Average Error: 10.9 → 0.6
Time: 4.1s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -2.816958346187167 \cdot 10^{-193} \lor \neg \left(y \leq 1.4477818662734736 \cdot 10^{-28}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -2.816958346187167 \cdot 10^{-193} \lor \neg \left(y \leq 1.4477818662734736 \cdot 10^{-28}\right):\\
\;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (z - a)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((y <= -2.816958346187167e-193) || !(y <= 1.4477818662734736e-28))) {
		VAR = ((double) (x + ((double) (y * ((double) ((z / ((double) (z - a))) - (t / ((double) (z - a)))))))));
	} else {
		VAR = ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (z - a)))));
	}
	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
Herbie0.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.81695834618716701e-193 or 1.4477818662734736e-28 < y

    1. Initial program Error: 16.4 bits

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

    2. SimplifiedError: 0.8 bits

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

    4. Applied div-subError: 0.8 bits

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

    if -2.81695834618716701e-193 < y < 1.4477818662734736e-28

    1. Initial program Error: 0.3 bits

      \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  3. Recombined 2 regimes into one program.

  4. Final simplificationError: 0.6 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.816958346187167 \cdot 10^{-193} \lor \neg \left(y \leq 1.4477818662734736 \cdot 10^{-28}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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