Average Error: 1.3 → 0.6
Time: 3.9s
Precision: binary64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -28393617975727.465 \lor \neg \left(y \leq 2.5959847217515504 \cdot 10^{-27}\right):\\ \;\;\;\;x + y \cdot \frac{1}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -28393617975727.465 \lor \neg \left(y \leq 2.5959847217515504 \cdot 10^{-27}\right):\\
\;\;\;\;x + y \cdot \frac{1}{\frac{z - a}{z - t}}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- z a)))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -28393617975727.465) (not (<= y 2.5959847217515504e-27)))
   (+ x (* y (/ 1.0 (/ (- z a) (- z t)))))
   (+ x (/ (* y (- z t)) (- z a)))))
double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -28393617975727.465) || !(y <= 2.5959847217515504e-27)) {
		tmp = x + (y * (1.0 / ((z - a) / (z - t))));
	} else {
		tmp = x + ((y * (z - t)) / (z - a));
	}
	return tmp;
}

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

Original1.3
Target1.3
Herbie0.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -28393617975727.4648 or 2.5959847217515504e-27 < y

    1. Initial program 0.6

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

    3. Applied clear-num_binary640.7

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

    if -28393617975727.4648 < y < 2.5959847217515504e-27

    1. Initial program 2.0

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

    3. Applied associate-*r/_binary640.4

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -28393617975727.465 \lor \neg \left(y \leq 2.5959847217515504 \cdot 10^{-27}\right):\\ \;\;\;\;x + y \cdot \frac{1}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020220 
(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)))))