Average Error: 1.4 → 1.4
Time: 10.2s
Precision: binary64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.65019681524920758 \cdot 10^{-107} \lor \neg \left(t \le 1.59745650028640169 \cdot 10^{-190}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.65019681524920758 \cdot 10^{-107} \lor \neg \left(t \le 1.59745650028640169 \cdot 10^{-190}\right):\\
\;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{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 (((t <= -1.6501968152492076e-107) || !(t <= 1.5974565002864017e-190))) {
		VAR = ((double) (x + (y / (((double) (a - t)) / ((double) (z - t))))));
	} else {
		VAR = ((double) (x + (((double) (y * ((double) (z - t)))) / ((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

Original1.4
Target0.4
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.65019681524920758e-107 or 1.59745650028640169e-190 < t

    1. Initial program 0.7

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

    3. Applied clear-num0.7

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
    4. Using strategy rm

    5. Applied un-div-inv0.7

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

    if -1.65019681524920758e-107 < t < 1.59745650028640169e-190

    1. Initial program 3.8

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

    3. Applied associate-*r/4.0

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.65019681524920758 \cdot 10^{-107} \lor \neg \left(t \le 1.59745650028640169 \cdot 10^{-190}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

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, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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