Average Error: 10.7 → 1.1
Time: 6.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -8.7537559398872107 \cdot 10^{-143} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 3.1147786030260667 \cdot 10^{225}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -8.7537559398872107 \cdot 10^{-143} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 3.1147786030260667 \cdot 10^{225}\right):\\
\;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\

\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 temp;
	if (((((y * (z - t)) / (z - a)) <= -8.75375593988721e-143) || !(((y * (z - t)) / (z - a)) <= 3.114778603026067e+225))) {
		temp = (x + (y / ((z - a) / (z - t))));
	} else {
		temp = (x + ((y * (z - t)) / (z - a)));
	}
	return temp;
}

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

Original10.7
Target1.4
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- z a)) < -8.75375593988721e-143 or 3.114778603026067e+225 < (/ (* y (- z t)) (- z a))

    1. Initial program 23.6

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

    3. Applied associate-/l*2.0

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

    if -8.75375593988721e-143 < (/ (* y (- z t)) (- z a)) < 3.114778603026067e+225

    1. Initial program 0.3

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -8.7537559398872107 \cdot 10^{-143} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 3.1147786030260667 \cdot 10^{225}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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