Average Error: 19.8 → 0.1
Time: 23.5s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.066154477353578 \cdot 10^{+45}:\\ \;\;\;\;\left(y \cdot 0.0692910599291889 + \left(\frac{y \cdot 0.07512208616047561}{z} - \frac{y \cdot 0.40462203869992125}{z \cdot z}\right)\right) + x\\ \mathbf{elif}\;z \le 566049.5164958073:\\ \;\;\;\;\frac{0.279195317918525 + \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right) \cdot z}{z \cdot \left(6.012459259764103 + z\right) + 3.350343815022304} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.0692910599291889 + \left(\frac{y \cdot 0.07512208616047561}{z} - \frac{y \cdot 0.40462203869992125}{z \cdot z}\right)\right) + x\\ \end{array}\]
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(y \cdot 0.0692910599291889 + \left(\frac{y \cdot 0.07512208616047561}{z} - \frac{y \cdot 0.40462203869992125}{z \cdot z}\right)\right) + x\\

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

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

\end{array}
double f(double x, double y, double z) {
        double r19532263 = x;
        double r19532264 = y;
        double r19532265 = z;
        double r19532266 = 0.0692910599291889;
        double r19532267 = r19532265 * r19532266;
        double r19532268 = 0.4917317610505968;
        double r19532269 = r19532267 + r19532268;
        double r19532270 = r19532269 * r19532265;
        double r19532271 = 0.279195317918525;
        double r19532272 = r19532270 + r19532271;
        double r19532273 = r19532264 * r19532272;
        double r19532274 = 6.012459259764103;
        double r19532275 = r19532265 + r19532274;
        double r19532276 = r19532275 * r19532265;
        double r19532277 = 3.350343815022304;
        double r19532278 = r19532276 + r19532277;
        double r19532279 = r19532273 / r19532278;
        double r19532280 = r19532263 + r19532279;
        return r19532280;
}
↓
double f(double x, double y, double z) {
        double r19532281 = z;
        double r19532282 = -6.066154477353578e+45;
        bool r19532283 = r19532281 <= r19532282;
        double r19532284 = y;
        double r19532285 = 0.0692910599291889;
        double r19532286 = r19532284 * r19532285;
        double r19532287 = 0.07512208616047561;
        double r19532288 = r19532284 * r19532287;
        double r19532289 = r19532288 / r19532281;
        double r19532290 = 0.40462203869992125;
        double r19532291 = r19532284 * r19532290;
        double r19532292 = r19532281 * r19532281;
        double r19532293 = r19532291 / r19532292;
        double r19532294 = r19532289 - r19532293;
        double r19532295 = r19532286 + r19532294;
        double r19532296 = x;
        double r19532297 = r19532295 + r19532296;
        double r19532298 = 566049.5164958073;
        bool r19532299 = r19532281 <= r19532298;
        double r19532300 = 0.279195317918525;
        double r19532301 = 0.4917317610505968;
        double r19532302 = r19532285 * r19532281;
        double r19532303 = r19532301 + r19532302;
        double r19532304 = r19532303 * r19532281;
        double r19532305 = r19532300 + r19532304;
        double r19532306 = 6.012459259764103;
        double r19532307 = r19532306 + r19532281;
        double r19532308 = r19532281 * r19532307;
        double r19532309 = 3.350343815022304;
        double r19532310 = r19532308 + r19532309;
        double r19532311 = r19532305 / r19532310;
        double r19532312 = r19532311 * r19532284;
        double r19532313 = r19532312 + r19532296;
        double r19532314 = r19532299 ? r19532313 : r19532297;
        double r19532315 = r19532283 ? r19532297 : r19532314;
        return r19532315;
}

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 add-sqr-sqrt42.1

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

    4. Applied times-frac34.4

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

    5. Taylor expanded around inf 0.0

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

    6. Simplified0.0

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

    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

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

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))))