Average Error: 10.9 → 0.6
Time: 8.0s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{z - a} \le -4.81203779151245 \cdot 10^{132} \lor \neg \left(x + \frac{y \cdot \left(z - t\right)}{z - a} \le 1.70906807278857919 \cdot 10^{289}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{z - a} \le -4.81203779151245 \cdot 10^{132} \lor \neg \left(x + \frac{y \cdot \left(z - t\right)}{z - a} \le 1.70906807278857919 \cdot 10^{289}\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 ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (z - a))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (z - a)))))) <= -4.81203779151245e+132) || !(((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (z - a)))))) <= 1.7090680727885792e+289))) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - t)) / ((double) (z - a))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (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

Original10.9
Target1.2
Herbie0.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z t)) (- z a))) < -4.81203779151245e132 or 1.70906807278857919e289 < (+ x (/ (* y (- z t)) (- z a)))

    1. Initial program 31.4

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

    3. Applied *-un-lft-identity31.4

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

    4. Applied times-frac1.2

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

    5. Simplified1.2

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

    if -4.81203779151245e132 < (+ x (/ (* y (- z t)) (- z a))) < 1.70906807278857919e289

    1. Initial program 0.3

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{z - a} \le -4.81203779151245 \cdot 10^{132} \lor \neg \left(x + \frac{y \cdot \left(z - t\right)}{z - a} \le 1.70906807278857919 \cdot 10^{289}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020169 
(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))))