Average Error: 1.4 → 0.5
Time: 4.0s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.5822315398269677 \cdot 10^{26} \lor \neg \left(y \le 3.08448179583523471 \cdot 10^{-125}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.5822315398269677 \cdot 10^{26} \lor \neg \left(y \le 3.08448179583523471 \cdot 10^{-125}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{a - t}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return (x + (y * ((z - t) / (a - t))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((y <= -4.582231539826968e+26) || !(y <= 3.0844817958352347e-125))) {
		VAR = (x + (y * ((z - t) / (a - t))));
	} else {
		VAR = (x + ((y * (z - t)) / (a - t)));
	}
	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
Target0.4
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.582231539826968e+26 or 3.0844817958352347e-125 < y

    1. Initial program 0.6

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

    if -4.582231539826968e+26 < y < 3.0844817958352347e-125

    1. Initial program 2.4

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

    3. Applied associate-*r/0.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.5822315398269677 \cdot 10^{26} \lor \neg \left(y \le 3.08448179583523471 \cdot 10^{-125}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020091 
(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 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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