Details

sample385.0ms

Algorithm

intervals

Results

243.0ms	47×	body	1280	valid
27.0ms	44×	body	640	valid
16.0ms	138×	body	80	valid
9.0ms	20×	body	320	valid
2.0ms	7×	body	160	valid

simplify93.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	21	15
3	26	15
4	34	15
5	37	15
done	37	15

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

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)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite157.0ms

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:

21.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
42.0ms	(* (tan x) (tan x))
83.0ms	(* (tan x) (tan x))

series300.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
37.0ms	(- 1.0 (* (tan x) (tan x)))
37.0ms	(* (tan x) (tan x))
76.0ms	(* (tan x) (tan x))

simplify1.1s

Counts

117 → 117

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	138	1632
1	351	1506
2	1541	1370
done	5002	1360

prune793.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)
0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

4.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)
3.0ms	(pow (cos x) 2)
4.0ms	(pow (cos x) 2)

series114.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (sin x) 2)
34.0ms	(pow (sin x) 2)
24.0ms	(pow (cos x) 2)
24.0ms	(pow (cos x) 2)

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: 2 (162.0ms)

Iter	Nodes	Cost
0	64	576
1	189	492
2	648	432
3	2390	432
done	5004	432

prune387.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

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` `associate-r/` `swap-sqr` `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-l/` `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:

19.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
16.0ms	(* (sin x) (tan x))
15.0ms	(/ (* (sin x) (tan x)) (cos x))
28.0ms	(* (tan x) (tan x))

series294.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
82.0ms	(* (sin x) (tan x))
78.0ms	(/ (* (sin x) (tan x)) (cos x))
45.0ms	(* (tan x) (tan x))

simplify1.2s

Counts

95 → 95

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	134	997
1	334	914
2	2001	824
done	5002	815

prune376.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
92×	`add-sqr-sqrt`
72×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-/r*`
21×	`add-exp-log`
19×	`pow1`
16×	`difference-of-squares`
15×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`tan-quot` `div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow2` `frac-times` `rec-exp` `frac-2neg` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`pow-flip` `flip3-+` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

67.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
39.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
15.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))

series422.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
162.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
42.0ms	(* (tan x) (tan x))
63.0ms	(* (tan x) (tan x))

simplify2.7s

Counts

199 → 199

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	260	4414
1	682	4023
2	3567	3749
done	5002	3549

prune497.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes291.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	23
1	12	23
done	12	23

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.9s	1483×	body	1280	valid
885.0ms	1239×	body	640	valid
714.0ms	4344×	body	80	valid
347.0ms	618×	body	320	valid
83.0ms	316×	body	160	valid