Average Error: 1.4 → 1.5
Time: 3.2s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.0102141775218175 \cdot 10^{-178} \lor \neg \left(z \le 1.00504175493536762 \cdot 10^{-41}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.0102141775218175 \cdot 10^{-178} \lor \neg \left(z \le 1.00504175493536762 \cdot 10^{-41}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

\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) (((double) (z - t)) / ((double) (z - a))))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((z <= -5.010214177521818e-178) || !(z <= 1.0050417549353676e-41))) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - t)) / ((double) (z - a))))))));
	} else {
		VAR = ((double) (x + ((double) (((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

Original1.4
Target1.3
Herbie1.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.010214177521818e-178 or 1.0050417549353676e-41 < z

    1. Initial program 0.6

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

    if -5.010214177521818e-178 < z < 1.0050417549353676e-41

    1. Initial program 3.4

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

    3. Applied associate-*r/3.6

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.0102141775218175 \cdot 10^{-178} \lor \neg \left(z \le 1.00504175493536762 \cdot 10^{-41}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020140 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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