Average Error: 26.5 → 1.0
Time: 13.5s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -6.75935725804580378 \cdot 10^{26} \lor \neg \left(x \le 2.33710636375954375 \cdot 10^{32}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]
\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}
↓
\begin{array}{l}
\mathbf{if}\;x \le -6.75935725804580378 \cdot 10^{26} \lor \neg \left(x \le 2.33710636375954375 \cdot 10^{32}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\

\end{array}
double f(double x, double y, double z) {
        double r402167 = x;
        double r402168 = 2.0;
        double r402169 = r402167 - r402168;
        double r402170 = 4.16438922228;
        double r402171 = r402167 * r402170;
        double r402172 = 78.6994924154;
        double r402173 = r402171 + r402172;
        double r402174 = r402173 * r402167;
        double r402175 = 137.519416416;
        double r402176 = r402174 + r402175;
        double r402177 = r402176 * r402167;
        double r402178 = y;
        double r402179 = r402177 + r402178;
        double r402180 = r402179 * r402167;
        double r402181 = z;
        double r402182 = r402180 + r402181;
        double r402183 = r402169 * r402182;
        double r402184 = 43.3400022514;
        double r402185 = r402167 + r402184;
        double r402186 = r402185 * r402167;
        double r402187 = 263.505074721;
        double r402188 = r402186 + r402187;
        double r402189 = r402188 * r402167;
        double r402190 = 313.399215894;
        double r402191 = r402189 + r402190;
        double r402192 = r402191 * r402167;
        double r402193 = 47.066876606;
        double r402194 = r402192 + r402193;
        double r402195 = r402183 / r402194;
        return r402195;
}
↓
double f(double x, double y, double z) {
        double r402196 = x;
        double r402197 = -6.759357258045804e+26;
        bool r402198 = r402196 <= r402197;
        double r402199 = 2.3371063637595438e+32;
        bool r402200 = r402196 <= r402199;
        double r402201 = !r402200;
        bool r402202 = r402198 || r402201;
        double r402203 = y;
        double r402204 = 2.0;
        double r402205 = pow(r402196, r402204);
        double r402206 = r402203 / r402205;
        double r402207 = 4.16438922228;
        double r402208 = r402207 * r402196;
        double r402209 = r402206 + r402208;
        double r402210 = 110.1139242984811;
        double r402211 = r402209 - r402210;
        double r402212 = 2.0;
        double r402213 = r402196 - r402212;
        double r402214 = r402196 * r402207;
        double r402215 = 78.6994924154;
        double r402216 = r402214 + r402215;
        double r402217 = r402216 * r402196;
        double r402218 = 137.519416416;
        double r402219 = r402217 + r402218;
        double r402220 = r402219 * r402196;
        double r402221 = r402220 + r402203;
        double r402222 = r402221 * r402196;
        double r402223 = z;
        double r402224 = r402222 + r402223;
        double r402225 = r402213 * r402224;
        double r402226 = 1.0;
        double r402227 = 43.3400022514;
        double r402228 = r402196 + r402227;
        double r402229 = r402228 * r402196;
        double r402230 = 263.505074721;
        double r402231 = r402229 + r402230;
        double r402232 = r402231 * r402196;
        double r402233 = 313.399215894;
        double r402234 = r402232 + r402233;
        double r402235 = r402234 * r402196;
        double r402236 = 47.066876606;
        double r402237 = r402235 + r402236;
        double r402238 = r402226 / r402237;
        double r402239 = r402225 * r402238;
        double r402240 = r402202 ? r402211 : r402239;
        return r402240;
}

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

Original26.5
Target0.4
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -6.759357258045804e+26 or 2.3371063637595438e+32 < x

    1. Initial program 58.3

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

    2. Taylor expanded around inf 1.0

      \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109}\]

    if -6.759357258045804e+26 < x < 2.3371063637595438e+32

    1. Initial program 0.6

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
    2. Using strategy rm

    3. Applied div-inv0.9

      \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.75935725804580378 \cdot 10^{26} \lor \neg \left(x \le 2.33710636375954375 \cdot 10^{32}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

  (/ (* (- x 2) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))