Average Error: 10.9 → 1.1
Time: 4.5s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.08016826159672186 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \le -7.96333578900575901 \cdot 10^{-299}:\\ \;\;\;\;x + \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{a - t}\right) \cdot \left(\left(z - t\right) \cdot \sqrt[3]{y}\right)\\ \mathbf{elif}\;t \le 3.463479683183646 \cdot 10^{-184}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.08016826159672186 \cdot 10^{-73}:\\
\;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\

\mathbf{elif}\;t \le -7.96333578900575901 \cdot 10^{-299}:\\
\;\;\;\;x + \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{a - t}\right) \cdot \left(\left(z - t\right) \cdot \sqrt[3]{y}\right)\\

\mathbf{elif}\;t \le 3.463479683183646 \cdot 10^{-184}:\\
\;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((t <= -1.0801682615967219e-73)) {
		VAR = ((double) (x + ((double) (y / ((double) (((double) (a - t)) / ((double) (z - t))))))));
	} else {
		double VAR_1;
		if ((t <= -7.963335789005759e-299)) {
			VAR_1 = ((double) (x + ((double) (((double) (((double) cbrt(y)) * ((double) (((double) cbrt(y)) / ((double) (a - t)))))) * ((double) (((double) (z - t)) * ((double) cbrt(y))))))));
		} else {
			double VAR_2;
			if ((t <= 3.463479683183646e-184)) {
				VAR_2 = ((double) (x + ((double) (((double) (z - t)) * ((double) (y / ((double) (a - t))))))));
			} else {
				VAR_2 = ((double) (x + ((double) (y / ((double) (((double) (a - t)) / ((double) (z - t))))))));
			}
			VAR_1 = VAR_2;
		}
		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

Original10.9
Target1.2
Herbie1.1
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.08016826159672186e-73 or 3.463479683183646e-184 < t

    1. Initial program 13.4

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

    2. Simplified0.4

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

    4. Applied clear-num0.5

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
    5. Using strategy rm

    6. Applied un-div-inv0.4

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

    if -1.08016826159672186e-73 < t < -7.96333578900575901e-299

    1. Initial program 4.3

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

    2. Simplified3.7

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

    4. Applied clear-num3.8

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
    5. Using strategy rm

    6. Applied un-div-inv3.5

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]
    7. Using strategy rm

    8. Applied div-inv3.5

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

    9. Applied add-cube-cbrt3.9

      \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\left(a - t\right) \cdot \frac{1}{z - t}}\]

    10. Applied times-frac2.7

      \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{a - t} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}}}\]

    11. Simplified2.7

      \[\leadsto x + \color{blue}{\left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{a - t}\right)} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}}\]

    12. Simplified2.7

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

    if -7.96333578900575901e-299 < t < 3.463479683183646e-184

    1. Initial program 4.1

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

    2. Simplified3.4

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

    4. Applied clear-num3.5

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
    5. Using strategy rm

    6. Applied associate-/r/3.5

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

    7. Applied associate-*r*3.9

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

    8. Simplified3.9

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.08016826159672186 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \le -7.96333578900575901 \cdot 10^{-299}:\\ \;\;\;\;x + \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{a - t}\right) \cdot \left(\left(z - t\right) \cdot \sqrt[3]{y}\right)\\ \mathbf{elif}\;t \le 3.463479683183646 \cdot 10^{-184}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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