Average Error: 11.2 → 0.8
Time: 3.2s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -3.1531961664318305 \cdot 10^{-188} \lor \neg \left(y \leq 1.2891461822977456 \cdot 10^{-151}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -3.1531961664318305 \cdot 10^{-188} \lor \neg \left(y \leq 1.2891461822977456 \cdot 10^{-151}\right):\\
\;\;\;\;x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\

\end{array}
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 VAR;
	if (((y <= -3.1531961664318305e-188) || !(y <= 1.2891461822977456e-151))) {
		VAR = ((double) (x + ((double) (y * ((double) ((z / ((double) (a - t))) - (t / ((double) (a - t)))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) * (1.0 / ((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

Original11.2
Target1.3
Herbie0.8
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.1531961664318305e-188 or 1.2891461822977456e-151 < y

    1. Initial program 14.7

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

    2. Simplified0.9

      \[\leadsto \color{blue}{x + y \cdot \frac{z - t}{a - t}}\]
    3. Using strategy rm

    4. Applied div-sub0.9

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

    if -3.1531961664318305e-188 < y < 1.2891461822977456e-151

    1. Initial program 0.6

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

    2. Simplified2.8

      \[\leadsto \color{blue}{x + y \cdot \frac{z - t}{a - t}}\]
    3. Using strategy rm

    4. Applied div-inv2.9

      \[\leadsto x + y \cdot \color{blue}{\left(\left(z - t\right) \cdot \frac{1}{a - t}\right)}\]

    5. Applied associate-*r*0.6

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1531961664318305 \cdot 10^{-188} \lor \neg \left(y \leq 1.2891461822977456 \cdot 10^{-151}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))))