Average Error: 16.5 → 8.4
Time: 6.2s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -4.633029569659858 \cdot 10^{-238} \lor \neg \left(\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 2.246342234530279 \cdot 10^{-220}\right):\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \end{array}\]
\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 -4.633029569659858 \cdot 10^{-238} \lor \neg \left(\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 2.246342234530279 \cdot 10^{-220}\right):\\
\;\;\;\;\left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r550259 = x;
        double r550260 = y;
        double r550261 = r550259 + r550260;
        double r550262 = z;
        double r550263 = t;
        double r550264 = r550262 - r550263;
        double r550265 = r550264 * r550260;
        double r550266 = a;
        double r550267 = r550266 - r550263;
        double r550268 = r550265 / r550267;
        double r550269 = r550261 - r550268;
        return r550269;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r550270 = x;
        double r550271 = y;
        double r550272 = r550270 + r550271;
        double r550273 = z;
        double r550274 = t;
        double r550275 = r550273 - r550274;
        double r550276 = r550275 * r550271;
        double r550277 = a;
        double r550278 = r550277 - r550274;
        double r550279 = r550276 / r550278;
        double r550280 = r550272 - r550279;
        double r550281 = -4.633029569659858e-238;
        bool r550282 = r550280 <= r550281;
        double r550283 = 2.2463422345302793e-220;
        bool r550284 = r550280 <= r550283;
        double r550285 = !r550284;
        bool r550286 = r550282 || r550285;
        double r550287 = cbrt(r550278);
        double r550288 = r550287 * r550287;
        double r550289 = r550275 / r550288;
        double r550290 = r550271 / r550287;
        double r550291 = r550289 * r550290;
        double r550292 = r550272 - r550291;
        double r550293 = r550273 * r550271;
        double r550294 = r550293 / r550274;
        double r550295 = r550294 + r550270;
        double r550296 = r550286 ? r550292 : r550295;
        return r550296;
}

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

Original16.5
Target8.5
Herbie8.4
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (+ x y) (/ (* (- z t) y) (- a t))) < -4.633029569659858e-238 or 2.2463422345302793e-220 < (- (+ x y) (/ (* (- z t) y) (- a t)))

    1. Initial program 13.0

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

    3. Applied add-cube-cbrt13.2

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

    4. Applied times-frac7.5

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

    if -4.633029569659858e-238 < (- (+ x y) (/ (* (- z t) y) (- a t))) < 2.2463422345302793e-220

    1. Initial program 52.7

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

    2. Taylor expanded around inf 17.2

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

  4. Final simplification8.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -4.633029569659858 \cdot 10^{-238} \lor \neg \left(\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 2.246342234530279 \cdot 10^{-220}\right):\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))))