Details

sample546.0ms

Algorithm

intervals

Results

217.0ms	51×	body	2560	valid
181.0ms	93×	body	1280	valid
42.0ms	55×	body	640	valid
15.0ms	33×	body	320	valid
4.0ms	12×	body	160	valid
2.0ms	12×	body	80	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.3b	(- x (sin x))

rewrite130.0ms

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:

47.0ms	(/ (- x (sin x)) (- x (tan x)))
15.0ms	(- x (tan x))
64.0ms	(- x (sin x))

series238.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(/ (- x (sin x)) (- x (tan x)))
81.0ms	(- x (tan x))
66.0ms	(- x (sin x))

simplify1.7s

Counts

89 → 89

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	915	1147
3	2339	1147
done	5000	1133

prune245.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
17.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite51.0ms

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:

17.0ms	(* 27/2800 (pow x 4))
13.0ms	(* 9/40 (pow x 2))
19.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series126.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(* 27/2800 (pow x 4))
27.0ms	(* 9/40 (pow x 2))
55.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify2.5s

Counts

75 → 75

Iterations

Useful iterations: done (2.5s)

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

prune260.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
17.1b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite74.0ms

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:

24.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 9/40 (pow x 2))
21.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series246.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* 27/2800 (pow x 4))
28.0ms	(* 9/40 (pow x 2))
171.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify2.4s

Counts

73 → 73

Iterations

Useful iterations: done (2.4s)

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

prune250.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.2b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite196.0ms

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:

17.0ms	(/ (sin x) (- x (tan x)))
156.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
9.0ms	(- x (tan x))
10.0ms	(- x (tan x))

series556.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (sin x) (- x (tan x)))
282.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
79.0ms	(- x (tan x))
101.0ms	(- x (tan x))

simplify1.9s

Counts

106 → 106

Iterations

Useful iterations: 3 (794.0ms)

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

prune349.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

100% (0.0b remaining)

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

bsearch105.0ms

Steps

Iters	Range		Point
9	3.244205803610274e-06	1902.9075791774285	0.026773927356951697
8	-45.38980787391071	-0.005411406272604966	-0.02818082991146234

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

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

end0.0ms

sample13.9s

Algorithm

intervals

Results

6.0s	1646×	body	2560	valid
5.5s	2707×	body	1280	valid
1.4s	1867×	body	640	valid
492.0ms	945×	body	320	valid
138.0ms	475×	body	160	valid
57.0ms	360×	body	80	valid