Details

sample699.0ms

Algorithm

intervals

Results

265.0ms	49×	body	2560	valid
131.0ms	81×	body	1280	valid
58.0ms	65×	body	640	valid
19.0ms	33×	body	320	valid
14.0ms	16×	body	160	valid
3.0ms	12×	body	80	valid

simplify28.0ms

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: 31.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.3b	(- x (tan x))
2.3b	(- x (sin x))

rewrite68.0ms

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:

46.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series266.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(/ (- x (sin x)) (- x (tan x)))
118.0ms	(- x (tan x))
44.0ms	(- x (sin x))

simplify909.0ms

Counts

89 → 89

Iterations

Useful iterations: done (905.0ms)

Iter	Nodes	Cost
0	157	1237
1	371	1200
2	1358	1149
done	5001	1147

prune276.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
2.2b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.3b	(- x (tan x))
2.3b	(- x (tan x))

rewrite161.0ms

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:

19.0ms	(/ (sin x) (- x (tan x)))
127.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
6.0ms	(- x (tan x))
6.0ms	(- x (tan x))

series554.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (sin x) (- x (tan x)))
318.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
71.0ms	(- x (tan x))
87.0ms	(- x (tan x))

simplify829.0ms

Counts

106 → 106

Iterations

Useful iterations: done (825.0ms)

Iter	Nodes	Cost
0	177	1565
1	388	1511
2	1424	1450
done	5000	1449

prune319.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.2b	(/ (sin x) (cos x))
2.3b	(- x (/ (sin x) (cos x)))
2.3b	(- x (sin x))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
46×	`times-frac`
25×	`add-cube-cbrt`
22×	`difference-of-squares`
15×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `div-inv` `associate-/l/`
1×	`quot-tan` `div-sub`

Counts

4 → 115

Calls

4 calls:

83.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
18.0ms	(/ (sin x) (cos x))
26.0ms	(- x (/ (sin x) (cos x)))
20.0ms	(- x (sin x))

series293.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
31.0ms	(/ (sin x) (cos x))
87.0ms	(- x (/ (sin x) (cos x)))
44.0ms	(- x (sin x))

simplify1.1s

Counts

127 → 127

Iterations

Useful iterations: 2 (270.0ms)

Iter	Nodes	Cost
0	206	2024
1	479	1960
2	1886	1880
done	5000	1880

prune390.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.3b	(* 27/2800 (pow x 4))
15.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite83.0ms

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:

19.0ms	(* 9/40 (pow x 2))
24.0ms	(* 27/2800 (pow x 4))
39.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series162.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* 9/40 (pow x 2))
49.0ms	(* 27/2800 (pow x 4))
54.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify752.0ms

Counts

75 → 75

Iterations

Useful iterations: done (750.0ms)

Iter	Nodes	Cost
0	121	788
1	291	703
2	1076	645
done	5000	643

prune205.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch138.0ms

Steps

Iters	Range		Point
8	0.01136632641909174	309.51167567074003	0.028269902272629245
10	-1950712569354.648	-0.00015980627971116164	-0.03059660473543996

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	49
1	34	49
done	34	49

end0.0ms

sample13.6s

Algorithm

intervals

Results

6.4s	1573×	body	2560	valid
4.1s	2754×	body	1280	valid
2.2s	1893×	body	640	valid
486.0ms	949×	body	320	valid
143.0ms	479×	body	160	valid
59.0ms	352×	body	80	valid