Average Error: 1.4 → 1.6
Time: 5.4s
Precision: binary64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -4.321341674109944 \cdot 10^{+118}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \leq 2.7346412179090334 \cdot 10^{-118}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -4.321341674109944 \cdot 10^{+118}:\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

\mathbf{elif}\;y \leq 2.7346412179090334 \cdot 10^{-118}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\

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

\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 (<= y -4.321341674109944e+118)
   (+ x (* y (/ (- z t) (- z a))))
   (if (<= y 2.7346412179090334e-118)
     (+ x (* (* y (- z t)) (/ 1.0 (- z a))))
     (+ x (/ y (/ (- z a) (- z t)))))))
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 <= -4.321341674109944e+118) {
		tmp = x + (y * ((z - t) / (z - a)));
	} else if (y <= 2.7346412179090334e-118) {
		tmp = x + ((y * (z - t)) * (1.0 / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / (z - t)));
	}
	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

Original1.4
Target1.2
Herbie1.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -4.32134167410994419e118

    1. Initial program 0.7

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

    if -4.32134167410994419e118 < y < 2.7346412179090334e-118

    1. Initial program 1.9

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

    3. Applied div-inv_binary641.9

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

    4. Applied associate-*r*_binary642.3

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

    if 2.7346412179090334e-118 < y

    1. Initial program 0.8

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

    3. Applied clear-num_binary640.9

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
    4. Using strategy rm

    5. Applied un-div-inv_binary640.7

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.321341674109944 \cdot 10^{+118}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \leq 2.7346412179090334 \cdot 10^{-118}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020260 
(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)))))