Average Error: 16.4 → 9.5
Time: 22.9s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -7.132241680778371439277305115805168064789 \cdot 10^{-88}:\\ \;\;\;\;\left(x + y\right) - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}} \cdot \left(\frac{y}{\sqrt[3]{\sqrt[3]{a - t}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right)\\ \mathbf{elif}\;a \le 1.027335171522283942303792214737225884323 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}} \cdot \left(\frac{y}{\sqrt[3]{\sqrt[3]{a - t}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right)\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -7.132241680778371439277305115805168064789 \cdot 10^{-88}:\\
\;\;\;\;\left(x + y\right) - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}} \cdot \left(\frac{y}{\sqrt[3]{\sqrt[3]{a - t}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right)\\

\mathbf{elif}\;a \le 1.027335171522283942303792214737225884323 \cdot 10^{-108}:\\
\;\;\;\;x + \frac{z \cdot y}{t}\\

\mathbf{else}:\\
\;\;\;\;\left(x + y\right) - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}} \cdot \left(\frac{y}{\sqrt[3]{\sqrt[3]{a - t}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r38243434 = x;
        double r38243435 = y;
        double r38243436 = r38243434 + r38243435;
        double r38243437 = z;
        double r38243438 = t;
        double r38243439 = r38243437 - r38243438;
        double r38243440 = r38243439 * r38243435;
        double r38243441 = a;
        double r38243442 = r38243441 - r38243438;
        double r38243443 = r38243440 / r38243442;
        double r38243444 = r38243436 - r38243443;
        return r38243444;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r38243445 = a;
        double r38243446 = -7.132241680778371e-88;
        bool r38243447 = r38243445 <= r38243446;
        double r38243448 = x;
        double r38243449 = y;
        double r38243450 = r38243448 + r38243449;
        double r38243451 = z;
        double r38243452 = t;
        double r38243453 = r38243451 - r38243452;
        double r38243454 = cbrt(r38243453);
        double r38243455 = r38243454 * r38243454;
        double r38243456 = r38243445 - r38243452;
        double r38243457 = cbrt(r38243456);
        double r38243458 = cbrt(r38243457);
        double r38243459 = r38243458 * r38243458;
        double r38243460 = r38243455 / r38243459;
        double r38243461 = r38243449 / r38243458;
        double r38243462 = r38243457 * r38243457;
        double r38243463 = r38243454 / r38243462;
        double r38243464 = r38243461 * r38243463;
        double r38243465 = r38243460 * r38243464;
        double r38243466 = r38243450 - r38243465;
        double r38243467 = 1.027335171522284e-108;
        bool r38243468 = r38243445 <= r38243467;
        double r38243469 = r38243451 * r38243449;
        double r38243470 = r38243469 / r38243452;
        double r38243471 = r38243448 + r38243470;
        double r38243472 = r38243468 ? r38243471 : r38243466;
        double r38243473 = r38243447 ? r38243466 : r38243472;
        return r38243473;
}

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
Target8.6
Herbie9.5
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.366497088939072697550672266103566343531 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.475429344457723334351036314450840066235 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -7.132241680778371e-88 or 1.027335171522284e-108 < a

    1. Initial program 14.7

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

    3. Applied add-cube-cbrt14.8

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

    4. Applied times-frac8.3

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

    6. Applied add-cube-cbrt8.3

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

    7. Applied *-un-lft-identity8.3

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

    8. Applied times-frac8.3

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

    9. Applied associate-*r*8.2

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

    10. Simplified8.2

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

    12. Applied add-cube-cbrt8.3

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

    13. Applied times-frac8.3

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

    14. Applied associate-*l*8.2

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

    if -7.132241680778371e-88 < a < 1.027335171522284e-108

    1. Initial program 20.3

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

    2. Taylor expanded around inf 12.3

      \[\leadsto \color{blue}{\frac{z \cdot y}{t} + x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification9.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -7.132241680778371439277305115805168064789 \cdot 10^{-88}:\\ \;\;\;\;\left(x + y\right) - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}} \cdot \left(\frac{y}{\sqrt[3]{\sqrt[3]{a - t}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right)\\ \mathbf{elif}\;a \le 1.027335171522283942303792214737225884323 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}} \cdot \left(\frac{y}{\sqrt[3]{\sqrt[3]{a - t}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(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))))