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

Average Error: 1.2 → 0.7

Time: 7.2s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -3.1529935051864828 \cdot 10^{47} \lor \neg \left(y \le 5.72235627477408708 \cdot 10^{-167}\right):\\ \;\;\;\;x + {\left(\frac{y}{\frac{z - a}{z - t}}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((y <= -3.152993505186483e+47) || !(y <= 5.722356274774087e-167))) {
		VAR = ((double) (x + ((double) pow(((double) (y / ((double) (((double) (z - a)) / ((double) (z - t)))))), 1.0))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (z - a))))));
	}
	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	1.2
Target	1.1
Herbie	0.7

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

Derivation

1. Split input into 2 regimes

2. if y < -3.1529935051864828e47 or 5.72235627477408708e-167 < y

   1. Initial program 0.7

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

   3. Applied add-cube-cbrt 1.4

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

   4. Applied associate-*l* 1.4

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

   6. Applied pow1 1.4

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

   7. Applied pow1 1.4

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

   8. Applied pow-prod-down 1.4

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

   9. Applied pow1 1.4

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

   10. Applied pow1 1.4

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

   11. Applied pow-prod-down 1.4

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

   12. Applied pow-prod-down 1.4

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

   13. Simplified 0.7

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

   if -3.1529935051864828e47 < y < 5.72235627477408708e-167

   1. Initial program 1.8

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

   3. Applied associate-*r/ 0.6

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.1529935051864828 \cdot 10^{47} \lor \neg \left(y \le 5.72235627477408708 \cdot 10^{-167}\right):\\ \;\;\;\;x + {\left(\frac{y}{\frac{z - a}{z - t}}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020173 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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