Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Average Error: 11.0 → 1.1

Time: 3.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -4.93401553254627053 \cdot 10^{126}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \le 1.5321512756361021 \cdot 10^{198}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a) {
	return (x + ((y * (z - t)) / (z - a)));
}

↓

double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((y * (z - t)) / (z - a)) <= -4.9340155325462705e+126)) {
		VAR = (x + ((y / (z - a)) * (z - t)));
	} else {
		double VAR_1;
		if ((((y * (z - t)) / (z - a)) <= 1.532151275636102e+198)) {
			VAR_1 = (x + ((y * (z - t)) / (z - a)));
		} else {
			VAR_1 = (x + (y / ((z - a) / (z - 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

Target

Original	11.0
Target	1.2
Herbie	1.1

\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

1. Split input into 3 regimes

2. if (/ (* y (- z t)) (- z a)) < -4.9340155325462705e+126

   1. Initial program 38.3

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

   3. Applied associate-/l* 2.4

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

   5. Applied associate-/r/ 4.8

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

   if -4.9340155325462705e+126 < (/ (* y (- z t)) (- z a)) < 1.532151275636102e+198

   1. Initial program 0.2

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

   if 1.532151275636102e+198 < (/ (* y (- z t)) (- z a))

   1. Initial program 46.9

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

   3. Applied associate-/l* 2.4

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

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -4.93401553254627053 \cdot 10^{126}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \le 1.5321512756361021 \cdot 10^{198}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020106 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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