Average Error: 1.5 → 1.3
Time: 8.0s
Precision: binary64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.00876388733083853 \cdot 10^{52}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \le 7.5879717494487083 \cdot 10^{-165}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.00876388733083853 \cdot 10^{52}:\\
\;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\

\mathbf{elif}\;y \le 7.5879717494487083 \cdot 10^{-165}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (y * (((double) (z - t)) / ((double) (z - a)))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((y <= -5.008763887330839e+52)) {
		VAR = ((double) (x + ((double) ((y / ((double) (z - a))) * ((double) (z - t))))));
	} else {
		double VAR_1;
		if ((y <= 7.587971749448708e-165)) {
			VAR_1 = ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (z - a)))));
		} else {
			VAR_1 = ((double) (x + ((double) (y * (((double) (z - t)) / ((double) (z - a)))))));
		}
		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

Original1.5
Target1.4
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -5.00876388733083853e52

    1. Initial program 0.6

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

    3. Applied pow10.6

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

    4. Applied pow10.6

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

    5. Applied pow-prod-down0.6

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

    6. Simplified3.3

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

    if -5.00876388733083853e52 < y < 7.5879717494487083e-165

    1. Initial program 2.3

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

    3. Applied associate-*r/0.7

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

    if 7.5879717494487083e-165 < y

    1. Initial program 1.0

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.00876388733083853 \cdot 10^{52}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \le 7.5879717494487083 \cdot 10^{-165}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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