Average Error: 19.8 → 0.1
Time: 24.4s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.066154477353578 \cdot 10^{+45}:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{\frac{z \cdot z}{y}}\right)\right) + x\\ \mathbf{elif}\;z \le 566049.5164958073:\\ \;\;\;\;y \cdot \frac{0.279195317918525 + \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right) \cdot z}{z \cdot \left(6.012459259764103 + z\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{\frac{z \cdot z}{y}}\right)\right) + x\\ \end{array}\]
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 \le -6.066154477353578 \cdot 10^{+45}:\\
\;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{\frac{z \cdot z}{y}}\right)\right) + x\\

\mathbf{elif}\;z \le 566049.5164958073:\\
\;\;\;\;y \cdot \frac{0.279195317918525 + \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right) \cdot z}{z \cdot \left(6.012459259764103 + z\right) + 3.350343815022304} + x\\

\mathbf{else}:\\
\;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{\frac{z \cdot z}{y}}\right)\right) + x\\

\end{array}
double f(double x, double y, double z) {
        double r16899157 = x;
        double r16899158 = y;
        double r16899159 = z;
        double r16899160 = 0.0692910599291889;
        double r16899161 = r16899159 * r16899160;
        double r16899162 = 0.4917317610505968;
        double r16899163 = r16899161 + r16899162;
        double r16899164 = r16899163 * r16899159;
        double r16899165 = 0.279195317918525;
        double r16899166 = r16899164 + r16899165;
        double r16899167 = r16899158 * r16899166;
        double r16899168 = 6.012459259764103;
        double r16899169 = r16899159 + r16899168;
        double r16899170 = r16899169 * r16899159;
        double r16899171 = 3.350343815022304;
        double r16899172 = r16899170 + r16899171;
        double r16899173 = r16899167 / r16899172;
        double r16899174 = r16899157 + r16899173;
        return r16899174;
}
↓
double f(double x, double y, double z) {
        double r16899175 = z;
        double r16899176 = -6.066154477353578e+45;
        bool r16899177 = r16899175 <= r16899176;
        double r16899178 = 0.0692910599291889;
        double r16899179 = y;
        double r16899180 = r16899178 * r16899179;
        double r16899181 = 0.07512208616047561;
        double r16899182 = r16899179 / r16899175;
        double r16899183 = r16899181 * r16899182;
        double r16899184 = 0.40462203869992125;
        double r16899185 = r16899175 * r16899175;
        double r16899186 = r16899185 / r16899179;
        double r16899187 = r16899184 / r16899186;
        double r16899188 = r16899183 - r16899187;
        double r16899189 = r16899180 + r16899188;
        double r16899190 = x;
        double r16899191 = r16899189 + r16899190;
        double r16899192 = 566049.5164958073;
        bool r16899193 = r16899175 <= r16899192;
        double r16899194 = 0.279195317918525;
        double r16899195 = 0.4917317610505968;
        double r16899196 = r16899178 * r16899175;
        double r16899197 = r16899195 + r16899196;
        double r16899198 = r16899197 * r16899175;
        double r16899199 = r16899194 + r16899198;
        double r16899200 = 6.012459259764103;
        double r16899201 = r16899200 + r16899175;
        double r16899202 = r16899175 * r16899201;
        double r16899203 = 3.350343815022304;
        double r16899204 = r16899202 + r16899203;
        double r16899205 = r16899199 / r16899204;
        double r16899206 = r16899179 * r16899205;
        double r16899207 = r16899206 + r16899190;
        double r16899208 = r16899193 ? r16899207 : r16899191;
        double r16899209 = r16899177 ? r16899191 : r16899208;
        return r16899209;
}

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

Original19.8
Target0.1
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.652456675:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.066154477353578e+45 or 566049.5164958073 < z

    1. Initial program 42.1

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

    3. Applied *-un-lft-identity42.1

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

    4. Applied times-frac34.2

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

    5. Simplified34.2

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

    6. Taylor expanded around inf 0.0

      \[\leadsto x + \color{blue}{\left(\left(0.0692910599291889 \cdot y + 0.07512208616047561 \cdot \frac{y}{z}\right) - 0.40462203869992125 \cdot \frac{y}{{z}^{2}}\right)}\]

    7. Simplified0.0

      \[\leadsto x + \color{blue}{\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{\frac{z \cdot z}{y}}\right)\right)}\]

    if -6.066154477353578e+45 < z < 566049.5164958073

    1. Initial program 0.5

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

    3. Applied *-un-lft-identity0.5

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.066154477353578 \cdot 10^{+45}:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{\frac{z \cdot z}{y}}\right)\right) + x\\ \mathbf{elif}\;z \le 566049.5164958073:\\ \;\;\;\;y \cdot \frac{0.279195317918525 + \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right) \cdot z}{z \cdot \left(6.012459259764103 + z\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{\frac{z \cdot z}{y}}\right)\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"

  :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 (+ (* (+ 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))))