Average Error: 1.4 → 0.7
Time: 10.4s
Precision: binary64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -2.1742114105338213 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{elif}\;y \leq 4.6416593455394884 \cdot 10^{+64}:\\ \;\;\;\;x + \left(\frac{y \cdot z}{z - a} - \frac{y \cdot t}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{1}{\frac{z - a}{z - t}}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -2.1742114105338213 \cdot 10^{-25}:\\
\;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\

\mathbf{elif}\;y \leq 4.6416593455394884 \cdot 10^{+64}:\\
\;\;\;\;x + \left(\frac{y \cdot z}{z - a} - \frac{y \cdot t}{z - a}\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{1}{\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 -2.1742114105338213e-25)
   (+ x (* y (- (/ z (- z a)) (/ t (- z a)))))
   (if (<= y 4.6416593455394884e+64)
     (+ x (- (/ (* y z) (- z a)) (/ (* y t) (- z a))))
     (+ x (* y (/ 1.0 (/ (- 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 <= -2.1742114105338213e-25) {
		tmp = x + (y * ((z / (z - a)) - (t / (z - a))));
	} else if (y <= 4.6416593455394884e+64) {
		tmp = x + (((y * z) / (z - a)) - ((y * t) / (z - a)));
	} else {
		tmp = x + (y * (1.0 / ((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
Target1.3
Herbie0.7
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -2.1742114105338213e-25

    1. Initial program 0.5

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

    3. Applied div-sub_binary64_127000.5

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

    if -2.1742114105338213e-25 < y < 4.6416593455394884e64

    1. Initial program 2.1

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

    2. Taylor expanded around 0 0.8

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

    if 4.6416593455394884e64 < y

    1. Initial program 0.6

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

    3. Applied clear-num_binary64_126940.7

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1742114105338213 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{elif}\;y \leq 4.6416593455394884 \cdot 10^{+64}:\\ \;\;\;\;x + \left(\frac{y \cdot z}{z - a} - \frac{y \cdot t}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{1}{\frac{z - a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021022 
(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)))))