Average Error: 1.3 → 0.5
Time: 4.7s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8.27012852365464511 \cdot 10^{43} \lor \neg \left(y \le 4.59337790585326484 \cdot 10^{-23}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -8.27012852365464511 \cdot 10^{43} \lor \neg \left(y \le 4.59337790585326484 \cdot 10^{-23}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

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

\end{array}
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 VAR;
	if (((y <= -8.270128523654645e+43) || !(y <= 4.593377905853265e-23))) {
		VAR = (x + (y * ((z - t) / (z - a))));
	} else {
		VAR = (x + ((y * (z - t)) / (z - a)));
	}
	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

Original1.3
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -8.270128523654645e+43 or 4.593377905853265e-23 < y

    1. Initial program 0.4

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

    if -8.270128523654645e+43 < y < 4.593377905853265e-23

    1. Initial program 2.0

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

    3. Applied associate-*r/0.7

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.27012852365464511 \cdot 10^{43} \lor \neg \left(y \le 4.59337790585326484 \cdot 10^{-23}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020106 
(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)))))