Average Error: 1.4 → 0.4
Time: 4.7s
Precision: binary64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -5.438913823975979 \cdot 10^{-21} \lor \neg \left(y \leq 6.819889407613578 \cdot 10^{-60}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -5.438913823975979 \cdot 10^{-21} \lor \neg \left(y \leq 6.819889407613578 \cdot 10^{-60}\right):\\
\;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.438913823975979e-21) (not (<= y 6.819889407613578e-60)))
   (+ x (/ y (/ (- a t) (- z t))))
   (+ x (/ (* y (- z t)) (- a t)))))
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (y * (((double) (z - t)) / ((double) (a - t)))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((y <= -5.438913823975979e-21) || !(y <= 6.819889407613578e-60))) {
		tmp = ((double) (x + (y / (((double) (a - t)) / ((double) (z - t))))));
	} else {
		tmp = ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (a - 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
Target0.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.43891382397597878e-21 or 6.81988940761357775e-60 < y

    1. Initial program Error: 0.5 bits

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

    3. Applied associate-*r/Error: 19.9 bits

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

    5. Applied associate-/l*Error: 0.5 bits

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

    if -5.43891382397597878e-21 < y < 6.81988940761357775e-60

    1. Initial program Error: 2.3 bits

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

    3. Applied associate-*r/Error: 0.2 bits

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

  4. Final simplificationError: 0.4 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.438913823975979 \cdot 10^{-21} \lor \neg \left(y \leq 6.819889407613578 \cdot 10^{-60}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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