Average Error: 17.0 → 7.9
Time: 7.0s
Precision: binary64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \le -1.16602368952335922 \cdot 10^{-234}:\\ \;\;\;\;x + \left(y + \frac{y}{\sqrt[3]{a - t}} \cdot \frac{\frac{t - z}{\sqrt[3]{a - t}}}{\sqrt[3]{a - t}}\right)\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + y \cdot \left(\left(t - z\right) \cdot \frac{1}{a - t}\right)\right)\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \le -1.16602368952335922 \cdot 10^{-234}:\\
\;\;\;\;x + \left(y + \frac{y}{\sqrt[3]{a - t}} \cdot \frac{\frac{t - z}{\sqrt[3]{a - t}}}{\sqrt[3]{a - t}}\right)\\

\mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \le 0.0:\\
\;\;\;\;x + y \cdot \frac{z}{t}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (x + y)) - ((double) (((double) (((double) (z - t)) * y)) / ((double) (a - t))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((double) (((double) (x + y)) - ((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t)))))) <= -1.1660236895233592e-234)) {
		VAR = ((double) (x + ((double) (y + ((double) (((double) (y / ((double) cbrt(((double) (a - t)))))) * ((double) (((double) (((double) (t - z)) / ((double) cbrt(((double) (a - t)))))) / ((double) cbrt(((double) (a - t))))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x + y)) - ((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t)))))) <= 0.0)) {
			VAR_1 = ((double) (x + ((double) (y * ((double) (z / t))))));
		} else {
			VAR_1 = ((double) (x + ((double) (y + ((double) (y * ((double) (((double) (t - z)) * ((double) (1.0 / ((double) (a - t))))))))))));
		}
		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

Original17.0
Target8.8
Herbie7.9
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (+ x y) (/ (* (- z t) y) (- a t))) < -1.16602368952335922e-234

    1. Initial program 13.2

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

    2. Simplified5.5

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

    4. Applied add-cube-cbrt7.6

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

    5. Applied associate-/r*7.7

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

    7. Applied *-un-lft-identity7.7

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

    8. Applied *-un-lft-identity7.7

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

    9. Applied times-frac7.6

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

    10. Applied times-frac7.7

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

    11. Applied associate-*r*7.5

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

    12. Simplified7.5

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

    if -1.16602368952335922e-234 < (- (+ x y) (/ (* (- z t) y) (- a t))) < 0.0

    1. Initial program 57.4

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

    2. Simplified33.3

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

    3. Taylor expanded around inf 20.7

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

    4. Simplified20.9

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

    if 0.0 < (- (+ x y) (/ (* (- z t) y) (- a t)))

    1. Initial program 13.5

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

    2. Simplified5.6

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

    4. Applied div-inv6.1

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

  4. Final simplification7.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \le -1.16602368952335922 \cdot 10^{-234}:\\ \;\;\;\;x + \left(y + \frac{y}{\sqrt[3]{a - t}} \cdot \frac{\frac{t - z}{\sqrt[3]{a - t}}}{\sqrt[3]{a - t}}\right)\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + y \cdot \left(\left(t - z\right) \cdot \frac{1}{a - t}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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))))