Details

sample433.0ms

Algorithm

intervals

Results

90.0ms	44×	body	2560	valid
56.0ms	87×	body	1280	valid
18.0ms	54×	body	640	valid
7.0ms	32×	body	320	valid
6.0ms	25×	body	160	valid
1.0ms	14×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite41.0ms

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:

15.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series172.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
56.0ms	(- x (tan x))
40.0ms	(- x (sin x))

simplify803.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (321.0ms)

Iter	Nodes	Cost
0	209	1823
1	476	1563
2	1413	1384
done	5001	1384

prune251.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.4b	(- x (sin x))
26.1b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`prod-diff`
6×	`cbrt-prod` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

0.0ms	(cbrt x)
1.0ms	(cbrt x)
4.0ms	(- x (sin x))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series696.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt x)
170.0ms	(cbrt x)
33.0ms	(- x (sin x))
324.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify1.3s

Counts

76 → 76

Iterations

Useful iterations: 3 (377.0ms)

Iter	Nodes	Cost
0	106	735
1	203	612
2	513	450
3	1627	375
done	5000	375

prune191.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
26.0b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x)))
26.1b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x)))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt x)
185.0ms	(cbrt x)
324.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x)))
335.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify1.3s

Counts

58 → 58

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	60	479
1	97	470
2	223	326
3	585	254
4	2132	254
done	5000	254

prune180.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite157.0ms

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:

8.0ms	(/ (sin x) (- x (tan x)))
78.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series360.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (sin x) (- x (tan x)))
187.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
50.0ms	(- x (tan x))
58.0ms	(- x (tan x))

simplify1.6s

Counts

600 → 600

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	617	35000
1	1342	31424
2	3398	24077
done	5001	24014

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch85.0ms

Steps

Iters	Range		Point
9	3.182061564411226e-09	0.0591185632533196	0.028578832745905277
8	-0.04390830018224924	-1.7961213486546931e-06	-0.02915897731694385

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	90
1	36	90
done	36	90

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.5s	1620×	body	2560	valid
2.0s	2690×	body	1280	valid
658.0ms	1887×	body	640	valid
217.0ms	951×	body	320	valid
81.0ms	476×	body	160	valid
35.0ms	376×	body	80	valid