Average Error: 16.6 → 8.8
Time: 9.2s
Precision: binary64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -2.8212014492182781 \cdot 10^{-121} \lor \neg \left(a \le 5.263488268156357 \cdot 10^{-155}\right):\\ \;\;\;\;x + \left(y + \sqrt[3]{y \cdot \frac{t - z}{a - t}} \cdot \left(\sqrt[3]{y \cdot \frac{t - z}{a - t}} \cdot \sqrt[3]{y \cdot \frac{t - z}{a - t}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -2.8212014492182781 \cdot 10^{-121} \lor \neg \left(a \le 5.263488268156357 \cdot 10^{-155}\right):\\
\;\;\;\;x + \left(y + \sqrt[3]{y \cdot \frac{t - z}{a - t}} \cdot \left(\sqrt[3]{y \cdot \frac{t - z}{a - t}} \cdot \sqrt[3]{y \cdot \frac{t - z}{a - t}}\right)\right)\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (x + y)) - ((double) (((double) (((double) (z - t)) * y)) / ((double) (a - t))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((a <= -2.821201449218278e-121) || !(a <= 5.263488268156357e-155))) {
		VAR = ((double) (x + ((double) (y + ((double) (((double) cbrt(((double) (y * ((double) (((double) (t - z)) / ((double) (a - t)))))))) * ((double) (((double) cbrt(((double) (y * ((double) (((double) (t - z)) / ((double) (a - t)))))))) * ((double) cbrt(((double) (y * ((double) (((double) (t - z)) / ((double) (a - t))))))))))))))));
	} else {
		VAR = ((double) (x + ((double) (y * ((double) (z / t))))));
	}
	return VAR;
}

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

Original16.6
Target8.8
Herbie8.8
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -2.8212014492182781e-121 or 5.263488268156357e-155 < a

    1. Initial program 15.3

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

    2. Simplified6.0

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

    4. Applied add-cube-cbrt8.5

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

    if -2.8212014492182781e-121 < a < 5.263488268156357e-155

    1. Initial program 20.3

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

    2. Simplified11.7

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

    3. Taylor expanded around inf 9.6

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

    4. Simplified9.7

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

  4. Final simplification8.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.8212014492182781 \cdot 10^{-121} \lor \neg \left(a \le 5.263488268156357 \cdot 10^{-155}\right):\\ \;\;\;\;x + \left(y + \sqrt[3]{y \cdot \frac{t - z}{a - t}} \cdot \left(\sqrt[3]{y \cdot \frac{t - z}{a - t}} \cdot \sqrt[3]{y \cdot \frac{t - z}{a - t}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(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) (/ 1.0 (- 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))))