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

Average Error: 1.4 → 1.9

Time: 3.7s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;a \le -2.20351639908775475 \cdot 10^{-163}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 3.41669861876213973 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + {\left(\frac{y}{\frac{a - t}{z - t}}\right)}^{1}\\ \end{array}\]

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) {
	double VAR;
	if ((a <= -2.2035163990877547e-163)) {
		VAR = (x + (y * ((z - t) / (a - t))));
	} else {
		double VAR_1;
		if ((a <= 3.4166986187621397e-99)) {
			VAR_1 = (x + ((y / (a - t)) * (z - t)));
		} else {
			VAR_1 = (x + pow((y / ((a - t) / (z - t))), 1.0));
		}
		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	1.4
Target	0.4
Herbie	1.9

\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Split input into 3 regimes

2. if a < -2.2035163990877547e-163

   1. Initial program 0.8

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

   if -2.2035163990877547e-163 < a < 3.4166986187621397e-99

   1. Initial program 3.2

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

   3. Applied clear-num 3.2

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
   4. Using strategy rm

   5. Applied associate-/r/ 3.2

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

   6. Applied associate-*r* 5.0

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

   7. Simplified 4.9

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

   if 3.4166986187621397e-99 < a

   1. Initial program 0.6

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

   3. Applied clear-num 0.7

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
   4. Using strategy rm

   5. Applied pow1 0.7

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

   6. Applied pow1 0.7

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

   7. Applied pow-prod-down 0.7

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

   8. Simplified 0.6

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

4. Final simplification 1.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.20351639908775475 \cdot 10^{-163}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 3.41669861876213973 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + {\left(\frac{y}{\frac{a - t}{z - t}}\right)}^{1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020079 
(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 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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