Details

sample530.0ms

Algorithm

intervals

Results

124.0ms	47×	body	2560	valid
64.0ms	87×	body	1280	valid
20.0ms	61×	body	640	valid
11.0ms	40×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	11×	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)))
2.1b	(- x (tan x))
2.1b	(- x (sin x))

rewrite49.0ms

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:

31.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series182.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
43.0ms	(- x (sin 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	2339	1147
done	5000	1133

prune201.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(* 27/2800 (pow x 4))
0.3b	(* 9/40 (pow x 2))
15.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite47.0ms

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:

12.0ms	(* 27/2800 (pow x 4))
14.0ms	(* 9/40 (pow x 2))
19.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series118.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* 27/2800 (pow x 4))
30.0ms	(* 9/40 (pow x 2))
48.0ms	(- (* 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

prune139.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (cos x))
0.3b	(* (pow x 2) (cos x))
2.5b	(- (/ (sin x) (cos x)) (sin x))
13.0b	(/ (sin x) (* (pow x 2) (cos x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`add-exp-log`
13×	`*-un-lft-identity` `add-cbrt-cube`
11×	`add-cube-cbrt` `associate-l`
7×	`prod-exp`
6×	`pow1` `associate-r` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `times-frac` `div-exp`
3×	`cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `pow-to-exp` `pow-exp` `*-commutative` `unpow2` `difference-of-squares` `sqr-pow`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `associate-/r*` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 83

Calls

4 calls:

8.0ms	(* x (cos x))
13.0ms	(* (pow x 2) (cos x))
27.0ms	(- (/ (sin x) (cos x)) (sin x))
14.0ms	(/ (sin x) (* (pow x 2) (cos x)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* x (cos x))
38.0ms	(* (pow x 2) (cos x))
56.0ms	(- (/ (sin x) (cos x)) (sin x))
47.0ms	(/ (sin x) (* (pow x 2) (cos x)))

simplify2.3s

Counts

95 → 95

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	156	1004
1	344	953
2	1003	848
3	4628	845
done	5000	845

prune260.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes50.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.7b

bsearch100.0ms

Steps

Iters	Range		Point
11	6.1632953816490534e-12	2923699147.8271213	2.4713749402345115
10	-21283307590.397102	-3.152803306627408e-07	-0.02620088919165833

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	63
1	46	63
done	46	63

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.6s	1608×	body	2560	valid
1.9s	2725×	body	1280	valid
651.0ms	1853×	body	640	valid
228.0ms	954×	body	320	valid
94.0ms	502×	body	160	valid
35.0ms	358×	body	80	valid