Average Error: 16.0 → 6.7
Time: 5.7s
Precision: binary64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -1.1546242419088314 \cdot 10^{-215}:\\ \;\;\;\;x + \left(\sqrt[3]{y + y \cdot \frac{z - t}{t - a}} \cdot \sqrt[3]{y + y \cdot \frac{z - t}{t - a}}\right) \cdot \sqrt[3]{y + \sqrt[3]{\frac{z - t}{t - a}} \cdot \left(y \cdot \left(\sqrt[3]{\frac{z - t}{t - a}} \cdot \sqrt[3]{\frac{z - t}{t - a}}\right)\right)}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 6.63936916839488 \cdot 10^{-296}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + y \cdot \left(\left(z - t\right) \cdot \frac{1}{t - a}\right)\right)\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -1.1546242419088314 \cdot 10^{-215}:\\
\;\;\;\;x + \left(\sqrt[3]{y + y \cdot \frac{z - t}{t - a}} \cdot \sqrt[3]{y + y \cdot \frac{z - t}{t - a}}\right) \cdot \sqrt[3]{y + \sqrt[3]{\frac{z - t}{t - a}} \cdot \left(y \cdot \left(\sqrt[3]{\frac{z - t}{t - a}} \cdot \sqrt[3]{\frac{z - t}{t - a}}\right)\right)}\\

\mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 6.63936916839488 \cdot 10^{-296}:\\
\;\;\;\;x + y \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(y + y \cdot \left(\left(z - t\right) \cdot \frac{1}{t - a}\right)\right)\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (x + y)) - (((double) (((double) (z - t)) * y)) / ((double) (a - t)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((double) (((double) (x + y)) + (((double) (y * ((double) (t - z)))) / ((double) (a - t))))) <= -1.1546242419088314e-215)) {
		VAR = ((double) (x + ((double) (((double) (((double) cbrt(((double) (y + ((double) (y * (((double) (z - t)) / ((double) (t - a))))))))) * ((double) cbrt(((double) (y + ((double) (y * (((double) (z - t)) / ((double) (t - a))))))))))) * ((double) cbrt(((double) (y + ((double) (((double) cbrt((((double) (z - t)) / ((double) (t - a))))) * ((double) (y * ((double) (((double) cbrt((((double) (z - t)) / ((double) (t - a))))) * ((double) cbrt((((double) (z - t)) / ((double) (t - a)))))))))))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x + y)) + (((double) (y * ((double) (t - z)))) / ((double) (a - t))))) <= 6.63936916839488e-296)) {
			VAR_1 = ((double) (x + ((double) (y * (z / t)))));
		} else {
			VAR_1 = ((double) (x + ((double) (y + ((double) (y * ((double) (((double) (z - t)) * (1.0 / ((double) (t - a)))))))))));
		}
		VAR = VAR_1;
	}
	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

Original16.0
Target8.4
Herbie6.7
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < -1.3664970889390727 \cdot 10^{-07}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (+ x y) (/ (* (- z t) y) (- a t))) < -1.1546242419088314e-215

    1. Initial program Error: 12.6 bits

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

    2. SimplifiedError: 5.3 bits

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

    4. Applied add-cube-cbrtError: 5.7 bits

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

    6. Applied add-cube-cbrtError: 5.7 bits

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

    7. Applied associate-*r*Error: 5.7 bits

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

    if -1.1546242419088314e-215 < (- (+ x y) (/ (* (- z t) y) (- a t))) < 6.6393691683949e-296

    1. Initial program Error: 55.8 bits

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

    2. SimplifiedError: 31.9 bits

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

    3. Taylor expanded around inf Error: 17.2 bits

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

    4. SimplifiedError: 17.3 bits

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

    if 6.6393691683949e-296 < (- (+ x y) (/ (* (- z t) y) (- a t)))

    1. Initial program Error: 12.3 bits

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

    2. SimplifiedError: 5.4 bits

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

    4. Applied div-invError: 5.8 bits

      \[\leadsto x + \left(y + y \cdot \color{blue}{\left(\left(z - t\right) \cdot \frac{1}{t - a}\right)}\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplificationError: 6.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -1.1546242419088314 \cdot 10^{-215}:\\ \;\;\;\;x + \left(\sqrt[3]{y + y \cdot \frac{z - t}{t - a}} \cdot \sqrt[3]{y + y \cdot \frac{z - t}{t - a}}\right) \cdot \sqrt[3]{y + \sqrt[3]{\frac{z - t}{t - a}} \cdot \left(y \cdot \left(\sqrt[3]{\frac{z - t}{t - a}} \cdot \sqrt[3]{\frac{z - t}{t - a}}\right)\right)}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 6.63936916839488 \cdot 10^{-296}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + y \cdot \left(\left(z - t\right) \cdot \frac{1}{t - a}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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))))