Average Error: 10.9 → 0.5
Time: 6.9s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.03525612992921227 \cdot 10^{-36}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \le 7.19694147554013157 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.03525612992921227 \cdot 10^{-36}:\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

\mathbf{elif}\;y \le 7.19694147554013157 \cdot 10^{-78}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\frac{z - a}{z - 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) (z - a))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((y <= -1.0352561299292123e-36)) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - t)) / ((double) (z - a))))))));
	} else {
		double VAR_1;
		if ((y <= 7.196941475540132e-78)) {
			VAR_1 = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (z - a))))));
		} else {
			VAR_1 = ((double) (x + ((double) (y / ((double) (((double) (z - a)) / ((double) (z - t))))))));
		}
		VAR = VAR_1;
	}
	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
Target1.3
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.0352561299292123e-36

    1. Initial program 20.8

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

    3. Applied *-un-lft-identity20.8

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

    4. Applied times-frac0.5

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

    5. Simplified0.5

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

    if -1.0352561299292123e-36 < y < 7.196941475540132e-78

    1. Initial program 0.4

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

    if 7.196941475540132e-78 < y

    1. Initial program 18.2

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

    3. Applied associate-/l*0.7

      \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.03525612992921227 \cdot 10^{-36}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \le 7.19694147554013157 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020148 
(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))))