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

Average Error: 11.3 → 0.9

Time: 3.8s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot t}{a - z} \le 3.33043009511256227 \cdot 10^{-175}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \frac{1}{\frac{1}{t}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot t}{a - z} \le 1.65381565469013311 \cdot 10^{288}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((double) (x + ((double) (((double) (((double) (y - z)) * t)) / ((double) (a - z)))))) <= 3.330430095112562e-175)) {
		VAR = ((double) (x + ((double) (((double) (((double) (y - z)) / ((double) (a - z)))) * ((double) (1.0 / ((double) (1.0 / t))))))));
	} else {
		double VAR_1;
		if ((((double) (x + ((double) (((double) (((double) (y - z)) * t)) / ((double) (a - z)))))) <= 1.653815654690133e+288)) {
			VAR_1 = ((double) (x + ((double) (((double) (((double) (y - z)) * t)) / ((double) (a - z))))));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (y - z)) * ((double) (t / ((double) (a - z))))))));
		}
		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	11.3
Target	0.6
Herbie	0.9

\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

1. Split input into 3 regimes

2. if (+ x (/ (* (- y z) t) (- a z))) < 3.33043009511256227e-175

   1. Initial program 10.9

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

   2. Simplified 3.5

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

   4. Applied clear-num 3.8

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

   6. Applied div-inv 3.8

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

   7. Applied *-un-lft-identity 3.8

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

   8. Applied times-frac 3.6

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

   9. Applied associate-*r* 1.3

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

   10. Simplified 1.3

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

   if 3.33043009511256227e-175 < (+ x (/ (* (- y z) t) (- a z))) < 1.65381565469013311e288

   1. Initial program 0.1

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

   if 1.65381565469013311e288 < (+ x (/ (* (- y z) t) (- a z)))

   1. Initial program 53.0

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

   2. Simplified 1.5

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

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot t}{a - z} \le 3.33043009511256227 \cdot 10^{-175}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \frac{1}{\frac{1}{t}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot t}{a - z} \le 1.65381565469013311 \cdot 10^{288}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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