Average Error: 20.1 → 0.2
Time: 27.0s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4230301041346655513100977098981376:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \mathbf{elif}\;z \le 203544506.3211925327777862548828125:\\ \;\;\;\;x + \frac{y}{\sqrt{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}} \cdot \frac{0.2791953179185249767080279070796677842736 + \left(0.4917317610505967939715787906607147306204 + z \cdot 0.06929105992918889456166908757950295694172\right) \cdot z}{\sqrt{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4230301041346655513100977098981376:\\
\;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\

\mathbf{elif}\;z \le 203544506.3211925327777862548828125:\\
\;\;\;\;x + \frac{y}{\sqrt{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}} \cdot \frac{0.2791953179185249767080279070796677842736 + \left(0.4917317610505967939715787906607147306204 + z \cdot 0.06929105992918889456166908757950295694172\right) \cdot z}{\sqrt{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}}\\

\mathbf{else}:\\
\;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\

\end{array}
double f(double x, double y, double z) {
        double r22430126 = x;
        double r22430127 = y;
        double r22430128 = z;
        double r22430129 = 0.0692910599291889;
        double r22430130 = r22430128 * r22430129;
        double r22430131 = 0.4917317610505968;
        double r22430132 = r22430130 + r22430131;
        double r22430133 = r22430132 * r22430128;
        double r22430134 = 0.279195317918525;
        double r22430135 = r22430133 + r22430134;
        double r22430136 = r22430127 * r22430135;
        double r22430137 = 6.012459259764103;
        double r22430138 = r22430128 + r22430137;
        double r22430139 = r22430138 * r22430128;
        double r22430140 = 3.350343815022304;
        double r22430141 = r22430139 + r22430140;
        double r22430142 = r22430136 / r22430141;
        double r22430143 = r22430126 + r22430142;
        return r22430143;
}
↓
double f(double x, double y, double z) {
        double r22430144 = z;
        double r22430145 = -4.2303010413466555e+33;
        bool r22430146 = r22430144 <= r22430145;
        double r22430147 = 0.0692910599291889;
        double r22430148 = y;
        double r22430149 = r22430147 * r22430148;
        double r22430150 = r22430148 / r22430144;
        double r22430151 = 0.07512208616047561;
        double r22430152 = r22430150 * r22430151;
        double r22430153 = r22430149 + r22430152;
        double r22430154 = x;
        double r22430155 = r22430153 + r22430154;
        double r22430156 = 203544506.32119253;
        bool r22430157 = r22430144 <= r22430156;
        double r22430158 = 3.350343815022304;
        double r22430159 = 6.012459259764103;
        double r22430160 = r22430159 + r22430144;
        double r22430161 = r22430160 * r22430144;
        double r22430162 = r22430158 + r22430161;
        double r22430163 = sqrt(r22430162);
        double r22430164 = r22430148 / r22430163;
        double r22430165 = 0.279195317918525;
        double r22430166 = 0.4917317610505968;
        double r22430167 = r22430144 * r22430147;
        double r22430168 = r22430166 + r22430167;
        double r22430169 = r22430168 * r22430144;
        double r22430170 = r22430165 + r22430169;
        double r22430171 = r22430170 / r22430163;
        double r22430172 = r22430164 * r22430171;
        double r22430173 = r22430154 + r22430172;
        double r22430174 = r22430157 ? r22430173 : r22430155;
        double r22430175 = r22430146 ? r22430155 : r22430174;
        return r22430175;
}

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

Original20.1
Target0.1
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.6524566747248172760009765625:\\ \;\;\;\;\left(\frac{0.07512208616047560960637952121032867580652}{z} + 0.06929105992918889456166908757950295694172\right) \cdot y - \left(\frac{0.4046220386999212492717958866705885156989 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 657611897278737678336:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047560960637952121032867580652}{z} + 0.06929105992918889456166908757950295694172\right) \cdot y - \left(\frac{0.4046220386999212492717958866705885156989 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.2303010413466555e+33 or 203544506.32119253 < z

    1. Initial program 42.7

      \[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]

    2. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{x + \left(0.07512208616047560960637952121032867580652 \cdot \frac{y}{z} + 0.06929105992918889456166908757950295694172 \cdot y\right)}\]

    if -4.2303010413466555e+33 < z < 203544506.32119253

    1. Initial program 0.3

      \[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt0.7

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\color{blue}{\sqrt{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084} \cdot \sqrt{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}}}\]

    4. Applied times-frac0.3

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}} \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\sqrt{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4230301041346655513100977098981376:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \mathbf{elif}\;z \le 203544506.3211925327777862548828125:\\ \;\;\;\;x + \frac{y}{\sqrt{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}} \cdot \frac{0.2791953179185249767080279070796677842736 + \left(0.4917317610505967939715787906607147306204 + z \cdot 0.06929105992918889456166908757950295694172\right) \cdot z}{\sqrt{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(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)) (/ 1.0 (+ (* (+ 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))))