Average Error: 15.9 → 8.9
Time: 5.1s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -65179893516015337000:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;y \le 3.4489295074513532 \cdot 10^{-114}:\\ \;\;\;\;x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - {\left(\frac{y}{a - t} \cdot \left(z - t\right)\right)}^{1}\right)\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -65179893516015337000:\\
\;\;\;\;\left(x + y\right) - \frac{z - t}{\frac{a - t}{y}}\\

\mathbf{elif}\;y \le 3.4489295074513532 \cdot 10^{-114}:\\
\;\;\;\;x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \left(y - {\left(\frac{y}{a - t} \cdot \left(z - t\right)\right)}^{1}\right)\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((x + y) - (((z - t) * y) / (a - t)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((y <= -6.517989351601534e+19)) {
		VAR = ((x + y) - ((z - t) / ((a - t) / y)));
	} else {
		double VAR_1;
		if ((y <= 3.448929507451353e-114)) {
			VAR_1 = (x + (y - (((z - t) * y) / (a - t))));
		} else {
			VAR_1 = (x + (y - pow(((y / (a - t)) * (z - t)), 1.0)));
		}
		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

Original15.9
Target8.7
Herbie8.9
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -6.517989351601534e+19

    1. Initial program 31.2

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

    3. Applied associate-/l*20.0

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

    if -6.517989351601534e+19 < y < 3.448929507451353e-114

    1. Initial program 4.0

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

    3. Applied associate--l+2.1

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

    if 3.448929507451353e-114 < y

    1. Initial program 22.6

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

    3. Applied add-cube-cbrt22.8

      \[\leadsto \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}\]

    4. Applied times-frac14.6

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}}\]
    5. Using strategy rm

    6. Applied associate--l+13.8

      \[\leadsto \color{blue}{x + \left(y - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)}\]
    7. Using strategy rm

    8. Applied pow113.8

      \[\leadsto x + \left(y - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \color{blue}{{\left(\frac{y}{\sqrt[3]{a - t}}\right)}^{1}}\right)\]

    9. Applied pow113.8

      \[\leadsto x + \left(y - \color{blue}{{\left(\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right)}^{1}} \cdot {\left(\frac{y}{\sqrt[3]{a - t}}\right)}^{1}\right)\]

    10. Applied pow-prod-down13.8

      \[\leadsto x + \left(y - \color{blue}{{\left(\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)}^{1}}\right)\]

    11. Simplified11.2

      \[\leadsto x + \left(y - {\color{blue}{\left(\frac{y}{a - t} \cdot \left(z - t\right)\right)}}^{1}\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification8.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -65179893516015337000:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;y \le 3.4489295074513532 \cdot 10^{-114}:\\ \;\;\;\;x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - {\left(\frac{y}{a - t} \cdot \left(z - t\right)\right)}^{1}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-07) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y))))

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