Average Error: 16.4 → 9.2
Time: 24.3s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -9.386308465497509720467835630743993245633 \cdot 10^{-194}:\\ \;\;\;\;\left(x + y\right) - \left(\left(\left(\sqrt[3]{z - t} \cdot \left(\sqrt[3]{\sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{z - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{a - t}\right) \cdot y\\ \mathbf{elif}\;a \le 2.036739242643270041432560957083164280439 \cdot 10^{-146}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\frac{a - t}{y}}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -9.386308465497509720467835630743993245633 \cdot 10^{-194}:\\
\;\;\;\;\left(x + y\right) - \left(\left(\left(\sqrt[3]{z - t} \cdot \left(\sqrt[3]{\sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{z - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{a - t}\right) \cdot y\\

\mathbf{elif}\;a \le 2.036739242643270041432560957083164280439 \cdot 10^{-146}:\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

\mathbf{else}:\\
\;\;\;\;\left(x + y\right) - \frac{z - t}{\frac{a - t}{y}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r277390434 = x;
        double r277390435 = y;
        double r277390436 = r277390434 + r277390435;
        double r277390437 = z;
        double r277390438 = t;
        double r277390439 = r277390437 - r277390438;
        double r277390440 = r277390439 * r277390435;
        double r277390441 = a;
        double r277390442 = r277390441 - r277390438;
        double r277390443 = r277390440 / r277390442;
        double r277390444 = r277390436 - r277390443;
        return r277390444;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r277390445 = a;
        double r277390446 = -9.38630846549751e-194;
        bool r277390447 = r277390445 <= r277390446;
        double r277390448 = x;
        double r277390449 = y;
        double r277390450 = r277390448 + r277390449;
        double r277390451 = z;
        double r277390452 = t;
        double r277390453 = r277390451 - r277390452;
        double r277390454 = cbrt(r277390453);
        double r277390455 = cbrt(r277390454);
        double r277390456 = r277390455 * r277390455;
        double r277390457 = r277390454 * r277390456;
        double r277390458 = r277390457 * r277390455;
        double r277390459 = r277390445 - r277390452;
        double r277390460 = r277390454 / r277390459;
        double r277390461 = r277390458 * r277390460;
        double r277390462 = r277390461 * r277390449;
        double r277390463 = r277390450 - r277390462;
        double r277390464 = 2.03673924264327e-146;
        bool r277390465 = r277390445 <= r277390464;
        double r277390466 = r277390451 * r277390449;
        double r277390467 = r277390466 / r277390452;
        double r277390468 = r277390467 + r277390448;
        double r277390469 = r277390459 / r277390449;
        double r277390470 = r277390453 / r277390469;
        double r277390471 = r277390450 - r277390470;
        double r277390472 = r277390465 ? r277390468 : r277390471;
        double r277390473 = r277390447 ? r277390463 : r277390472;
        return r277390473;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.4
Target8.2
Herbie9.2
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.366497088939072697550672266103566343531 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.475429344457723334351036314450840066235 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -9.38630846549751e-194

    1. Initial program 15.5

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

    3. Applied associate-/l*10.0

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{\frac{a - t}{y}}}\]
    4. Using strategy rm

    5. Applied associate-/r/9.1

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{a - t} \cdot y}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity9.1

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

    8. Applied add-cube-cbrt9.3

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

    9. Applied times-frac9.3

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

    10. Simplified9.3

      \[\leadsto \left(x + y\right) - \left(\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \frac{\sqrt[3]{z - t}}{a - t}\right) \cdot y\]
    11. Using strategy rm

    12. Applied add-cube-cbrt9.3

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

    13. Applied associate-*r*9.3

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

    if -9.38630846549751e-194 < a < 2.03673924264327e-146

    1. Initial program 21.2

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

    2. Taylor expanded around inf 8.8

      \[\leadsto \color{blue}{\frac{z \cdot y}{t} + x}\]

    if 2.03673924264327e-146 < a

    1. Initial program 14.8

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

    3. Applied associate-/l*9.3

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{\frac{a - t}{y}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification9.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -9.386308465497509720467835630743993245633 \cdot 10^{-194}:\\ \;\;\;\;\left(x + y\right) - \left(\left(\left(\sqrt[3]{z - t} \cdot \left(\sqrt[3]{\sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{z - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{a - t}\right) \cdot y\\ \mathbf{elif}\;a \le 2.036739242643270041432560957083164280439 \cdot 10^{-146}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\frac{a - t}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-07) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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