Details

sample525.0ms

Algorithm

intervals

Results

127.0ms	52×	body	2560	valid
57.0ms	85×	body	1280	valid
24.0ms	68×	body	640	valid
5.0ms	22×	body	320	valid
3.0ms	20×	body	160	valid
1.0ms	9×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (sin x))
0.9b	(- x (tan x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

29.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (sin x))
7.0ms	(- x (tan x))

series186.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- x (sin x)) (- x (tan x)))
38.0ms	(- x (sin x))
67.0ms	(- x (tan x))

simplify1.0s

Counts

89 → 89

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	915	1147
3	2332	1147
done	5000	1133

prune203.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
16.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

14.0ms	(* 27/2800 (pow x 4))
12.0ms	(* 9/40 (pow x 2))
18.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series121.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* 27/2800 (pow x 4))
31.0ms	(* 9/40 (pow x 2))
50.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify1.5s

Counts

75 → 75

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	121	788
1	277	703
2	674	643
3	2581	637
done	5000	634

prune145.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
16.1b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

12.0ms	(* 27/2800 (pow x 4))
11.0ms	(* 9/40 (pow x 2))
10.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series182.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* 27/2800 (pow x 4))
27.0ms	(* 9/40 (pow x 2))
116.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify1.5s

Counts

73 → 73

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	113	715
1	254	624
2	574	570
3	2285	560
done	5000	555

prune143.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.9b	(- x (tan x))
0.9b	(- x (tan x))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

15.0ms	(/ (sin x) (- x (tan x)))
78.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series359.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (sin x) (- x (tan x)))
184.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
53.0ms	(- x (tan x))
57.0ms	(- x (tan x))

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: 3 (531.0ms)

Iter	Nodes	Cost
0	177	1565
1	377	1511
2	938	1449
3	2824	1445
done	5001	1445

prune238.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch83.0ms

Steps

Iters	Range		Point
10	0.0001820196720056695	1126179.5725289274	0.026533802681284316
9	-76786.820650899	-0.0002772006047103471	-0.028801687005274378

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	49
1	29	36
done	29	36

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.7s	1719×	body	2560	valid
1.9s	2751×	body	1280	valid
601.0ms	1804×	body	640	valid
225.0ms	911×	body	320	valid
72.0ms	468×	body	160	valid
31.0ms	347×	body	80	valid