Average Error: 16.8 → 9.3
Time: 10.4s
Precision: binary64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.4183402044220067 \cdot 10^{-130}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \le 1.0472146471931212 \cdot 10^{-158}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \left(\sqrt[3]{\frac{y}{\sqrt[3]{a - t}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{a - t}}}\right)\right) \cdot \sqrt[3]{\frac{y}{\sqrt[3]{a - t}}}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.4183402044220067 \cdot 10^{-130}:\\
\;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\

\mathbf{elif}\;a \le 1.0472146471931212 \cdot 10^{-158}:\\
\;\;\;\;\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 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 ((a <= -1.4183402044220067e-130)) {
		VAR = ((double) (((double) (x + y)) - ((double) (((double) (z - t)) * (y / ((double) (a - t)))))));
	} else {
		double VAR_1;
		if ((a <= 1.0472146471931212e-158)) {
			VAR_1 = ((double) ((((double) (z * y)) / t) + x));
		} else {
			VAR_1 = ((double) (((double) (x + y)) - ((double) (((double) ((((double) (z - t)) / ((double) (((double) cbrt(((double) (a - t)))) * ((double) cbrt(((double) (a - t))))))) * ((double) (((double) cbrt((y / ((double) cbrt(((double) (a - t))))))) * ((double) cbrt((y / ((double) cbrt(((double) (a - t))))))))))) * ((double) cbrt((y / ((double) cbrt(((double) (a - t)))))))))));
		}
		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

Original16.8
Target8.6
Herbie9.3
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -1.4183402044220067e-130

    1. Initial program 15.1

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

    3. Applied *-un-lft-identity15.1

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

    4. Applied times-frac9.4

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

    5. Simplified9.4

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

    if -1.4183402044220067e-130 < a < 1.0472146471931212e-158

    1. Initial program 21.0

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

    2. Taylor expanded around inf 9.0

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

    if 1.0472146471931212e-158 < a

    1. Initial program 15.7

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

    3. Applied add-cube-cbrt15.8

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

    4. Applied times-frac9.5

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

    6. Applied add-cube-cbrt9.5

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

    7. Applied associate-*r*9.5

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

  4. Final simplification9.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.4183402044220067 \cdot 10^{-130}:\\ \;\;\;\;\left(x + y\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \le 1.0472146471931212 \cdot 10^{-158}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \left(\sqrt[3]{\frac{y}{\sqrt[3]{a - t}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{a - t}}}\right)\right) \cdot \sqrt[3]{\frac{y}{\sqrt[3]{a - t}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))))