Details

sample251.0ms

Algorithm

intervals

Results

48.0ms	46×	body	1280	valid
21.0ms	141×	body	80	valid
20.0ms	28×	body	640	valid
13.0ms	26×	body	320	valid
5.0ms	15×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

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:

19.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
37.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))

series383.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
66.0ms	(- 1.0 (* (tan x) (tan x)))
51.0ms	(* (tan x) (tan x))
90.0ms	(* (tan x) (tan x))

simplify2.2s

Counts

117 → 117

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	138	1632
1	315	1486
2	861	1368
3	2678	1346
done	5001	1342

prune351.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

17.0ms	(+ (sqrt 1.0) (tan x))
18.0ms	(- (sqrt 1.0) (tan x))
108.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
16.0ms	(* (tan x) (tan x))

series315.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (sqrt 1.0) (tan x))
66.0ms	(- (sqrt 1.0) (tan x))
143.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
44.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

101 → 101

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	135	1238
1	322	1033
2	1203	955
done	5000	949

prune355.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
80×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube` `difference-of-squares`
9×	`associate-/r/`
8×	`tan-quot`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 165

Calls

4 calls:

10.0ms	(- 1.0 (* (tan x) (tan x)))
46.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
23.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))

series292.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- 1.0 (* (tan x) (tan x)))
126.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
47.0ms	(* (tan x) (tan x))
54.0ms	(* (tan x) (tan x))

simplify2.7s

Counts

177 → 177

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	249	3696
1	532	3293
2	1243	3001
3	3529	2878
done	5000	2874

prune387.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.4b	(pow (tan x) 4)
0.6b	(pow (tan x) 6)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log`
8×	`tan-quot` `add-cbrt-cube`
6×	`unpow-prod-down` `pow-unpow` `swap-sqr` `associate-r` `associate-l`
4×	`add-log-exp`
2×	`pow2` `frac-times` `pow-to-exp` `pow-pow` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

32.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
8.0ms	(pow (tan x) 4)
9.0ms	(pow (tan x) 6)

series246.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))
58.0ms	(pow (tan x) 4)
94.0ms	(pow (tan x) 6)

simplify2.3s

Counts

102 → 102

Iterations

Useful iterations: 3 (675.0ms)

Iter	Nodes	Cost
0	113	804
1	236	645
2	536	571
3	2188	539
done	5000	539

prune490.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes150.0ms

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	9	17
1	12	17
done	12	17

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.6s	1546×	body	1280	valid
916.0ms	1258×	body	640	valid
666.0ms	4253×	body	80	valid
330.0ms	634×	body	320	valid
84.0ms	309×	body	160	valid