Details

sample477.0ms

Algorithm

intervals

Results

150.0ms	46×	body	2560	valid
48.0ms	89×	body	1280	valid
18.0ms	63×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	17×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (sin x))
1.1b	(- x (tan x))

rewrite37.0ms

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:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (sin x))
6.0ms	(- x (tan x))

series172.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
36.0ms	(- x (sin x))
61.0ms	(- x (tan x))

simplify56.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

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

prune234.0ms

Filtered

119 candidates to 79 candidates (66.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

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))))
1.1b	(- x (tan x))
1.1b	(- x (tan x))

rewrite105.0ms

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:

10.0ms	(/ (sin x) (- x (tan x)))
37.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series337.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (sin x) (- x (tan x)))
170.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
51.0ms	(- x (tan x))
56.0ms	(- x (tan x))

simplify205.0ms

Algorithm

egg-herbie

Counts

600 → 600

Iterations

Useful iterations: 2 (79.0ms)

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

prune984.0ms

Filtered

600 candidates to 256 candidates (42.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (sin x))
1.1b	(- x (tan x))

rewrite23.0ms

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:

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

series156.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ (- x (sin x)) (- x (tan x)))
35.0ms	(- x (sin x))
49.0ms	(- x (tan x))

simplify59.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

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

prune217.0ms

Filtered

119 candidates to 77 candidates (64.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
18.8b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
1.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series130.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(fma 27/2800 (pow x 4) 1/2)
48.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify145.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	51	133
1	162	117
2	626	117
3	3552	117
4	5001	117

prune67.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.1b

bsearch88.0ms

Steps

Iters	Range		Point
10	9.598072339636849e-08	814.2255113159289	0.028993276489121412
11	-402.67606408878214	-1.1015269942960052e-19	-0.030685173958992108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	26	13

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.1s	1667×	body	2560	valid
1.6s	2669×	body	1280	valid
483.0ms	1896×	body	640	valid
151.0ms	929×	body	320	valid
56.0ms	467×	body	160	valid
28.0ms	372×	body	80	valid