Average Error: 10.7 → 0.5
Time: 6.4s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.74328329258889717 \cdot 10^{46} \lor \neg \left(y \le 1.81313242607608628 \cdot 10^{-24}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.74328329258889717 \cdot 10^{46} \lor \neg \left(y \le 1.81313242607608628 \cdot 10^{-24}\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 ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((y <= -1.7432832925888972e+46) || !(y <= 1.8131324260760863e-24))) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - t)) / ((double) (a - t))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (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

Original10.7
Target1.3
Herbie0.5
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.74328329258889717e46 or 1.81313242607608628e-24 < y

    1. Initial program 23.9

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

    2. Simplified0.5

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

    if -1.74328329258889717e46 < y < 1.81313242607608628e-24

    1. Initial program 0.5

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.74328329258889717 \cdot 10^{46} \lor \neg \left(y \le 1.81313242607608628 \cdot 10^{-24}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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