Details

sample151.0ms

Algorithm

intervals

Results

27.0ms	45×	body	1280	valid
15.0ms	39×	body	640	valid
12.0ms	129×	body	80	valid
7.0ms	27×	body	320	valid
3.0ms	16×	body	160	valid

simplify156.0ms

Counts

1 → 1

Iterations

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

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize82.0ms

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))

rewrite85.0ms

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:

26.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))
30.0ms	(* (tan x) (tan x))

series574.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
98.0ms	(- 1.0 (* (tan x) (tan x)))
93.0ms	(* (tan x) (tan x))
95.0ms	(* (tan x) (tan x))

simplify1.1s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	1540
1	350
0	138

prune571.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `pow-unpow` `unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `add-cbrt-cube` `pow-exp` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

6.0ms	(pow (sin x) 2)
5.0ms	(pow (sin x) 2)
5.0ms	(pow (cos x) 2)
5.0ms	(pow (cos x) 2)

series104.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin x) 2)
35.0ms	(pow (sin x) 2)
18.0ms	(pow (cos x) 2)
30.0ms	(pow (cos x) 2)

simplify1.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
3	2364
2	667
1	189
0	64

prune516.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

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 (/ (+ (* (tan x) (tan x)) 1.0) (- 1.0 (* (tan x) (tan x)))))
8.0ms	(- 1.0 (* (tan x) (tan x)))
25.0ms	(* (tan x) (tan x))
30.0ms	(* (tan x) (tan x))

series285.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ 1 (/ (+ (* (tan x) (tan x)) 1.0) (- 1.0 (* (tan x) (tan x)))))
43.0ms	(- 1.0 (* (tan x) (tan x)))
39.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
2	3640
1	638
0	252

prune683.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

633×	`times-frac`
326×	`add-sqr-sqrt`
273×	`*-un-lft-identity` `add-cube-cbrt`
71×	`associate-/r/`
49×	`difference-of-squares`
48×	`add-exp-log`
36×	`div-inv`
32×	`div-exp`
20×	`add-cbrt-cube`
19×	`flip3-+` `flip-+`
18×	`pow1` `associate-/r*`
17×	`flip3--` `flip--`
15×	`associate-/l*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
2×	`pow2` `frac-times` `pow-plus` `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` `associate-/l/`

Counts

4 → 404

Calls

4 calls:

4.0ms	(- 1.0 (* (tan x) (tan x)))
65.0ms	(/ (/ 1 (+ (* (tan x) (tan x)) 1.0)) (/ 1 (- 1.0 (* (tan x) (tan x)))))
12.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))

series284.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- 1.0 (* (tan x) (tan x)))
149.0ms	(/ (/ 1 (+ (* (tan x) (tan x)) 1.0)) (/ 1 (- 1.0 (* (tan x) (tan x)))))
48.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

416 → 416

Iterations

Iter	Nodes
done	5000
1	2234
0	657

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes502.0ms

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
done	12
1	12
0	11

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.0s	1519×	body	1280	valid
1.3s	1213×	body	640	valid
786.0ms	4310×	body	80	valid
350.0ms	632×	body	320	valid
87.0ms	326×	body	160	valid