Average Error: 1.5 → 2.3
Time: 3.5s
Precision: binary64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le 7.24164925083284105 \cdot 10^{-306}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le 7.24164925083284105 \cdot 10^{-306}:\\
\;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (y * ((double) (((double) (z - t)) / ((double) (z - a))))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((y <= 7.241649250832841e-306)) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z / ((double) (z - a)))) - ((double) (t / ((double) (z - a))))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y / ((double) (z - a)))) * ((double) (z - 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

Original1.5
Target1.3
Herbie2.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < 7.24164925083284105e-306

    1. Initial program 1.6

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

    3. Applied div-sub1.6

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

    if 7.24164925083284105e-306 < y

    1. Initial program 1.3

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

    3. Applied div-sub1.3

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

    5. Applied div-inv1.3

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

    6. Applied div-inv1.4

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

    7. Applied distribute-rgt-out--1.4

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

    8. Applied associate-*r*3.0

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

    9. Simplified3.0

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 7.24164925083284105 \cdot 10^{-306}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020152 
(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)))))