Average Error: 16.4 → 8.4
Time: 17.9s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -5.431542966296771230179073834641863315755 \cdot 10^{-176}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 6.923440804318688711918271167587033883785 \cdot 10^{-308}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\left(\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y}}{\sqrt{\sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt{\sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}}}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -5.431542966296771230179073834641863315755 \cdot 10^{-176}:\\
\;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\

\mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 6.923440804318688711918271167587033883785 \cdot 10^{-308}:\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r413354 = x;
        double r413355 = y;
        double r413356 = r413354 + r413355;
        double r413357 = z;
        double r413358 = t;
        double r413359 = r413357 - r413358;
        double r413360 = r413359 * r413355;
        double r413361 = a;
        double r413362 = r413361 - r413358;
        double r413363 = r413360 / r413362;
        double r413364 = r413356 - r413363;
        return r413364;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r413365 = x;
        double r413366 = y;
        double r413367 = r413365 + r413366;
        double r413368 = z;
        double r413369 = t;
        double r413370 = r413368 - r413369;
        double r413371 = r413370 * r413366;
        double r413372 = a;
        double r413373 = r413372 - r413369;
        double r413374 = r413371 / r413373;
        double r413375 = r413367 - r413374;
        double r413376 = -5.431542966296771e-176;
        bool r413377 = r413375 <= r413376;
        double r413378 = r413366 / r413373;
        double r413379 = r413370 * r413378;
        double r413380 = r413367 - r413379;
        double r413381 = 6.923440804318689e-308;
        bool r413382 = r413375 <= r413381;
        double r413383 = r413368 * r413366;
        double r413384 = r413383 / r413369;
        double r413385 = r413384 + r413365;
        double r413386 = cbrt(r413373);
        double r413387 = r413386 * r413386;
        double r413388 = r413370 / r413387;
        double r413389 = cbrt(r413366);
        double r413390 = cbrt(r413387);
        double r413391 = sqrt(r413390);
        double r413392 = r413389 / r413391;
        double r413393 = r413388 * r413392;
        double r413394 = r413393 * r413392;
        double r413395 = cbrt(r413386);
        double r413396 = r413389 / r413395;
        double r413397 = r413394 * r413396;
        double r413398 = r413367 - r413397;
        double r413399 = r413382 ? r413385 : r413398;
        double r413400 = r413377 ? r413380 : r413399;
        return r413400;
}

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
Herbie8.4
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.366497088939072697550672266103566343531 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.475429344457723334351036314450840066235 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (+ x y) (/ (* (- z t) y) (- a t))) < -5.431542966296771e-176

    1. Initial program 12.8

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

    3. Applied *-un-lft-identity12.8

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

    4. Applied times-frac7.7

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

    5. Simplified7.7

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

    if -5.431542966296771e-176 < (- (+ x y) (/ (* (- z t) y) (- a t))) < 6.923440804318689e-308

    1. Initial program 52.4

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

    2. Taylor expanded around inf 19.0

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

    if 6.923440804318689e-308 < (- (+ x y) (/ (* (- z t) y) (- a t)))

    1. Initial program 12.5

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

    3. Applied add-cube-cbrt12.7

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

    4. Applied times-frac7.1

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

    6. Applied add-cube-cbrt7.1

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

    7. Applied cbrt-prod7.1

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

    8. Applied add-cube-cbrt7.2

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

    9. Applied times-frac7.2

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

    10. Applied associate-*r*6.9

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

    12. Applied add-sqr-sqrt6.9

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

    13. Applied times-frac6.9

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

    14. Applied associate-*r*6.9

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

  4. Final simplification8.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -5.431542966296771230179073834641863315755 \cdot 10^{-176}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 6.923440804318688711918271167587033883785 \cdot 10^{-308}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\left(\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y}}{\sqrt{\sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt{\sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.47542934445772333e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y))))

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