Average Error: 16.8 → 7.5
Time: 5.1s
Precision: binary64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.8190142657740654 \cdot 10^{-22} \lor \neg \left(y \le 3.11797660037939162 \cdot 10^{-12}\right):\\ \;\;\;\;x + \left(y + y \cdot \left(\left(t - z\right) \cdot \frac{1}{a - t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{1}{a - t} \cdot \left(y \cdot \left(t - z\right)\right)\right)\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.8190142657740654 \cdot 10^{-22} \lor \neg \left(y \le 3.11797660037939162 \cdot 10^{-12}\right):\\
\;\;\;\;x + \left(y + y \cdot \left(\left(t - z\right) \cdot \frac{1}{a - t}\right)\right)\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (x + y)) - (((double) (((double) (z - t)) * y)) / ((double) (a - t)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((y <= -1.8190142657740654e-22) || !(y <= 3.1179766003793916e-12))) {
		VAR = ((double) (x + ((double) (y + ((double) (y * ((double) (((double) (t - z)) * (1.0 / ((double) (a - t)))))))))));
	} else {
		VAR = ((double) (x + ((double) (y + ((double) ((1.0 / ((double) (a - t))) * ((double) (y * ((double) (t - z))))))))));
	}
	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

Original16.8
Target8.6
Herbie7.5
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.8190142657740654e-22 or 3.11797660037939162e-12 < y

    1. Initial program 29.9

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

    2. Simplified12.1

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

    4. Applied div-inv12.9

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

    if -1.8190142657740654e-22 < y < 3.11797660037939162e-12

    1. Initial program 4.1

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

    2. Simplified3.7

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

    4. Applied div-inv4.2

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

    5. Applied associate-*r*2.4

      \[\leadsto x + \left(y + \color{blue}{\left(y \cdot \left(t - z\right)\right) \cdot \frac{1}{a - t}}\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification7.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.8190142657740654 \cdot 10^{-22} \lor \neg \left(y \le 3.11797660037939162 \cdot 10^{-12}\right):\\ \;\;\;\;x + \left(y + y \cdot \left(\left(t - z\right) \cdot \frac{1}{a - t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{1}{a - t} \cdot \left(y \cdot \left(t - z\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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) (/ 1.0 (- 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) (/ 1.0 (- a t))) y))))

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