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

Average Error: 10.6 → 0.7

Time: 4.6s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -8.02507296804989 \cdot 10^{+199}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(t \cdot \frac{1}{a - z}\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 6.154305159463207 \cdot 10^{+278}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array}\]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (* (- y z) t) (- a z)) -8.02507296804989e+199)
   (+ x (* (- y z) (* t (/ 1.0 (- a z)))))
   (if (<= (/ (* (- y z) t) (- a z)) 6.154305159463207e+278)
     (+ (/ (* (- y z) t) (- a z)) x)
     (+ x (* (- y z) (/ t (- a z)))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((((double) (((double) (y - z)) * t)) / ((double) (a - z))) <= -8.02507296804989e+199)) {
		tmp = ((double) (x + ((double) (((double) (y - z)) * ((double) (t * (1.0 / ((double) (a - z)))))))));
	} else {
		double tmp_1;
		if (((((double) (((double) (y - z)) * t)) / ((double) (a - z))) <= 6.154305159463207e+278)) {
			tmp_1 = ((double) ((((double) (((double) (y - z)) * t)) / ((double) (a - z))) + x));
		} else {
			tmp_1 = ((double) (x + ((double) (((double) (y - z)) * (t / ((double) (a - z)))))));
		}
		tmp = tmp_1;
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.6
Target	0.5
Herbie	0.7

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

Derivation

1. Split input into 3 regimes

2. if (/ (* (- y z) t) (- a z)) < -8.02507296804988997e199

   1. Initial program Error: 47.7 bits

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

   2. Simplified Error: 3.4 bits

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

   4. Applied div-inv Error: 3.5 bits

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

   if -8.02507296804988997e199 < (/ (* (- y z) t) (- a z)) < 6.1543051594632072e278

   1. Initial program Error: 0.2 bits

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

   if 6.1543051594632072e278 < (/ (* (- y z) t) (- a z))

   1. Initial program Error: 60.7 bits

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

   2. Simplified Error: 1.3 bits

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

4. Final simplification Error: 0.7 bits

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -8.02507296804989 \cdot 10^{+199}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(t \cdot \frac{1}{a - z}\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 6.154305159463207 \cdot 10^{+278}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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))))