Average Error: 27.2 → 0.6
Time: 6.5s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -9.0944108871381443 \cdot 10^{65} \lor \neg \left(x \le 7.2564691634128278 \cdot 10^{43}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right) \cdot \left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot x\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]
\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 -9.0944108871381443 \cdot 10^{65} \lor \neg \left(x \le 7.2564691634128278 \cdot 10^{43}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\left(x - 2\right) \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(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right) \cdot \left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot x\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\

\end{array}
double f(double x, double y, double z) {
        double r436163 = x;
        double r436164 = 2.0;
        double r436165 = r436163 - r436164;
        double r436166 = 4.16438922228;
        double r436167 = r436163 * r436166;
        double r436168 = 78.6994924154;
        double r436169 = r436167 + r436168;
        double r436170 = r436169 * r436163;
        double r436171 = 137.519416416;
        double r436172 = r436170 + r436171;
        double r436173 = r436172 * r436163;
        double r436174 = y;
        double r436175 = r436173 + r436174;
        double r436176 = r436175 * r436163;
        double r436177 = z;
        double r436178 = r436176 + r436177;
        double r436179 = r436165 * r436178;
        double r436180 = 43.3400022514;
        double r436181 = r436163 + r436180;
        double r436182 = r436181 * r436163;
        double r436183 = 263.505074721;
        double r436184 = r436182 + r436183;
        double r436185 = r436184 * r436163;
        double r436186 = 313.399215894;
        double r436187 = r436185 + r436186;
        double r436188 = r436187 * r436163;
        double r436189 = 47.066876606;
        double r436190 = r436188 + r436189;
        double r436191 = r436179 / r436190;
        return r436191;
}
↓
double f(double x, double y, double z) {
        double r436192 = x;
        double r436193 = -9.094410887138144e+65;
        bool r436194 = r436192 <= r436193;
        double r436195 = 7.256469163412828e+43;
        bool r436196 = r436192 <= r436195;
        double r436197 = !r436196;
        bool r436198 = r436194 || r436197;
        double r436199 = y;
        double r436200 = 2.0;
        double r436201 = pow(r436192, r436200);
        double r436202 = r436199 / r436201;
        double r436203 = 4.16438922228;
        double r436204 = r436203 * r436192;
        double r436205 = r436202 + r436204;
        double r436206 = 110.1139242984811;
        double r436207 = r436205 - r436206;
        double r436208 = 2.0;
        double r436209 = r436192 - r436208;
        double r436210 = r436192 * r436203;
        double r436211 = 78.6994924154;
        double r436212 = r436210 + r436211;
        double r436213 = r436212 * r436192;
        double r436214 = 137.519416416;
        double r436215 = r436213 + r436214;
        double r436216 = r436215 * r436192;
        double r436217 = r436216 + r436199;
        double r436218 = r436217 * r436192;
        double r436219 = z;
        double r436220 = r436218 + r436219;
        double r436221 = 43.3400022514;
        double r436222 = r436192 + r436221;
        double r436223 = r436222 * r436192;
        double r436224 = 263.505074721;
        double r436225 = r436223 + r436224;
        double r436226 = cbrt(r436225);
        double r436227 = r436226 * r436226;
        double r436228 = r436226 * r436192;
        double r436229 = r436227 * r436228;
        double r436230 = 313.399215894;
        double r436231 = r436229 + r436230;
        double r436232 = r436231 * r436192;
        double r436233 = 47.066876606;
        double r436234 = r436232 + r436233;
        double r436235 = r436220 / r436234;
        double r436236 = r436209 * r436235;
        double r436237 = r436198 ? r436207 : r436236;
        return r436237;
}

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

Original27.2
Target0.4
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -9.094410887138144e+65 or 7.256469163412828e+43 < x

    1. Initial program 62.4

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

    2. Taylor expanded around inf 0.4

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

    if -9.094410887138144e+65 < x < 7.256469163412828e+43

    1. Initial program 1.7

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

    3. Applied *-un-lft-identity1.7

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    7. Applied add-cube-cbrt0.7

      \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\color{blue}{\left(\left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right) \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right)} \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

    8. Applied associate-*l*0.7

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -9.0944108871381443 \cdot 10^{65} \lor \neg \left(x \le 7.2564691634128278 \cdot 10^{43}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right) \cdot \left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot x\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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)))