Average Error: 29.0 → 4.9
Time: 16.5s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\
\;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r1018332 = x;
        double r1018333 = y;
        double r1018334 = z;
        double r1018335 = 3.13060547623;
        double r1018336 = r1018334 * r1018335;
        double r1018337 = 11.1667541262;
        double r1018338 = r1018336 + r1018337;
        double r1018339 = r1018338 * r1018334;
        double r1018340 = t;
        double r1018341 = r1018339 + r1018340;
        double r1018342 = r1018341 * r1018334;
        double r1018343 = a;
        double r1018344 = r1018342 + r1018343;
        double r1018345 = r1018344 * r1018334;
        double r1018346 = b;
        double r1018347 = r1018345 + r1018346;
        double r1018348 = r1018333 * r1018347;
        double r1018349 = 15.234687407;
        double r1018350 = r1018334 + r1018349;
        double r1018351 = r1018350 * r1018334;
        double r1018352 = 31.4690115749;
        double r1018353 = r1018351 + r1018352;
        double r1018354 = r1018353 * r1018334;
        double r1018355 = 11.9400905721;
        double r1018356 = r1018354 + r1018355;
        double r1018357 = r1018356 * r1018334;
        double r1018358 = 0.607771387771;
        double r1018359 = r1018357 + r1018358;
        double r1018360 = r1018348 / r1018359;
        double r1018361 = r1018332 + r1018360;
        return r1018361;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1018362 = z;
        double r1018363 = -1.7407917578078988e+36;
        bool r1018364 = r1018362 <= r1018363;
        double r1018365 = 10094.050046646438;
        bool r1018366 = r1018362 <= r1018365;
        double r1018367 = !r1018366;
        bool r1018368 = r1018364 || r1018367;
        double r1018369 = x;
        double r1018370 = 3.13060547623;
        double r1018371 = y;
        double r1018372 = r1018370 * r1018371;
        double r1018373 = t;
        double r1018374 = r1018373 * r1018371;
        double r1018375 = 2.0;
        double r1018376 = pow(r1018362, r1018375);
        double r1018377 = r1018374 / r1018376;
        double r1018378 = r1018372 + r1018377;
        double r1018379 = 36.527041698806414;
        double r1018380 = r1018371 / r1018362;
        double r1018381 = r1018379 * r1018380;
        double r1018382 = r1018378 - r1018381;
        double r1018383 = r1018369 + r1018382;
        double r1018384 = 15.234687407;
        double r1018385 = r1018362 + r1018384;
        double r1018386 = r1018385 * r1018362;
        double r1018387 = 31.4690115749;
        double r1018388 = r1018386 + r1018387;
        double r1018389 = r1018388 * r1018362;
        double r1018390 = 11.9400905721;
        double r1018391 = r1018389 + r1018390;
        double r1018392 = r1018391 * r1018362;
        double r1018393 = 0.607771387771;
        double r1018394 = r1018392 + r1018393;
        double r1018395 = r1018362 * r1018370;
        double r1018396 = 11.1667541262;
        double r1018397 = r1018395 + r1018396;
        double r1018398 = r1018397 * r1018362;
        double r1018399 = r1018398 + r1018373;
        double r1018400 = r1018399 * r1018362;
        double r1018401 = a;
        double r1018402 = r1018400 + r1018401;
        double r1018403 = r1018402 * r1018362;
        double r1018404 = b;
        double r1018405 = r1018403 + r1018404;
        double r1018406 = r1018394 / r1018405;
        double r1018407 = r1018371 / r1018406;
        double r1018408 = r1018369 + r1018407;
        double r1018409 = r1018368 ? r1018383 : r1018408;
        return r1018409;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.0
Target1.1
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.7407917578078988e+36 or 10094.050046646438 < z

    1. Initial program 57.3

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]

    2. Taylor expanded around inf 9.3

      \[\leadsto x + \color{blue}{\left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    if -1.7407917578078988e+36 < z < 10094.050046646438

    1. Initial program 0.7

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
    2. Using strategy rm

    3. Applied associate-/l*0.4

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))