Details

sample453.0ms

Algorithm

intervals

Results

201.0ms	57×	body	2560	valid
135.0ms	82×	body	1280	valid
41.0ms	59×	body	640	valid
15.0ms	38×	body	320	valid
4.0ms	12×	body	160	valid
1.0ms	8×	body	80	valid

simplify61.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.0b	(- x (sin x))
1.0b	(- x (tan x))

rewrite40.0ms

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×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 80

Calls

3 calls:

25.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))
6.0ms	(- x (tan x))

series256.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (sin x))
85.0ms	(- x (tan x))

simplify1.8s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
3	3309
2	961
1	372
0	157

prune392.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.0b	(- x (tan x))
1.0b	(- x (tan x))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite119.0ms

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×	`flip3--` `add-cbrt-cube` `add-exp-log` `associate-/r/` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

24.0ms	(/ (sin x) (- x (tan x)))
6.0ms	(- x (tan x))
4.0ms	(- x (tan x))
79.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

series547.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (sin x) (- x (tan x)))
88.0ms	(- x (tan x))
92.0ms	(- x (tan x))
283.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

simplify2.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5015
3	4080
2	1132
1	389
0	177

prune545.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 27/2800 (* x x)) (* x x))
0.2b	(* 9/40 (* x x))
0.2b	(* 27/2800 (* x x))
15.1b	(- (* 9/40 (* x x)) (* (* 27/2800 (* x x)) (* x x)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

35×	`pow1` `add-cbrt-cube` `add-exp-log`
21×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`associate-l`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`associate-r` `*-commutative`
2×	`unswap-sqr`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `flip--`

Counts

4 → 79

Calls

4 calls:

77.0ms	(* (* 27/2800 (* x x)) (* x x))
25.0ms	(* 9/40 (* x x))
22.0ms	(* 27/2800 (* x x))
15.0ms	(- (* 9/40 (* x x)) (* (* 27/2800 (* x x)) (* x x)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* 27/2800 (* x x)) (* x x))
37.0ms	(* 9/40 (* x x))
33.0ms	(* 27/2800 (* x x))
145.0ms	(- (* 9/40 (* x x)) (* (* 27/2800 (* x x)) (* x x)))

simplify1.9s

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1106
1	302
0	102

prune254.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes128.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch179.0ms

Steps

Iters	Range		Point
11	3.4817375791661903e-26	573579.0075499975	0.0289731118094174
10	-84463.33967257517	-3.2432757514909933e-09	-0.029114572981685117

simplify9.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample13.6s

Algorithm

intervals

Results

6.0s	1654×	body	2560	valid
4.9s	2751×	body	1280	valid
1.3s	1866×	body	640	valid
577.0ms	925×	body	320	valid
526.0ms	345×	body	80	valid
137.0ms	459×	body	160	valid