Details

sample645.0ms

Algorithm

intervals

Results

201.0ms	46×	body	1280	valid
196.0ms	51×	body	640	valid
39.0ms	133×	body	80	valid
19.0ms	20×	body	320	valid
5.0ms	6×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	36
5	36
4	34
3	26
2	21
1	13
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan x)))
0.2b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`insert-posit16`
3×	`associate-/r*`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 114

Calls

4 calls:

5.0ms	(- 1 (* (tan x) (tan x)))
14.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
16.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))

series414.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- 1 (* (tan x) (tan x)))
133.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
106.0ms	(* (tan x) (tan x))
137.0ms	(* (tan x) (tan x))

simplify4.4s

Counts

126 → 126

Iterations

Iter	Nodes
3	2955
2	941
1	358
0	144

prune557.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1 (tan x))
0.2b	(/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x))))
0.2b	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
37×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-r`
16×	`difference-of-squares`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`distribute-lft-out--`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`flip3-+` `tan-quot` `associate-/r/` `flip-+` `insert-posit16`
3×	`frac-times` `associate-/r` `swap-sqr` `associate-l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `flip--` `associate-/l/`
1×	`pow2` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `pow-sqr` `pow-prod-up` `distribute-lft-out`

Counts

4 → 139

Calls

4 calls:

5.0ms	(- 1 (tan x))
19.0ms	(/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x))))
60.0ms	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
27.0ms	(* (tan x) (tan x))

series301.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(- 1 (tan x))
74.0ms	(/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x))))
149.0ms	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
52.0ms	(* (tan x) (tan x))

simplify43.7s

Counts

151 → 151

Iterations

Iter	Nodes
3	6440
2	1864
1	568
0	210

prune646.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
25×	`pow1`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
8×	`times-frac`
6×	`add-log-exp` `difference-of-squares`
5×	`distribute-rgt-out--` `div-inv`
4×	`associate-/r/` `insert-posit16`
3×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 115

Calls

4 calls:

14.0ms	(* (tan x) (tan x))
23.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))
64.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))
171.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

simplify1.4s

Counts

127 → 127

Iterations

Iter	Nodes
3	2697
2	796
1	293
0	121

prune409.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
22×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
21×	`pow-plus`
20×	`frac-times`
16×	`pow2` `*-un-lft-identity` `add-cube-cbrt`
14×	`associate-l/` `associate-r/`
11×	`prod-exp` `cbrt-unprod`
10×	`swap-sqr` `associate-r` `associate-l`
4×	`*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`

Counts

4 → 166

Calls

4 calls:

15.0ms	(* (tan x) (tan x))
13.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
81.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (tan x) (tan x))
55.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))
87.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify2.9s

Counts

178 → 178

Iterations

Iter	Nodes
4	4413
3	1927
2	870
1	287
0	108

prune486.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes322.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.6s	1521×	body	1280	valid
1.6s	4276×	body	80	valid
1.3s	1284×	body	640	valid
478.0ms	631×	body	320	valid
128.0ms	288×	body	160	valid