Average Error: 19.7 → 0.3
Time: 6.5s
Precision: binary64
Cost: 1672
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -9.990746456204017 \cdot 10^{+35} \lor \neg \left(z \leq 48.17602907496802\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \end{array}\]
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 -9.990746456204017 \cdot 10^{+35} \lor \neg \left(z \leq 48.17602907496802\right):\\
\;\;\;\;x + y \cdot 0.0692910599291889\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\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 -9.990746456204017e+35) (not (<= z 48.17602907496802)))
   (+ x (* y 0.0692910599291889))
   (+
    x
    (/
     (*
      y
      (+
       (* z (+ (* z 0.0692910599291889) 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 <= -9.990746456204017e+35) || !(z <= 48.17602907496802)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = x + ((y * ((z * ((z * 0.0692910599291889) + 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

Original19.7
Target0.2
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z < -8120153.652456675:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z < 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Alternatives

Alternative 1
Error0.5
Cost1281
\[\begin{array}{l} \mathbf{if}\;z \leq -5.411826093399547:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 + \frac{y}{z} \cdot \left(0.07512208616047561 - \frac{0.4046220386999212}{z}\right)\right)\\ \mathbf{elif}\;z \leq 5.0434340818853745:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.0027777777775172103\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array}\]
Alternative 2
Error0.6
Cost904
\[\begin{array}{l} \mathbf{if}\;z \leq -5.411826093399547 \lor \neg \left(z \leq 5.0434340818853745\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.0027777777775172103\right)\\ \end{array}\]
Alternative 3
Error0.7
Cost648
\[\begin{array}{l} \mathbf{if}\;z \leq -5.411826093399547 \lor \neg \left(z \leq 5.9254727893358545\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array}\]
Alternative 4
Error13.2
Cost320
\[x + y \cdot 0.0692910599291889\]
Alternative 5
Error24.8
Cost834
\[\begin{array}{l} \mathbf{if}\;x \leq -3.0864478654520087 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.632870605740012 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
Alternative 6
Error31.1
Cost64
\[x\]
Alternative 7
Error61.9
Cost64
\[-1\]
Alternative 8
Error61.9
Cost64
\[1\]

Error

Derivation

  1. Split input into 2 regimes

  2. if z < -9.9907464562040168e35 or 48.1760290749680209 < z

    1. Initial program 42.5

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

    2. Taylor expanded around inf 0.4

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

    3. Simplified0.4

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

    4. Simplified0.4

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

    if -9.9907464562040168e35 < z < 48.1760290749680209

    1. Initial program 0.3

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

    2. Simplified0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.990746456204017 \cdot 10^{+35} \lor \neg \left(z \leq 48.17602907496802\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \end{array}\]

Reproduce

herbie shell --seed 2021044 
(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))))