Details

sample544.0ms

Algorithm

intervals

Results

207.0ms	57×	body	2560	valid
157.0ms	83×	body	1280	valid
38.0ms	55×	body	640	valid
21.0ms	38×	body	320	valid
6.0ms	16×	body	160	valid
1.0ms	7×	body	80	valid

simplify20.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize25.0ms

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))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 110

Calls

3 calls:

28.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
13.0ms	(- x (sin x))

series277.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(/ (- x (sin x)) (- x (tan x)))
106.0ms	(- x (tan x))
57.0ms	(- x (sin x))

simplify1.6s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2273
1	502
0	209

prune582.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

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))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 588

Calls

4 calls:

14.0ms	(/ (sin x) (- x (tan x)))
120.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
14.0ms	(- x (tan x))
10.0ms	(- x (tan x))

series473.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (sin x) (- x (tan x)))
237.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
59.0ms	(- x (tan x))
78.0ms	(- x (tan x))

simplify3.1s

Counts

600 → 600

Iterations

Iter	Nodes
done	5000
2	4814
1	1405
0	617

prune2.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize118.0ms

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))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

10.0ms	(- x (tan x))
10.0ms	(- x (tan x))
12.0ms	(- x (tan x))
11.0ms	(- x (tan x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- x (tan x))
73.0ms	(- x (tan x))
81.0ms	(- x (tan x))
64.0ms	(- x (tan x))

simplify6.5s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
3	4686
2	582
1	162
0	73

prune646.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin x) (cos x))
0.5b	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
15.3b	(/ (sin x) (* x x))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
214×	`add-sqr-sqrt`
207×	`*-un-lft-identity`
205×	`add-cube-cbrt`
129×	`prod-diff`
43×	`fma-neg`
19×	`div-inv`
13×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
7×	`associate-/r*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `difference-of-squares`
2×	`quot-tan`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `cbrt-unprod` `fma-udef` `flip--` `associate--r+` `distribute-lft-out--`

Counts

4 → 274

Calls

4 calls:

12.0ms	(/ (sin x) (cos x))
12.0ms	(/ (sin x) (cos x))
64.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
10.0ms	(/ (sin x) (* x x))

series355.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (sin x) (cos x))
21.0ms	(/ (sin x) (cos x))
242.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
59.0ms	(/ (sin x) (* x x))

simplify2.2s

Counts

286 → 286

Iterations

Iter	Nodes
done	5001
2	3743
1	859
0	370

prune2.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes93.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.7b

bsearch123.0ms

Steps

Iters	Range		Point
10	2.777137017098532e-16	1126.7541422477805	1.5873405327964933
9	-291337.82152789796	-0.7274215675205146	-2.444222751025643

simplify15.0ms

Iterations

Iter	Nodes
done	40
1	40
0	34

end0.0ms

sample13.2s

Algorithm

intervals

Results

5.6s	1636×	body	2560	valid
5.2s	2718×	body	1280	valid
1.4s	1883×	body	640	valid
483.0ms	929×	body	320	valid
137.0ms	493×	body	160	valid
53.0ms	341×	body	80	valid