Details

sample544.0ms

Algorithm

intervals

Results

115.0ms	44×	body	2560	valid
49.0ms	77×	body	1280	valid
31.0ms	38×	body	320	valid
24.0ms	65×	body	640	valid
3.0ms	17×	body	80	valid
2.0ms	15×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5
done	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize12.0ms

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))

rewrite56.0ms

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×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

34.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (sin x))
9.0ms	(- x (tan x))

series180.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
65.0ms	(- x (tan x))

simplify55.0ms

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854
done	5001	854

prune235.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.0b	(- x (tan x))
1.0b	(- x (tan x))

rewrite202.0ms

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-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 588

Calls

4 calls:

17.0ms	(/ (sin x) (- x (tan x)))
112.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
7.0ms	(- x (tan x))
7.0ms	(- x (tan x))

series356.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (sin x) (- x (tan x)))
184.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
55.0ms	(- x (tan x))
52.0ms	(- x (tan x))

simplify195.0ms

Counts

600 → 600

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1359	22035
1	3883	15840
2	5001	15776
done	5001	15776

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (- (/ x (- x (tan x))) (/ (sin x) (- x (tan x)))))
0.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.0b	(- x (tan x))
1.0b	(- x (tan x))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

695×	`*-un-lft-identity`
685×	`add-sqr-sqrt`
663×	`times-frac`
459×	`prod-diff`
407×	`add-cube-cbrt`
143×	`distribute-lft-out--`
137×	`difference-of-squares`
90×	`associate-/r/`
48×	`flip3--` `flip--`
45×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube`
3×	`sub-neg` `distribute-rgt-out--` `diff-log`
1×	`expm1-log1p` `frac-sub` `expm1-udef` `sub-div`

Counts

4 → 560

Calls

4 calls:

0.0ms	(expm1 (- (/ x (- x (tan x))) (/ (sin x) (- x (tan x)))))
112.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
7.0ms	(- x (tan x))
7.0ms	(- x (tan x))

series538.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(expm1 (- (/ x (- x (tan x))) (/ (sin x) (- x (tan x)))))
184.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
59.0ms	(- x (tan x))
53.0ms	(- x (tan x))

simplify196.0ms

Counts

572 → 572

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	1398	21905
1	3937	15695
2	5001	15635
done	5001	15635

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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))
1.1b	(fma x (/ 1 (- x (tan x))) (- (/ (sin x) (- x (tan x)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

16.0ms	(/ (sin x) (- x (tan x)))
10.0ms	(- x (tan x))
7.0ms	(- x (tan x))
0.0ms	(fma x (/ 1 (- x (tan x))) (- (/ (sin x) (- x (tan x)))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (sin x) (- x (tan x)))
56.0ms	(- x (tan x))
57.0ms	(- x (tan x))
206.0ms	(fma x (/ 1 (- x (tan x))) (- (/ (sin x) (- x (tan x)))))

simplify40.0ms

Counts

117 → 117

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	353	1013
1	1246	795
2	5002	795
done	5002	795

prune276.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

100% (0.0b remaining)

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

bsearch90.0ms

Steps

Iters	Range		Point
8	0.016621422887445694	5.276955647516397	0.040791126062083655
9	-0.05800990145057735	-1.1864783425707322e-08	-0.03558841906319749

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	22
1	40	22
done	40	22

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1613×	body	2560	valid
1.8s	2704×	body	1280	valid
661.0ms	1926×	body	640	valid
214.0ms	934×	body	320	valid
82.0ms	475×	body	160	valid
32.0ms	348×	body	80	valid