Details

sample216.0ms

Algorithm

intervals

Results

39.0ms	45×	body	1280	valid
22.0ms	39×	body	640	valid
18.0ms	129×	body	80	valid
11.0ms	27×	body	320	valid
5.0ms	16×	body	160	valid

simplify83.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
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` `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 → 105

Calls

4 calls:

33.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
12.0ms	(* (tan x) (tan x))
26.0ms	(* (tan x) (tan x))

series459.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
57.0ms	(- 1.0 (* (tan x) (tan x)))
54.0ms	(* (tan x) (tan x))
50.0ms	(* (tan x) (tan x))

simplify1.0s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	1540
1	350
0	138

prune572.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

7.0ms	(- (sqrt 1.0) (tan x))
68.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
14.0ms	(+ (sqrt 1.0) (tan x))
24.0ms	(* (tan x) (tan x))

series312.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (sqrt 1.0) (tan x))
142.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
66.0ms	(+ (sqrt 1.0) (tan x))
41.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	2278
1	374
0	133

prune570.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
16×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
8×	`add-cbrt-cube` `tan-quot` `add-exp-log` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
2×	`pow2` `frac-times` `+-commutative` `sum-log` `flip3-+` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

7.0ms	(+ (sqrt 1.0) (tan x))
7.0ms	(+ (sqrt 1.0) (tan x))
23.0ms	(* (tan x) (tan x))
30.0ms	(* (tan x) (tan x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (sqrt 1.0) (tan x))
60.0ms	(+ (sqrt 1.0) (tan x))
61.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))

simplify901.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	956
1	204
0	79

prune663.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
80×	`add-sqr-sqrt`
63×	`*-un-lft-identity` `add-cube-cbrt`
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--` `div-inv` `flip--`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 165

Calls

4 calls:

36.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
8.0ms	(- 1.0 (* (tan x) (tan x)))
23.0ms	(* (tan x) (tan x))
23.0ms	(* (tan x) (tan x))

series288.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
42.0ms	(- 1.0 (* (tan x) (tan x)))
69.0ms	(* (tan x) (tan x))
39.0ms	(* (tan x) (tan x))

simplify2.2s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
2	3534
1	634
0	249

prune864.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes372.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.0s	1519×	body	1280	valid
1.2s	4310×	body	80	valid
771.0ms	1213×	body	640	valid
261.0ms	632×	body	320	valid
82.0ms	326×	body	160	valid