Details

sample370.0ms

Algorithm

intervals

Results

49.0ms	50×	body	1280	valid
24.0ms	163×	body	80	valid
21.0ms	34×	body	640	valid
12.0ms	28×	body	320	valid
4.0ms	37×	body	80	nan
2.0ms	6×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	80	26
3	147	26
4	329	26
5	878	26
6	2973	26
done	5001	26

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
9.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`associate-l` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`pow-neg` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-r/` `pow-exp` `associate-/r` `associate-/l*` `pow-sub`
2×	`frac-times` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `associate-/r/` `un-div-inv`

Counts

4 → 154

Calls

4 calls:

2.0ms	(/ F (sin B))
10.0ms	(* x (/ 1.0 (tan B)))
83.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ F (sin B))
110.0ms	(* x (/ 1.0 (tan B)))
289.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
154.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify691.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (219.0ms)

Iter	Nodes	Cost
0	303	2726
1	778	2555
2	2332	2401
done	5001	2401

prune640.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.4b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
16.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
31×	`times-frac`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`pow-neg` `associate-*r/` `div-exp` `unswap-sqr`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `pow-exp` `associate-/r*` `associate-/l/` `pow-sub` `sqr-pow`
2×	`un-div-inv` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 133

Calls

4 calls:

8.0ms	(* x (/ 1.0 (tan B)))
74.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
29.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series835.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* x (/ 1.0 (tan B)))
211.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
358.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
150.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify60.0ms

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	285	2554