Average Error: 26.5 → 0.7
Time: 22.6s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -610174964095929189082170612776960 \lor \neg \left(x \le 44829074708994786496638441807151104\right):\\ \;\;\;\;\left(4.16438922227999963610045597306452691555 \cdot x - 110.1139242984810948655649553984403610229\right) + \frac{\frac{y}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{z + \left(x \cdot \left(x \cdot \left(4.16438922227999963610045597306452691555 \cdot x + 78.69949241540000173245061887428164482117\right) + 137.5194164160000127594685181975364685059\right) + y\right) \cdot x}{\left(313.3992158940000081202015280723571777344 + \left(\sqrt{x \cdot \left(43.3400022514000013984514225739985704422 + x\right) + 263.5050747210000281484099105000495910645} \cdot x\right) \cdot \sqrt{x \cdot \left(43.3400022514000013984514225739985704422 + x\right) + 263.5050747210000281484099105000495910645}\right) \cdot x + 47.06687660600000100430406746454536914825}\\ \end{array}\]
\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}
↓
\begin{array}{l}
\mathbf{if}\;x \le -610174964095929189082170612776960 \lor \neg \left(x \le 44829074708994786496638441807151104\right):\\
\;\;\;\;\left(4.16438922227999963610045597306452691555 \cdot x - 110.1139242984810948655649553984403610229\right) + \frac{\frac{y}{x}}{x}\\

\mathbf{else}:\\
\;\;\;\;\left(x - 2\right) \cdot \frac{z + \left(x \cdot \left(x \cdot \left(4.16438922227999963610045597306452691555 \cdot x + 78.69949241540000173245061887428164482117\right) + 137.5194164160000127594685181975364685059\right) + y\right) \cdot x}{\left(313.3992158940000081202015280723571777344 + \left(\sqrt{x \cdot \left(43.3400022514000013984514225739985704422 + x\right) + 263.5050747210000281484099105000495910645} \cdot x\right) \cdot \sqrt{x \cdot \left(43.3400022514000013984514225739985704422 + x\right) + 263.5050747210000281484099105000495910645}\right) \cdot x + 47.06687660600000100430406746454536914825}\\

\end{array}
double f(double x, double y, double z) {
        double r295135 = x;
        double r295136 = 2.0;
        double r295137 = r295135 - r295136;
        double r295138 = 4.16438922228;
        double r295139 = r295135 * r295138;
        double r295140 = 78.6994924154;
        double r295141 = r295139 + r295140;
        double r295142 = r295141 * r295135;
        double r295143 = 137.519416416;
        double r295144 = r295142 + r295143;
        double r295145 = r295144 * r295135;
        double r295146 = y;
        double r295147 = r295145 + r295146;
        double r295148 = r295147 * r295135;
        double r295149 = z;
        double r295150 = r295148 + r295149;
        double r295151 = r295137 * r295150;
        double r295152 = 43.3400022514;
        double r295153 = r295135 + r295152;
        double r295154 = r295153 * r295135;
        double r295155 = 263.505074721;
        double r295156 = r295154 + r295155;
        double r295157 = r295156 * r295135;
        double r295158 = 313.399215894;
        double r295159 = r295157 + r295158;
        double r295160 = r295159 * r295135;
        double r295161 = 47.066876606;
        double r295162 = r295160 + r295161;
        double r295163 = r295151 / r295162;
        return r295163;
}
↓
double f(double x, double y, double z) {
        double r295164 = x;
        double r295165 = -6.101749640959292e+32;
        bool r295166 = r295164 <= r295165;
        double r295167 = 4.482907470899479e+34;
        bool r295168 = r295164 <= r295167;
        double r295169 = !r295168;
        bool r295170 = r295166 || r295169;
        double r295171 = 4.16438922228;
        double r295172 = r295171 * r295164;
        double r295173 = 110.1139242984811;
        double r295174 = r295172 - r295173;
        double r295175 = y;
        double r295176 = r295175 / r295164;
        double r295177 = r295176 / r295164;
        double r295178 = r295174 + r295177;
        double r295179 = 2.0;
        double r295180 = r295164 - r295179;
        double r295181 = z;
        double r295182 = 78.6994924154;
        double r295183 = r295172 + r295182;
        double r295184 = r295164 * r295183;
        double r295185 = 137.519416416;
        double r295186 = r295184 + r295185;
        double r295187 = r295164 * r295186;
        double r295188 = r295187 + r295175;
        double r295189 = r295188 * r295164;
        double r295190 = r295181 + r295189;
        double r295191 = 313.399215894;
        double r295192 = 43.3400022514;
        double r295193 = r295192 + r295164;
        double r295194 = r295164 * r295193;
        double r295195 = 263.505074721;
        double r295196 = r295194 + r295195;
        double r295197 = sqrt(r295196);
        double r295198 = r295197 * r295164;
        double r295199 = r295198 * r295197;
        double r295200 = r295191 + r295199;
        double r295201 = r295200 * r295164;
        double r295202 = 47.066876606;
        double r295203 = r295201 + r295202;
        double r295204 = r295190 / r295203;
        double r295205 = r295180 * r295204;
        double r295206 = r295170 ? r295178 : r295205;
        return r295206;
}

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
Target0.5
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;x \lt -3.326128725870004842699683658678411714981 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \mathbf{elif}\;x \lt 9.429991714554672672712552870340896976735 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.5050747210000281484099105000495910645 \cdot x + \left(43.3400022514000013984514225739985704422 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -6.101749640959292e+32 or 4.482907470899479e+34 < x

    1. Initial program 58.6

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\]

    2. Simplified54.7

      \[\leadsto \color{blue}{\frac{x - 2}{x \cdot \left(313.3992158940000081202015280723571777344 + \left(263.5050747210000281484099105000495910645 + x \cdot \left(43.3400022514000013984514225739985704422 + x\right)\right) \cdot x\right) + 47.06687660600000100430406746454536914825} \cdot \left(\left(y + \left(x \cdot \left(78.69949241540000173245061887428164482117 + 4.16438922227999963610045597306452691555 \cdot x\right) + 137.5194164160000127594685181975364685059\right) \cdot x\right) \cdot x + z\right)}\]

    3. Taylor expanded around inf 1.1

      \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229}\]

    4. Simplified1.1

      \[\leadsto \color{blue}{\left(4.16438922227999963610045597306452691555 \cdot x - 110.1139242984810948655649553984403610229\right) + \frac{\frac{y}{x}}{x}}\]

    if -6.101749640959292e+32 < x < 4.482907470899479e+34

    1. Initial program 0.7

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\]

    2. Simplified0.7

      \[\leadsto \color{blue}{\frac{x - 2}{x \cdot \left(313.3992158940000081202015280723571777344 + \left(263.5050747210000281484099105000495910645 + x \cdot \left(43.3400022514000013984514225739985704422 + x\right)\right) \cdot x\right) + 47.06687660600000100430406746454536914825} \cdot \left(\left(y + \left(x \cdot \left(78.69949241540000173245061887428164482117 + 4.16438922227999963610045597306452691555 \cdot x\right) + 137.5194164160000127594685181975364685059\right) \cdot x\right) \cdot x + z\right)}\]
    3. Using strategy rm

    4. Applied div-inv0.7

      \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot \frac{1}{x \cdot \left(313.3992158940000081202015280723571777344 + \left(263.5050747210000281484099105000495910645 + x \cdot \left(43.3400022514000013984514225739985704422 + x\right)\right) \cdot x\right) + 47.06687660600000100430406746454536914825}\right)} \cdot \left(\left(y + \left(x \cdot \left(78.69949241540000173245061887428164482117 + 4.16438922227999963610045597306452691555 \cdot x\right) + 137.5194164160000127594685181975364685059\right) \cdot x\right) \cdot x + z\right)\]

    5. Applied associate-*l*0.7

      \[\leadsto \color{blue}{\left(x - 2\right) \cdot \left(\frac{1}{x \cdot \left(313.3992158940000081202015280723571777344 + \left(263.5050747210000281484099105000495910645 + x \cdot \left(43.3400022514000013984514225739985704422 + x\right)\right) \cdot x\right) + 47.06687660600000100430406746454536914825} \cdot \left(\left(y + \left(x \cdot \left(78.69949241540000173245061887428164482117 + 4.16438922227999963610045597306452691555 \cdot x\right) + 137.5194164160000127594685181975364685059\right) \cdot x\right) \cdot x + z\right)\right)}\]

    6. Simplified0.3

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(4.16438922227999963610045597306452691555 \cdot x + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}{47.06687660600000100430406746454536914825 + \left(313.3992158940000081202015280723571777344 + \left(\left(43.3400022514000013984514225739985704422 + x\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x\right) \cdot x}}\]
    7. Using strategy rm

    8. Applied add-sqr-sqrt0.4

      \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(4.16438922227999963610045597306452691555 \cdot x + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}{47.06687660600000100430406746454536914825 + \left(313.3992158940000081202015280723571777344 + \color{blue}{\left(\sqrt{\left(43.3400022514000013984514225739985704422 + x\right) \cdot x + 263.5050747210000281484099105000495910645} \cdot \sqrt{\left(43.3400022514000013984514225739985704422 + x\right) \cdot x + 263.5050747210000281484099105000495910645}\right)} \cdot x\right) \cdot x}\]

    9. Applied associate-*l*0.4

      \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(4.16438922227999963610045597306452691555 \cdot x + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}{47.06687660600000100430406746454536914825 + \left(313.3992158940000081202015280723571777344 + \color{blue}{\sqrt{\left(43.3400022514000013984514225739985704422 + x\right) \cdot x + 263.5050747210000281484099105000495910645} \cdot \left(\sqrt{\left(43.3400022514000013984514225739985704422 + x\right) \cdot x + 263.5050747210000281484099105000495910645} \cdot x\right)}\right) \cdot x}\]

    10. Simplified0.4

      \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(4.16438922227999963610045597306452691555 \cdot x + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}{47.06687660600000100430406746454536914825 + \left(313.3992158940000081202015280723571777344 + \sqrt{\left(43.3400022514000013984514225739985704422 + x\right) \cdot x + 263.5050747210000281484099105000495910645} \cdot \color{blue}{\left(\sqrt{263.5050747210000281484099105000495910645 + \left(43.3400022514000013984514225739985704422 + x\right) \cdot x} \cdot x\right)}\right) \cdot x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -610174964095929189082170612776960 \lor \neg \left(x \le 44829074708994786496638441807151104\right):\\ \;\;\;\;\left(4.16438922227999963610045597306452691555 \cdot x - 110.1139242984810948655649553984403610229\right) + \frac{\frac{y}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{z + \left(x \cdot \left(x \cdot \left(4.16438922227999963610045597306452691555 \cdot x + 78.69949241540000173245061887428164482117\right) + 137.5194164160000127594685181975364685059\right) + y\right) \cdot x}{\left(313.3992158940000081202015280723571777344 + \left(\sqrt{x \cdot \left(43.3400022514000013984514225739985704422 + x\right) + 263.5050747210000281484099105000495910645} \cdot x\right) \cdot \sqrt{x \cdot \left(43.3400022514000013984514225739985704422 + x\right) + 263.5050747210000281484099105000495910645}\right) \cdot x + 47.06687660600000100430406746454536914825}\\ \end{array}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2.0) 1.0) (/ (+ (* (+ (* (+ (* (+ (* 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 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))