Average Error: 1.4 → 1.5
Time: 3.2s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.3050585222382704 \cdot 10^{-124} \lor \neg \left(t \le 7.2979868695563967 \cdot 10^{-146}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.3050585222382704 \cdot 10^{-124} \lor \neg \left(t \le 7.2979868695563967 \cdot 10^{-146}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{a - 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 (x + (y * ((z - t) / (a - t))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((t <= -3.3050585222382704e-124) || !(t <= 7.297986869556397e-146))) {
		VAR = (x + (y * ((z - t) / (a - t))));
	} else {
		VAR = (x + ((y * (z - t)) / (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
Target0.5
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.3050585222382704e-124 or 7.297986869556397e-146 < t

    1. Initial program 0.7

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

    if -3.3050585222382704e-124 < t < 7.297986869556397e-146

    1. Initial program 3.4

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

    3. Applied clear-num3.5

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

    4. Applied un-div-inv3.3

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

    6. Applied div-inv3.3

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

    8. Applied *-commutative3.3

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

    9. Applied associate-/r*3.7

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

    10. Simplified3.7

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.3050585222382704 \cdot 10^{-124} \lor \neg \left(t \le 7.2979868695563967 \cdot 10^{-146}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(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 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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