Average Error: 10.8 → 0.3
Time: 4.9s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -inf.0:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.50265489255120844 \cdot 10^{266}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{1}{\frac{a - t}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -inf.0:\\
\;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\

\mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.50265489255120844 \cdot 10^{266}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{1}{\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 ((((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t)))) <= -inf.0)) {
		VAR = ((double) (x + ((double) (((double) (y / ((double) (a - t)))) * ((double) (z - t))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t)))) <= 3.5026548925512084e+266)) {
			VAR_1 = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t))))));
		} else {
			VAR_1 = ((double) (x + ((double) (y * ((double) (1.0 / ((double) (((double) (a - t)) / ((double) (z - 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

Original10.8
Target1.1
Herbie0.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* y (- z t)) (- a t)) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.1

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

    5. Applied associate-/r/0.1

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

    if -inf.0 < (/ (* y (- z t)) (- a t)) < 3.50265489255120844e266

    1. Initial program 0.2

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

    if 3.50265489255120844e266 < (/ (* y (- z t)) (- a t))

    1. Initial program 57.1

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

    3. Applied *-un-lft-identity57.1

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

    4. Applied times-frac1.0

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

    5. Simplified1.0

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

    7. Applied clear-num1.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -inf.0:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.50265489255120844 \cdot 10^{266}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{1}{\frac{a - t}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020173 
(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))))