Details

sample299.0ms

Algorithm

intervals

Results

23.0ms	49×	body	1280	valid
12.0ms	44×	body	640	valid
8.0ms	140×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	21	15
3	26	15
4	34	15
5	37	15
done	37	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

2.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series207.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1.0 (* (tan x) (tan x)))
96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify500.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	138	1632
1	314	1486
2	1045	1368
done	5000	1368

prune248.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(+ (tan x) (sqrt 1.0))
0.2b	(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
0.2b	(* (tan x) (tan x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt`
9×	`frac-times` `associate-r`
8×	`flip3-+` `flip-+` `associate-/l/`
7×	`associate-l`
6×	`flip3--` `flip--` `add-log-exp`
5×	`associate-r/` `associate-l/`
4×	`tan-quot`
3×	`times-frac` `swap-sqr` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `pow2` `frac-2neg` `pow-plus` `clear-num` `sum-log` `sqrt-prod` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 105

Calls

4 calls:

17.0ms	(/ (* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
4.0ms	(+ (tan x) (sqrt 1.0))
28.0ms	(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series363.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(+ (tan x) (sqrt 1.0))
103.0ms	(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
33.0ms	(* (tan x) (tan x))

simplify981.0ms

Counts

117 → 117

Iterations

Useful iterations: done (977.0ms)

Iter	Nodes	Cost
0	197	1981
1	540	1646
2	2644	1470
done	5001	1452

prune279.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ 1.0 (* (tan x) (tan x))) (+ (sqrt 1.0) (tan x)))
0.2b	(* (+ (tan x) (sqrt 1.0)) (- (* (sqrt 1.0) (sqrt 1.0)) (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`pow1`
20×	`*-un-lft-identity`
16×	`add-cube-cbrt`
14×	`associate-r`
13×	`associate-l`
12×	`add-exp-log` `add-cbrt-cube`
10×	`frac-times`
9×	`flip3-+` `flip-+`
8×	`tan-quot`
6×	`associate-r/` `swap-sqr` `associate-l/`
4×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`
2×	`pow2` `sub-neg` `pow-plus` `pow-sqr` `pow-prod-up` `distribute-lft-out`
1×	`difference-of-squares`

Counts

4 → 117

Calls

4 calls:

20.0ms	(* (+ 1.0 (* (tan x) (tan x))) (+ (sqrt 1.0) (tan x)))
31.0ms	(* (+ (tan x) (sqrt 1.0)) (- (* (sqrt 1.0) (sqrt 1.0)) (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series269.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (+ 1.0 (* (tan x) (tan x))) (+ (sqrt 1.0) (tan x)))
129.0ms	(* (+ (tan x) (sqrt 1.0)) (- (* (sqrt 1.0) (sqrt 1.0)) (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))

simplify1.1s

Counts

129 → 129

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	190	2152
1	554	1716
2	2768	1534
done	5001	1530

prune342.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (sqrt 1.0))
0.2b	(* (* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.2b	(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
0.2b	(* (tan x) (tan x))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
25×	`add-sqr-sqrt`
24×	`associate-r`
23×	`*-un-lft-identity`
21×	`frac-times`
20×	`add-cbrt-cube`
18×	`pow1`
17×	`add-cube-cbrt`
15×	`associate-*l/`
14×	`prod-exp`
11×	`flip3-+` `flip-+`
9×	`flip3--` `times-frac` `flip--`
8×	`associate-r/` `associate-l*` `cbrt-unprod`
6×	`add-log-exp`
5×	`pow-prod-down`
4×	`tan-quot` `div-exp`
3×	`swap-sqr` `*-commutative`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `rec-exp` `distribute-lft-in` `1-exp` `associate-/r/` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `sum-log` `sqrt-prod` `pow-sqr` `un-div-inv` `pow-prod-up` `div-inv` `distribute-lft-out--`

Counts

4 → 130

Calls

4 calls:

4.0ms	(+ (tan x) (sqrt 1.0))
43.0ms	(* (* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
31.0ms	(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series370.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (tan x) (sqrt 1.0))
193.0ms	(* (* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
103.0ms	(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
36.0ms	(* (tan x) (tan x))

simplify1.8s

Counts

142 → 142

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	248	2846
1	758	2267
2	3745	1983
done	5001	1965

prune311.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes174.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	14	27
done	14	27

end0.0ms

sample1.5s

Algorithm

intervals

Results

652.0ms	1464×	body	1280	valid
342.0ms	1208×	body	640	valid
245.0ms	4339×	body	80	valid
124.0ms	651×	body	320	valid
44.0ms	338×	body	160	valid