}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot e^{\log \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)}\\ \end{array}\]
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 \leq -3.900244530557504 \cdot 10^{+73}:\\
\;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\

\mathbf{elif}\;z \leq 12837.105356225598:\\
\;\;\;\;x + y \cdot \frac{0.279195317918525 + z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right)}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)}\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot e^{\log \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)}\\

\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 (<= z -3.900244530557504e+73)
   (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z))))
   (if (<= z 12837.105356225598)
     (+
      x
      (*
       y
       (/
        (+
         0.279195317918525
         (* z (+ 0.4917317610505968 (* z 0.0692910599291889))))
        (+ 3.350343815022304 (* z (+ z 6.012459259764103))))))
     (+
      x
      (* y (exp (log (+ 0.0692910599291889 (/ 0.07512208616047561 z)))))))))
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 <= -3.900244530557504e+73) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else if (z <= 12837.105356225598) {
		tmp = x + (y * ((0.279195317918525 + (z * (0.4917317610505968 + (z * 0.0692910599291889)))) / (3.350343815022304 + (z * (z + 6.012459259764103)))));
	} else {
		tmp = x + (y * exp(log(0.0692910599291889 + (0.07512208616047561 / z))));
	}
	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

Original20.0
Target0.2
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;z < -8120153.652456675:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z < 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -3.9002445305575039e73

    1. Initial program 49.5

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

    3. Applied *-un-lft-identity_binary64_1133149.5

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

    4. Applied times-frac_binary64_1133740.9

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

    5. Simplified40.9

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

    6. Simplified40.9

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

    7. Taylor expanded around inf 0.0

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

    8. Simplified0.0

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

    if -3.9002445305575039e73 < z < 12837.105356225598

    1. Initial program 0.9

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

    3. Applied *-un-lft-identity_binary64_113310.9

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

    4. Applied times-frac_binary64_113370.1

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

    5. Simplified0.1

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

    6. Simplified0.1

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

    if 12837.105356225598 < z

    1. Initial program 41.2

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

    3. Applied *-un-lft-identity_binary64_1133141.2

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

    4. Applied times-frac_binary64_1133732.8

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

    5. Simplified32.8

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

    6. Simplified32.8

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

    7. Taylor expanded around inf 0.1

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

    8. Simplified0.1

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)}\]
    9. Using strategy rm

    10. Applied add-exp-log_binary64_113690.1

      \[\leadsto x + y \cdot \color{blue}{e^{\log \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.900244530557504 \cdot 10^{+73}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{elif}\;z \leq 12837.105356225598:\\ \;\;\;\;x + y \cdot \frac{0.279195317918525 + z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right)}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot e^{\log \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2021093 
(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))))