Average Error: 10.8 → 0.5
Time: 4.6s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -2.1489962221699905 \cdot 10^{+293}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 5.080356852598769 \cdot 10^{+273}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -2.1489962221699905 \cdot 10^{+293}:\\
\;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 5.080356852598769 \cdot 10^{+273}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (((double) (y - z)) * t)) / ((double) (a - z)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((((double) (((double) (y - z)) * t)) / ((double) (a - z))) <= -2.1489962221699905e+293)) {
		VAR = ((double) (x + ((double) (((double) (y - z)) * (t / ((double) (a - z)))))));
	} else {
		double VAR_1;
		if (((((double) (((double) (y - z)) * t)) / ((double) (a - z))) <= 5.080356852598769e+273)) {
			VAR_1 = ((double) ((((double) (((double) (y - z)) * t)) / ((double) (a - z))) + x));
		} else {
			VAR_1 = ((double) (x + (((double) (y - z)) / (((double) (a - 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
Target0.6
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (- y z) t) (- a z)) < -2.1489962221699905e293

    1. Initial program Error: 60.8 bits

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

    2. SimplifiedError: 1.7 bits

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

    if -2.1489962221699905e293 < (/ (* (- y z) t) (- a z)) < 5.08035685259876878e273

    1. Initial program Error: 0.3 bits

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

    if 5.08035685259876878e273 < (/ (* (- y z) t) (- a z))

    1. Initial program Error: 59.5 bits

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

    3. Applied associate-/l*Error: 1.3 bits

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

  4. Final simplificationError: 0.5 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -2.1489962221699905 \cdot 10^{+293}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 5.080356852598769 \cdot 10^{+273}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array}\]

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, 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))))