Average Error: 11.0 → 1.3
Time: 9.5s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.83623193339276556 \cdot 10^{-160} \lor \neg \left(z \le 2.2797119945194364 \cdot 10^{-41}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.83623193339276556 \cdot 10^{-160} \lor \neg \left(z \le 2.2797119945194364 \cdot 10^{-41}\right):\\
\;\;\;\;x + \frac{y - z}{a - z} \cdot t\\

\mathbf{else}:\\
\;\;\;\;x + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (((double) (y - z)) * t)) / ((double) (a - z))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((z <= -3.8362319333927656e-160) || !(z <= 2.2797119945194364e-41))) {
		VAR = ((double) (x + ((double) (((double) (((double) (y - z)) / ((double) (a - z)))) * t))));
	} else {
		VAR = ((double) (x + ((double) (1.0 / ((double) (((double) (((double) (a - z)) / t)) / ((double) (y - z))))))));
	}
	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

Original11.0
Target0.5
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.83623193339276556e-160 or 2.2797119945194364e-41 < z

    1. Initial program 14.5

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

    3. Applied associate-/l*2.9

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

    5. Applied associate-/r/0.5

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

    if -3.83623193339276556e-160 < z < 2.2797119945194364e-41

    1. Initial program 3.4

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

    3. Applied associate-/l*3.2

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

    5. Applied clear-num3.2

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.83623193339276556 \cdot 10^{-160} \lor \neg \left(z \le 2.2797119945194364 \cdot 10^{-41}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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