Average Error: 16.0 → 9.1
Time: 24.9s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.607251433835726116796618339295063866918 \cdot 10^{-162}:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \left(\sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}\right)} \cdot \frac{y}{\sqrt[3]{a - t}}\\ \mathbf{elif}\;a \le 4.889529153193783306974873529274732222518 \cdot 10^{-116}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \left(\sqrt[3]{\frac{y}{\sqrt[3]{a - t}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{a - t}}}\right)\right) \cdot \sqrt[3]{\frac{y}{\sqrt[3]{a - t}}}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.607251433835726116796618339295063866918 \cdot 10^{-162}:\\
\;\;\;\;\left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \left(\sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}\right)} \cdot \frac{y}{\sqrt[3]{a - t}}\\

\mathbf{elif}\;a \le 4.889529153193783306974873529274732222518 \cdot 10^{-116}:\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r411255 = x;
        double r411256 = y;
        double r411257 = r411255 + r411256;
        double r411258 = z;
        double r411259 = t;
        double r411260 = r411258 - r411259;
        double r411261 = r411260 * r411256;
        double r411262 = a;
        double r411263 = r411262 - r411259;
        double r411264 = r411261 / r411263;
        double r411265 = r411257 - r411264;
        return r411265;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r411266 = a;
        double r411267 = -1.607251433835726e-162;
        bool r411268 = r411266 <= r411267;
        double r411269 = x;
        double r411270 = y;
        double r411271 = r411269 + r411270;
        double r411272 = z;
        double r411273 = t;
        double r411274 = r411272 - r411273;
        double r411275 = r411266 - r411273;
        double r411276 = cbrt(r411275);
        double r411277 = r411276 * r411276;
        double r411278 = cbrt(r411277);
        double r411279 = cbrt(r411276);
        double r411280 = r411278 * r411279;
        double r411281 = r411276 * r411280;
        double r411282 = r411274 / r411281;
        double r411283 = r411270 / r411276;
        double r411284 = r411282 * r411283;
        double r411285 = r411271 - r411284;
        double r411286 = 4.8895291531937833e-116;
        bool r411287 = r411266 <= r411286;
        double r411288 = r411272 * r411270;
        double r411289 = r411288 / r411273;
        double r411290 = r411289 + r411269;
        double r411291 = r411274 / r411277;
        double r411292 = cbrt(r411283);
        double r411293 = r411292 * r411292;
        double r411294 = r411291 * r411293;
        double r411295 = r411294 * r411292;
        double r411296 = r411271 - r411295;
        double r411297 = r411287 ? r411290 : r411296;
        double r411298 = r411268 ? r411285 : r411297;
        return r411298;
}

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

Original16.0
Target8.1
Herbie9.1
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.366497088939072697550672266103566343531 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.475429344457723334351036314450840066235 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -1.607251433835726e-162

    1. Initial program 14.6

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

    3. Applied add-cube-cbrt14.7

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

    4. Applied times-frac8.8

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

    6. Applied add-cube-cbrt8.8

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

    7. Applied cbrt-prod8.9

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

    if -1.607251433835726e-162 < a < 4.8895291531937833e-116

    1. Initial program 20.3

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

    2. Taylor expanded around inf 10.5

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

    if 4.8895291531937833e-116 < a

    1. Initial program 14.5

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

    3. Applied add-cube-cbrt14.6

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

    4. Applied times-frac8.4

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

    6. Applied add-cube-cbrt8.5

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

    7. Applied associate-*r*8.5

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

  4. Final simplification9.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.607251433835726116796618339295063866918 \cdot 10^{-162}:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \left(\sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}\right)} \cdot \frac{y}{\sqrt[3]{a - t}}\\ \mathbf{elif}\;a \le 4.889529153193783306974873529274732222518 \cdot 10^{-116}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \left(\sqrt[3]{\frac{y}{\sqrt[3]{a - t}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{a - t}}}\right)\right) \cdot \sqrt[3]{\frac{y}{\sqrt[3]{a - t}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(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-07) (- (+ y x) (* (* (- z t) (/ 1 (- 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 (- a t))) y))))

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