AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Average Error: 26.4 → 20.4

Time: 7.7s

Precision: 64

Math

\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -6.3766260127845671 \cdot 10^{136}:\\ \;\;\;\;z - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le -7.5553554336738665 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \frac{1}{\frac{\frac{\left(x + t\right) + y}{b}}{y}}\\ \mathbf{elif}\;z \le -1.4420526235398581 \cdot 10^{-96}:\\ \;\;\;\;a - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le -5.2560627363695754 \cdot 10^{-198}:\\ \;\;\;\;\left(\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}\right) \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y} - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le -3.0011721532957425 \cdot 10^{-279}:\\ \;\;\;\;a - \frac{y}{\frac{\left(x + t\right) + y}{b}}\\ \mathbf{elif}\;z \le -8.4694881761373042 \cdot 10^{-290}:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\\ \mathbf{elif}\;z \le 1.829058436943914 \cdot 10^{-282}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(z, y, \mathsf{fma}\left(a, t, a \cdot y\right)\right)}{1}}{\left(x + t\right) + y} - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le 5.14388566176424308 \cdot 10^{-183}:\\ \;\;\;\;a - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le 1.1248158106174079 \cdot 10^{-25}:\\ \;\;\;\;\left(\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}\right) \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y} - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le 4.44861392459712437 \cdot 10^{27}:\\ \;\;\;\;a - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le 1.07400177686964386 \cdot 10^{86}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \frac{1}{\frac{\frac{\left(x + t\right) + y}{b}}{y}}\\ \mathbf{else}:\\ \;\;\;\;z - \frac{y}{\left(x + t\right) + y} \cdot b\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r871498 = x;
        double r871499 = y;
        double r871500 = r871498 + r871499;
        double r871501 = z;
        double r871502 = r871500 * r871501;
        double r871503 = t;
        double r871504 = r871503 + r871499;
        double r871505 = a;
        double r871506 = r871504 * r871505;
        double r871507 = r871502 + r871506;
        double r871508 = b;
        double r871509 = r871499 * r871508;
        double r871510 = r871507 - r871509;
        double r871511 = r871498 + r871503;
        double r871512 = r871511 + r871499;
        double r871513 = r871510 / r871512;
        return r871513;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r871514 = z;
        double r871515 = -6.376626012784567e+136;
        bool r871516 = r871514 <= r871515;
        double r871517 = y;
        double r871518 = x;
        double r871519 = t;
        double r871520 = r871518 + r871519;
        double r871521 = r871520 + r871517;
        double r871522 = r871517 / r871521;
        double r871523 = b;
        double r871524 = r871522 * r871523;
        double r871525 = r871514 - r871524;
        double r871526 = -7.5553554336738665e-50;
        bool r871527 = r871514 <= r871526;
        double r871528 = r871518 + r871517;
        double r871529 = r871519 + r871517;
        double r871530 = a;
        double r871531 = r871529 * r871530;
        double r871532 = fma(r871528, r871514, r871531);
        double r871533 = 1.0;
        double r871534 = r871532 / r871533;
        double r871535 = r871534 / r871521;
        double r871536 = r871521 / r871523;
        double r871537 = r871536 / r871517;
        double r871538 = r871533 / r871537;
        double r871539 = r871535 - r871538;
        double r871540 = -1.442052623539858e-96;
        bool r871541 = r871514 <= r871540;
        double r871542 = r871530 - r871524;
        double r871543 = -5.2560627363695754e-198;
        bool r871544 = r871514 <= r871543;
        double r871545 = cbrt(r871532);
        double r871546 = r871545 * r871545;
        double r871547 = r871545 / r871521;
        double r871548 = r871546 * r871547;
        double r871549 = r871548 - r871524;
        double r871550 = -3.0011721532957425e-279;
        bool r871551 = r871514 <= r871550;
        double r871552 = r871517 / r871536;
        double r871553 = r871530 - r871552;
        double r871554 = -8.469488176137304e-290;
        bool r871555 = r871514 <= r871554;
        double r871556 = r871528 * r871514;
        double r871557 = r871556 + r871531;
        double r871558 = r871517 * r871523;
        double r871559 = r871557 - r871558;
        double r871560 = r871533 / r871521;
        double r871561 = r871559 * r871560;
        double r871562 = 1.829058436943914e-282;
        bool r871563 = r871514 <= r871562;
        double r871564 = r871530 * r871517;
        double r871565 = fma(r871530, r871519, r871564);
        double r871566 = fma(r871514, r871517, r871565);
        double r871567 = r871566 / r871533;
        double r871568 = r871567 / r871521;
        double r871569 = r871568 - r871524;
        double r871570 = 5.143885661764243e-183;
        bool r871571 = r871514 <= r871570;
        double r871572 = 1.124815810617408e-25;
        bool r871573 = r871514 <= r871572;
        double r871574 = 4.4486139245971244e+27;
        bool r871575 = r871514 <= r871574;
        double r871576 = 1.0740017768696439e+86;
        bool r871577 = r871514 <= r871576;
        double r871578 = r871577 ? r871539 : r871525;
        double r871579 = r871575 ? r871542 : r871578;
        double r871580 = r871573 ? r871549 : r871579;
        double r871581 = r871571 ? r871542 : r871580;
        double r871582 = r871563 ? r871569 : r871581;
        double r871583 = r871555 ? r871561 : r871582;
        double r871584 = r871551 ? r871553 : r871583;
        double r871585 = r871544 ? r871549 : r871584;
        double r871586 = r871541 ? r871542 : r871585;
        double r871587 = r871527 ? r871539 : r871586;
        double r871588 = r871516 ? r871525 : r871587;
        return r871588;
}

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

Target

Original	26.4
Target	11.1
Herbie	20.4

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.5813117084150564 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.2285964308315609 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

1. Split input into 7 regimes

2. if z < -6.376626012784567e+136 or 1.0740017768696439e+86 < z

   1. Initial program 39.4

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
   2. Using strategy rm

   3. Applied div-sub 39.4

      \[\leadsto \color{blue}{\frac{\left(x + y\right) \cdot z + \left(t + y\right) \cdot a}{\left(x + t\right) + y} - \frac{y \cdot b}{\left(x + t\right) + y}}\]

   4. Simplified 39.4

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y}} - \frac{y \cdot b}{\left(x + t\right) + y}\]
   5. Using strategy rm

   6. Applied associate-/l* 39.7

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{b}}}\]
   7. Using strategy rm

   8. Applied associate-/r/ 38.8

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{y}{\left(x + t\right) + y} \cdot b}\]

   9. Taylor expanded around inf 24.4

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

   if -6.376626012784567e+136 < z < -7.5553554336738665e-50 or 4.4486139245971244e+27 < z < 1.0740017768696439e+86

   1. Initial program 24.2

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
   2. Using strategy rm

   3. Applied div-sub 24.2

      \[\leadsto \color{blue}{\frac{\left(x + y\right) \cdot z + \left(t + y\right) \cdot a}{\left(x + t\right) + y} - \frac{y \cdot b}{\left(x + t\right) + y}}\]

   4. Simplified 24.2

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y}} - \frac{y \cdot b}{\left(x + t\right) + y}\]
   5. Using strategy rm

   6. Applied associate-/l* 21.5

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{b}}}\]
   7. Using strategy rm

   8. Applied clear-num 21.5

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{1}{\frac{\frac{\left(x + t\right) + y}{b}}{y}}}\]

   if -7.5553554336738665e-50 < z < -1.442052623539858e-96 or 1.829058436943914e-282 < z < 5.143885661764243e-183 or 1.124815810617408e-25 < z < 4.4486139245971244e+27

   1. Initial program 19.1

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
   2. Using strategy rm

   3. Applied div-sub 19.1

      \[\leadsto \color{blue}{\frac{\left(x + y\right) \cdot z + \left(t + y\right) \cdot a}{\left(x + t\right) + y} - \frac{y \cdot b}{\left(x + t\right) + y}}\]

   4. Simplified 19.1

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y}} - \frac{y \cdot b}{\left(x + t\right) + y}\]
   5. Using strategy rm

   6. Applied associate-/l* 16.5

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{b}}}\]
   7. Using strategy rm

   8. Applied associate-/r/ 14.8

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{y}{\left(x + t\right) + y} \cdot b}\]

   9. Taylor expanded around 0 21.8

      \[\leadsto \color{blue}{a} - \frac{y}{\left(x + t\right) + y} \cdot b\]

   if -1.442052623539858e-96 < z < -5.2560627363695754e-198 or 5.143885661764243e-183 < z < 1.124815810617408e-25

   1. Initial program 17.7

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
   2. Using strategy rm

   3. Applied div-sub 17.7

      \[\leadsto \color{blue}{\frac{\left(x + y\right) \cdot z + \left(t + y\right) \cdot a}{\left(x + t\right) + y} - \frac{y \cdot b}{\left(x + t\right) + y}}\]

   4. Simplified 17.7

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y}} - \frac{y \cdot b}{\left(x + t\right) + y}\]
   5. Using strategy rm

   6. Applied associate-/l* 14.1

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{b}}}\]
   7. Using strategy rm

   8. Applied associate-/r/ 13.0

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{y}{\left(x + t\right) + y} \cdot b}\]
   9. Using strategy rm

   10. Applied *-un-lft-identity 13.0

       \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\color{blue}{1 \cdot \left(\left(x + t\right) + y\right)}} - \frac{y}{\left(x + t\right) + y} \cdot b\]

   11. Applied add-cube-cbrt 13.6

       \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}} \cdot \sqrt[3]{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}\right) \cdot \sqrt[3]{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}}}{1 \cdot \left(\left(x + t\right) + y\right)} - \frac{y}{\left(x + t\right) + y} \cdot b\]

   12. Applied times-frac 13.6

       \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}} \cdot \sqrt[3]{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}}{1} \cdot \frac{\sqrt[3]{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}}{\left(x + t\right) + y}} - \frac{y}{\left(x + t\right) + y} \cdot b\]

   13. Simplified 13.6

       \[\leadsto \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}\right)} \cdot \frac{\sqrt[3]{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}}{\left(x + t\right) + y} - \frac{y}{\left(x + t\right) + y} \cdot b\]

   14. Simplified 13.6

       \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}\right) \cdot \color{blue}{\frac{\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y}} - \frac{y}{\left(x + t\right) + y} \cdot b\]

   if -5.2560627363695754e-198 < z < -3.0011721532957425e-279

   1. Initial program 20.2

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
   2. Using strategy rm

   3. Applied div-sub 20.1

      \[\leadsto \color{blue}{\frac{\left(x + y\right) \cdot z + \left(t + y\right) \cdot a}{\left(x + t\right) + y} - \frac{y \cdot b}{\left(x + t\right) + y}}\]

   4. Simplified 20.1

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y}} - \frac{y \cdot b}{\left(x + t\right) + y}\]
   5. Using strategy rm

   6. Applied associate-/l* 16.2

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{b}}}\]

   7. Taylor expanded around 0 18.7

      \[\leadsto \color{blue}{a} - \frac{y}{\frac{\left(x + t\right) + y}{b}}\]

   if -3.0011721532957425e-279 < z < -8.469488176137304e-290

   1. Initial program 17.9

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
   2. Using strategy rm

   3. Applied div-inv 17.9

      \[\leadsto \color{blue}{\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}}\]

   if -8.469488176137304e-290 < z < 1.829058436943914e-282

   1. Initial program 18.4

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
   2. Using strategy rm

   3. Applied div-sub 18.3

      \[\leadsto \color{blue}{\frac{\left(x + y\right) \cdot z + \left(t + y\right) \cdot a}{\left(x + t\right) + y} - \frac{y \cdot b}{\left(x + t\right) + y}}\]

   4. Simplified 18.3

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y}} - \frac{y \cdot b}{\left(x + t\right) + y}\]
   5. Using strategy rm

   6. Applied associate-/l* 15.2

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{b}}}\]
   7. Using strategy rm

   8. Applied associate-/r/ 13.4

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \color{blue}{\frac{y}{\left(x + t\right) + y} \cdot b}\]

   9. Taylor expanded around inf 15.8

      \[\leadsto \frac{\frac{\color{blue}{z \cdot y + \left(a \cdot t + a \cdot y\right)}}{1}}{\left(x + t\right) + y} - \frac{y}{\left(x + t\right) + y} \cdot b\]

   10. Simplified 15.8

       \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(z, y, \mathsf{fma}\left(a, t, a \cdot y\right)\right)}}{1}}{\left(x + t\right) + y} - \frac{y}{\left(x + t\right) + y} \cdot b\]
3. Recombined 7 regimes into one program.

4. Final simplification 20.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.3766260127845671 \cdot 10^{136}:\\ \;\;\;\;z - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le -7.5553554336738665 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \frac{1}{\frac{\frac{\left(x + t\right) + y}{b}}{y}}\\ \mathbf{elif}\;z \le -1.4420526235398581 \cdot 10^{-96}:\\ \;\;\;\;a - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le -5.2560627363695754 \cdot 10^{-198}:\\ \;\;\;\;\left(\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}\right) \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y} - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le -3.0011721532957425 \cdot 10^{-279}:\\ \;\;\;\;a - \frac{y}{\frac{\left(x + t\right) + y}{b}}\\ \mathbf{elif}\;z \le -8.4694881761373042 \cdot 10^{-290}:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\\ \mathbf{elif}\;z \le 1.829058436943914 \cdot 10^{-282}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(z, y, \mathsf{fma}\left(a, t, a \cdot y\right)\right)}{1}}{\left(x + t\right) + y} - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le 5.14388566176424308 \cdot 10^{-183}:\\ \;\;\;\;a - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le 1.1248158106174079 \cdot 10^{-25}:\\ \;\;\;\;\left(\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}\right) \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y} - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le 4.44861392459712437 \cdot 10^{27}:\\ \;\;\;\;a - \frac{y}{\left(x + t\right) + y} \cdot b\\ \mathbf{elif}\;z \le 1.07400177686964386 \cdot 10^{86}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{1}}{\left(x + t\right) + y} - \frac{1}{\frac{\frac{\left(x + t\right) + y}{b}}{y}}\\ \mathbf{else}:\\ \;\;\;\;z - \frac{y}{\left(x + t\right) + y} \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b)))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))