Details

sample494.0ms

Algorithm

intervals

Results

197.0ms	57×	body	2560	valid
159.0ms	83×	body	1280	valid
36.0ms	55×	body	640	valid
18.0ms	38×	body	320	valid
5.0ms	16×	body	160	valid
1.0ms	7×	body	80	valid

simplify25.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite83.0ms

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:

29.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
43.0ms	(- x (sin x))

series313.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(/ (- x (sin x)) (- x (tan x)))
106.0ms	(- x (tan x))
88.0ms	(- x (sin x))

simplify1.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1382
1	372
0	157

prune455.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.2b	(/ (sin x) (cos x))
1.7b	(- x (/ (sin x) (cos x)))
1.7b	(- x (sin x))

rewrite96.0ms

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

Counts

4 → 115

Calls

4 calls:

61.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
13.0ms	(/ (sin x) (cos x))
13.0ms	(- x (/ (sin x) (cos x)))
5.0ms	(- x (sin x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
22.0ms	(/ (sin x) (cos x))
74.0ms	(- x (/ (sin x) (cos x)))
42.0ms	(- x (sin x))

simplify1.3s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	1881
1	479
0	206

prune567.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.5b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.7b	(- x (tan x))
1.7b	(- x (tan x))

rewrite147.0ms

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:

23.0ms	(/ (sin x) (- x (tan x)))
102.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
8.0ms	(- x (tan x))
8.0ms	(- x (tan x))

series575.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (sin x) (- x (tan x)))
307.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
103.0ms	(- x (tan x))
84.0ms	(- x (tan x))

simplify1.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1452
1	389
0	177

prune457.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize157.0ms

Local error

Found 4 expressions with local error:

1.7b	(- x (tan x))
1.7b	(- x (tan x))
1.7b	(- x (tan x))
1.7b	(- x (tan x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

4.0ms	(- x (tan x))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series382.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- x (tan x))
100.0ms	(- x (tan x))
101.0ms	(- x (tan x))
74.0ms	(- x (tan x))

simplify1.6s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
4	1711
3	566
2	215
1	94
0	46

prune333.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.3b

bsearch190.0ms

Steps

Iters	Range		Point
10	2.777137017098532e-16	1126.7541422477805	0.028895895787442862
9	-0.042530208599811804	-3.2052418334402957e-07	-0.027282959219290626

simplify10.0ms

Iterations

Iter	Nodes
done	47
1	47
0	35

end0.0ms

sample12.7s

Algorithm

intervals

Results

5.4s	1636×	body	2560	valid
4.6s	2718×	body	1280	valid
1.5s	1883×	body	640	valid
569.0ms	493×	body	160	valid
371.0ms	929×	body	320	valid
123.0ms	341×	body	80	valid