Average Error: 16.4 → 9.6
Time: 4.8s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -2.5508524678139594 \cdot 10^{-129}:\\ \;\;\;\;\left(\left(x + y\right) - \frac{z}{\frac{a - t}{y}}\right) + \frac{t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \le 2.970242852533054 \cdot 10^{-70}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{a - t} \cdot y\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -2.5508524678139594 \cdot 10^{-129}:\\
\;\;\;\;\left(\left(x + y\right) - \frac{z}{\frac{a - t}{y}}\right) + \frac{t}{\frac{a - t}{y}}\\

\mathbf{elif}\;a \le 2.970242852533054 \cdot 10^{-70}:\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

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

\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 ((a <= -2.5508524678139594e-129)) {
		VAR = (((x + y) - (z / ((a - t) / y))) + (t / ((a - t) / y)));
	} else {
		double VAR_1;
		if ((a <= 2.970242852533054e-70)) {
			VAR_1 = (((z * y) / t) + x);
		} else {
			VAR_1 = ((x + y) - (((z - t) / (a - t)) * y));
		}
		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

Original16.4
Target8.5
Herbie9.6
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -2.5508524678139594e-129

    1. Initial program 15.6

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

    3. Applied associate-/l*9.6

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

    5. Applied div-sub9.6

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

    6. Applied associate--r-9.6

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

    if -2.5508524678139594e-129 < a < 2.970242852533054e-70

    1. Initial program 20.0

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

    2. Taylor expanded around inf 11.6

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

    if 2.970242852533054e-70 < a

    1. Initial program 13.9

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

    3. Applied associate-/l*8.5

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

    5. Applied associate-/r/7.6

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

  4. Final simplification9.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.5508524678139594 \cdot 10^{-129}:\\ \;\;\;\;\left(\left(x + y\right) - \frac{z}{\frac{a - t}{y}}\right) + \frac{t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \le 2.970242852533054 \cdot 10^{-70}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{a - t} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020102 
(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))))