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

Average Error: 1.3 → 1.3

Time: 10.2s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))

↓

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))

C

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

↓

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.3
Target	0.4
Herbie	1.3

\[\begin{array}{l} \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Alternatives

Alternative 1
Error	2.3
Cost	2691

\[\begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5660.970633165909:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 1.3563897748827889 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 1:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array}\]

Alternative 2
Error	10.4
Cost	904

\[\begin{array}{l} \mathbf{if}\;t \leq -1.2953388124349229 \cdot 10^{+47} \lor \neg \left(t \leq 2.0868173352952202 \cdot 10^{+43}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array}\]

Alternative 3
Error	13.5
Cost	904

\[\begin{array}{l} \mathbf{if}\;t \leq -1.813655537906052 \cdot 10^{+38} \lor \neg \left(t \leq 2.3859125965592656 \cdot 10^{-43}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Alternative 4
Error	12.9
Cost	904

\[\begin{array}{l} \mathbf{if}\;t \leq -1.8517502828614007 \cdot 10^{+41} \lor \neg \left(t \leq 1.502996282001404 \cdot 10^{-29}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]

Alternative 5
Error	13.8
Cost	776

\[\begin{array}{l} \mathbf{if}\;t \leq -1.1525003590229609 \cdot 10^{+45} \lor \neg \left(t \leq 5.364226396298406 \cdot 10^{-32}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array}\]

Alternative 6
Error	19.6
Cost	520

\[\begin{array}{l} \mathbf{if}\;t \leq -2.1304546780209903 \cdot 10^{-27} \lor \neg \left(t \leq 1.906926088687382 \cdot 10^{-98}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Alternative 7
Error	28.8
Cost	64

\[x\]

Alternative 8
Error	61.8
Cost	64

\[1\]

Derivation

1. Initial program 1.3

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

2. Simplified 1.3

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

3. Final simplification 1.3

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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