Details

sample983.0ms

Algorithm

intervals

Results

422.0ms	57×	body	2560	valid
227.0ms	70×	body	640	valid
145.0ms	72×	body	1280	valid
33.0ms	14×	body	160	valid
23.0ms	29×	body	320	valid
4.0ms	14×	body	80	valid

simplify21.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.7b	(- x (sin x))

rewrite46.0ms

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` `insert-posit16` `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 → 113

Calls

3 calls:

20.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series269.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(/ (- x (sin x)) (- x (tan x)))
104.0ms	(- x (tan x))
44.0ms	(- x (sin x))

simplify1.1s

Counts

122 → 122

Iterations

Iter	Nodes
done	2007
3	2007
2	1279
1	504
0	212

prune438.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
1.6b	(- x (tan x))
1.7b	(- x (sin x))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
42×	`add-cube-cbrt`
32×	`log-pow`
31×	`exp-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp`

Counts

4 → 160

Calls

4 calls:

28.0ms	(/ (- x (sin x)) (- x (tan x)))
52.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
5.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series391.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (- x (sin x)) (- x (tan x)))
132.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
97.0ms	(- x (tan x))
54.0ms	(- x (sin x))

simplify1.2s

Counts

172 → 172

Iterations

Iter	Nodes
done	2000
3	2000
2	1382
1	577
0	277

prune744.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.5b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.6b	(- x (tan x))
1.6b	(- x (tan x))

rewrite119.0ms

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` `insert-posit16` `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 → 592

Calls

4 calls:

18.0ms	(/ (sin x) (- x (tan x)))
71.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
8.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series496.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (sin x) (- x (tan x)))
267.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
61.0ms	(- x (tan x))
90.0ms	(- x (tan x))

simplify2.0s

Counts

604 → 604

Iterations

Iter	Nodes
done	2001
2	2001
1	1405
0	620

prune2.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

1.6b	(- x (tan x))
1.7b	(- x (sin x))
1.7b	(- x (sin x))
1.7b	(- x (sin x))

rewrite53.0ms

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` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

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

series252.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- x (tan x))
66.0ms	(- x (sin x))
62.0ms	(- x (sin x))
68.0ms	(- x (sin x))

simplify1.2s

Counts

128 → 128

Iterations

Iter	Nodes
done	2008
4	2008
3	1653
2	633
1	279
0	129

prune552.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes73.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.9b

bsearch130.0ms

Steps

Iters	Range		Point
11	5.037382729650074e-10	1937402784720.5117	0.031240215431948184
6	-0.09018726350273112	-0.009521407882115243	-0.028213729881585915

simplify7.0ms

Iterations

Iter	Nodes
done	25
1	25
0	21

end0.0ms

sample16.1s

Algorithm

intervals

Results

7.7s	1640×	body	2560	valid
5.0s	2718×	body	1280	valid
2.1s	1830×	body	640	valid
797.0ms	962×	body	320	valid
257.0ms	486×	body	160	valid
90.0ms	364×	body	80	valid