Average Error: 1.3 → 0.9
Time: 3.5s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \le -5.50508004782713098 \cdot 10^{143}:\\ \;\;\;\;x + \frac{1}{\frac{a - t}{\left(z - t\right) \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{z - t}{a - t} \le -5.50508004782713098 \cdot 10^{143}:\\
\;\;\;\;x + \frac{1}{\frac{a - t}{\left(z - t\right) \cdot y}}\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{z - t}{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 ((((z - t) / (a - t)) <= -5.505080047827131e+143)) {
		VAR = (x + (1.0 / ((a - t) / ((z - t) * y))));
	} 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

Original1.3
Target0.4
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- z t) (- a t)) < -5.505080047827131e+143

    1. Initial program 11.9

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

    3. Applied div-inv11.9

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

    5. Applied un-div-inv11.9

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

    6. Applied associate-*r/3.1

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

    7. Simplified3.1

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

    9. Applied clear-num3.1

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

    if -5.505080047827131e+143 < (/ (- z t) (- a t))

    1. Initial program 0.8

      \[x + y \cdot \frac{z - t}{a - t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \le -5.50508004782713098 \cdot 10^{143}:\\ \;\;\;\;x + \frac{1}{\frac{a - t}{\left(z - t\right) \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020075 
(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)))))