Details

sample450.0ms

Algorithm

intervals

Results

197.0ms	40×	body	2560	valid
120.0ms	97×	body	1280	valid
33.0ms	55×	body	640	valid
15.0ms	36×	body	320	valid
7.0ms	21×	body	160	valid
1.0ms	7×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.4b	(- x (sin x))

rewrite62.0ms

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:

46.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series262.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(/ (- x (sin x)) (- x (tan x)))
97.0ms	(- x (tan x))
44.0ms	(- x (sin x))

simplify694.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1382
1	372
0	157

prune398.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.3b	(- x (tan x))
1.3b	(- x (tan x))
1.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite152.0ms

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:

12.0ms	(/ (sin x) (- x (tan x)))
4.0ms	(- x (tan x))
6.0ms	(- x (tan x))
127.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (sin x) (- x (tan x)))
101.0ms	(- x (tan x))
65.0ms	(- x (tan x))
235.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

simplify726.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1427
1	389
0	177

prune497.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
1.3b	(- x (tan x))
1.4b	(- x (sin x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
62×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-log-exp`
7×	`add-cbrt-cube` `add-exp-log`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-undiv` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 188

Calls

4 calls:

24.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
21.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
8.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series374.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
121.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
75.0ms	(- x (tan x))
44.0ms	(- x (sin x))

simplify1.9s

Counts

200 → 200

Iterations

Iter	Nodes
done	5002
2	4582
1	910
0	273

prune721.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sin x) (* (+ x (tan x)) (- x (tan x))))
1.3b	(- (/ (/ x (+ (tan x) x)) (- x (tan x))) (/ (sin x) (* (+ x (tan x)) (- x (tan x)))))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `associate-/r/`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`flip3--` `flip--`
6×	`times-frac` `add-cube-cbrt`
5×	`difference-of-squares`
4×	`frac-times` `pow1` `associate-*r/`
3×	`sub-neg` `flip3-+` `diff-log` `flip-+` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `distribute-rgt-out--` `div-exp` `associate-*l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `frac-sub` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

23.0ms	(/ (sin x) (* (+ x (tan x)) (- x (tan x))))
272.0ms	(- (/ (/ x (+ (tan x) x)) (- x (tan x))) (/ (sin x) (* (+ x (tan x)) (- x (tan x)))))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ (sin x) (* (+ x (tan x)) (- x (tan x))))
660.0ms	(- (/ (/ x (+ (tan x) x)) (- x (tan x))) (/ (sin x) (* (+ x (tan x)) (- x (tan x)))))
87.0ms	(- x (tan x))
93.0ms	(- x (tan x))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2329
1	443
0	187

prune500.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes91.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch189.0ms

Steps

Iters	Range		Point
7	0.00012587414935880383	0.030359728269424062	0.02891102314655495
11	-14746478108.679678	-8.433739504313006e-14	-0.028396277205580838

simplify3.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample13.5s

Algorithm

intervals

Results

6.9s	1573×	body	2560	valid
3.9s	2763×	body	1280	valid
1.6s	1835×	body	640	valid
450.0ms	969×	body	320	valid
229.0ms	483×	body	160	valid
64.0ms	377×	body	80	valid