Details

sample230.0ms

Algorithm

intervals

Results

61.0ms	50×	body	1280	valid
35.0ms	41×	body	640	valid
27.0ms	140×	body	80	valid
11.0ms	17×	body	320	valid
3.0ms	8×	body	160	valid

simplify77.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	36
5	36
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

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

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:

15.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms	(- 1 (* (tan x) (tan x)))
38.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))

series296.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
58.0ms	(- 1 (* (tan x) (tan x)))
53.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))

simplify2.8s

Counts

126 → 126

Iterations

Iter	Nodes
3	2613
2	939
1	356
0	144

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
0.2b	(- 1 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(* (tan x) (sin x))
0.2b	(* (tan x) (tan x))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

44.0ms	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
9.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
16.0ms	(* (tan x) (sin x))
29.0ms	(* (tan x) (tan x))

series294.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
77.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
60.0ms	(* (tan x) (sin x))
39.0ms	(* (tan x) (tan x))

simplify10.5s

Counts

122 → 122

Iterations

Iter	Nodes
3	4188
2	1249
1	433
0	179

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.3b	(- 1 (sqrt (/ (* (tan x) (sin x)) (cos x))))
16.1b	(sqrt (/ (* (tan x) (sin x)) (cos x)))
16.1b	(sqrt (/ (* (tan x) (sin x)) (cos x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `sqrt-prod`
13×	`pow1`
12×	`add-cube-cbrt`
6×	`times-frac` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`tan-quot` `insert-posit16` `difference-of-squares`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div` `div-inv` `distribute-lft-out--`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

14.0ms	(* (tan x) (tan x))
9.0ms	(- 1 (sqrt (/ (* (tan x) (sin x)) (cos x))))
7.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))
9.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (tan x) (tan x))
72.0ms	(- 1 (sqrt (/ (* (tan x) (sin x)) (cos x))))
93.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))
101.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))

simplify3.4s

Counts

98 → 98

Iterations

Iter	Nodes
4	4336
3	1445
2	603
1	245
0	122

prune1.4s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.4b	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

rewrite120.0ms

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:

28.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))
36.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))
41.0ms	(* (tan x) (tan x))
150.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

simplify2.2s

Counts

127 → 127

Iterations

Iter	Nodes
3	2697
2	796
1	293
0	121

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes378.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	19
1	19
0	15

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.3s	1520×	body	1280	valid
1.3s	1261×	body	640	valid
934.0ms	4317×	body	80	valid
821.0ms	600×	body	320	valid
119.0ms	302×	body	160	valid