Details

sample815.0ms

Algorithm

intervals

Results

275.0ms	90×	body	1280	valid
217.0ms	39×	body	2560	valid
87.0ms	73×	body	640	valid
12.0ms	24×	body	320	valid
7.0ms	18×	body	160	valid
2.0ms	12×	body	80	valid

simplify30.0ms

Counts

1 → 1

Iterations

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

prune44.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite541.0ms

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:

505.0ms	(/ (- x (sin x)) (- x (tan x)))
13.0ms	(- x (sin x))
14.0ms	(- x (tan x))

series287.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(/ (- x (sin x)) (- x (tan x)))
64.0ms	(- x (sin x))
126.0ms	(- x (tan x))

simplify1.1s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	2272
1	502
0	209

prune416.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

1.3b	(- x (sin x))
1.3b	(- x (sin x))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite54.0ms

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:

12.0ms	(- x (sin x))
13.0ms	(- x (sin x))
11.0ms	(- x (tan x))
12.0ms	(- x (tan x))

series236.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- x (sin x))
44.0ms	(- x (sin x))
63.0ms	(- x (tan x))
96.0ms	(- x (tan x))

simplify1.1s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1075
1	278
0	127

prune555.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (pow (cos x) 2))
0.3b	(pow (cos x) 2)
12.0b	(/ (sin x) (* x x))
12.0b	(/ (sin x) (* x x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

30×	`times-frac`
27×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
20×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`unpow-prod-down`
10×	`associate-/r*`
9×	`associate-/l*`
7×	`div-exp`
5×	`pow1` `cbrt-undiv` `unpow2` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg` `div-inv`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`
1×	`pow-pow`

Counts

4 → 117

Calls

4 calls:

26.0ms	(/ (sin x) (pow (cos x) 2))
5.0ms	(pow (cos x) 2)
11.0ms	(/ (sin x) (* x x))
10.0ms	(/ (sin x) (* x x))

series175.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (sin x) (pow (cos x) 2))
31.0ms	(pow (cos x) 2)
41.0ms	(/ (sin x) (* x x))
60.0ms	(/ (sin x) (* x x))

simplify840.0ms

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	2063
1	364
0	158

prune774.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

1.3b	(- x (sin x))
1.3b	(- x (tan x))
1.5b	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
26.9b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite43.0ms

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-cbrt-cube` `fma-neg` `add-exp-log` `distribute-lft-out--` `difference-of-squares`
5×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`associate-/r*` `flip3--` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 106

Calls

4 calls:

6.0ms	(- x (sin x))
5.0ms	(- x (tan x))
28.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.4s

Counts

4 → 12

Calls

4 calls:

44.0ms	(- x (sin x))
76.0ms	(- x (tan x))
800.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
481.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify1.7s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	1895
1	451
0	201

prune650.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes119.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.1b

bsearch122.0ms

Steps

Iters	Range		Point
8	0.00104763160503943	5.1212688054922095	1.5874744023794976
9	-205.8624528279525	-0.0007095347148853646	-1.5696248202346277

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample13.1s

Algorithm

intervals

Results

6.1s	1512×	body	2560	valid
4.5s	2746×	body	1280	valid
1.4s	1928×	body	640	valid
698.0ms	987×	body	320	valid
134.0ms	476×	body	160	valid
62.0ms	351×	body	80	valid