Details

sample398.0ms

Algorithm

intervals

Results

48.0ms	30×	body	320	valid
44.0ms	40×	body	1280	valid
31.0ms	46×	body	640	valid
19.0ms	127×	body	80	valid
4.0ms	13×	body	160	valid

simplify72.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	21	15
3	26	15
4	34	15
5	36	15
done	36	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite163.0ms

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:

9.0ms	(- 1.0 (* (tan x) (tan x)))
61.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
49.0ms	(* (tan x) (tan x))
39.0ms	(* (tan x) (tan x))

series545.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- 1.0 (* (tan x) (tan x)))
288.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
55.0ms	(* (tan x) (tan x))
160.0ms	(* (tan x) (tan x))

simplify1.9s

Counts

117 → 117

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	138	1632
1	315	1486
2	856	1368
3	2669	1346
done	5000	1342

prune443.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

51.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
18.0ms	(- (sqrt 1.0) (tan x))
96.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
21.0ms	(* (tan x) (tan x))

series582.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
50.0ms	(- (sqrt 1.0) (tan x))
176.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
46.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

120 → 120

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	193	2015
1	506	1658
2	2207	1479
done	5002	1466

prune836.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.2b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

32.0ms	(/ (* (tan x) (sin x)) (cos x))
25.0ms	(* (tan x) (sin x))
47.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
19.0ms	(* (tan x) (tan x))

series394.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (* (tan x) (sin x)) (cos x))
76.0ms	(* (tan x) (sin x))
168.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
60.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

121 → 121

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	190	1949
1	438	1848
2	1414	1693
done	5000	1689

prune490.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.2b	(* (tan x) (sin x))
0.2b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (/ (* (tan x) (sin x)) (cos x))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
23×	`times-frac`
21×	`add-cube-cbrt`
15×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
7×	`associate-/r*`
6×	`associate-r` `associate-l` `distribute-lft-out` `associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`add-log-exp`
3×	`tan-quot` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`flip3--` `flip3-+` `div-sub` `flip--` `flip-+`

Counts

4 → 106

Calls

4 calls:

16.0ms	(/ (* (tan x) (sin x)) (cos x))
15.0ms	(* (tan x) (sin x))
16.0ms	(* (tan x) (sin x))
49.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (/ (* (tan x) (sin x)) (cos x))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (* (tan x) (sin x)) (cos x))
93.0ms	(* (tan x) (sin x))
85.0ms	(* (tan x) (sin x))
239.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (/ (* (tan x) (sin x)) (cos x))))

simplify1.4s

Counts

118 → 118

Iterations

Useful iterations: 2 (225.0ms)

Iter	Nodes	Cost
0	168	2242
1	391	2168
2	1222	2018
done	5000	2018

prune386.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes249.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	24
1	15	24
done	15	24

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	1456×	body	1280	valid
1.5s	1307×	body	640	valid
726.0ms	4341×	body	80	valid
302.0ms	621×	body	320	valid
147.0ms	275×	body	160	valid