Details

sample476.0ms

Algorithm

intervals

Results

79.0ms	23×	body	320	valid
72.0ms	57×	body	1280	valid
70.0ms	44×	body	640	valid
24.0ms	123×	body	80	valid
4.0ms	9×	body	160	valid

simplify69.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))

rewrite145.0ms

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:

55.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
8.0ms	(- 1.0 (* (tan x) (tan x)))
45.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))

series361.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
43.0ms	(- 1.0 (* (tan x) (tan x)))
65.0ms	(* (tan x) (tan x))
141.0ms	(* (tan x) (tan x))

simplify2.0s

Counts

117 → 117

Iterations

Useful iterations: done (2.0s)

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

prune411.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

36.0ms	(/ (* (tan x) (sin x)) (cos x))
18.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
28.0ms	(* (tan x) (sin x))
22.0ms	(* (tan x) (tan x))

series260.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (* (tan x) (sin x)) (cos x))
80.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
56.0ms	(* (tan x) (sin x))
36.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

95 → 95

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	134	997
1	289	912
2	954	816
done	5001	807

prune357.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(/ (cos x) (* (tan x) (sin x)))
0.3b	(* (tan x) (tan x))
0.6b	(/ 1 (/ (cos x) (* (tan x) (sin x))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
34×	`add-exp-log`
33×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
14×	`pow1` `div-exp`
10×	`tan-quot`
9×	`associate-/r*`
7×	`cbrt-undiv` `associate-*l/`
6×	`associate-r` `associate-l` `prod-exp` `associate-/r/` `div-inv` `associate-/l*`
4×	`cbrt-unprod` `add-log-exp`
3×	`rec-exp` `1-exp` `swap-sqr`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `unswap-sqr`
1×	`pow2` `frac-times` `pow-flip` `pow-plus` `associate-*r/` `pow-sqr` `pow-prod-up` `inv-pow`

Counts

4 → 129

Calls

4 calls:

16.0ms	(* (tan x) (sin x))
16.0ms	(/ (cos x) (* (tan x) (sin x)))
39.0ms	(* (tan x) (tan x))
26.0ms	(/ 1 (/ (cos x) (* (tan x) (sin x))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (tan x) (sin x))
86.0ms	(/ (cos x) (* (tan x) (sin x)))
60.0ms	(* (tan x) (tan x))
99.0ms	(/ 1 (/ (cos x) (* (tan x) (sin x))))

simplify2.0s

Counts

141 → 141

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	186	1690
1	392	1492
2	1107	1284
done	5000	1249

prune398.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos x) (* (tan x) (sin x)))
0.3b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.6b	(/ 1 (/ (cos x) (* (tan x) (sin x))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
32×	`add-exp-log`
27×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`add-cbrt-cube`
14×	`div-exp`
9×	`associate-/r*`
7×	`pow1` `cbrt-undiv`
6×	`unpow-prod-down` `pow-unpow` `associate-/r/` `div-inv` `associate-/l*`
5×	`tan-quot` `associate-*l/`
4×	`prod-exp` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`pow-to-exp` `pow-pow` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `unpow2` `sqr-pow`
1×	`pow-flip` `inv-pow`

Counts

4 → 118

Calls

4 calls:

16.0ms	(/ (cos x) (* (tan x) (sin x)))
7.0ms	(pow (cos x) 2)
8.0ms	(pow (sin x) 2)
34.0ms	(/ 1 (/ (cos x) (* (tan x) (sin x))))

series245.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (cos x) (* (tan x) (sin x)))
25.0ms	(pow (cos x) 2)
20.0ms	(pow (sin x) 2)
85.0ms	(/ 1 (/ (cos x) (* (tan x) (sin x))))

simplify1.3s

Counts

130 → 130

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	192	1558
1	413	1355
2	1146	1163
done	5000	1133

prune417.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes381.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	25
1	22	25
done	22	25

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.8s	1570×	body	1280	valid
1.3s	1219×	body	640	valid
1.0s	4235×	body	80	valid
351.0ms	641×	body	320	valid
91.0ms	335×	body	160	valid