Details

sample545.0ms

Algorithm

intervals

Results

146.0ms	49×	body	2560	valid
64.0ms	88×	body	1280	valid
20.0ms	62×	body	640	valid
5.0ms	24×	body	320	valid
3.0ms	20×	body	160	valid
1.0ms	13×	body	80	valid

simplify10.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite54.0ms

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:

32.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series177.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

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

prune237.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
13.1b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite1.0ms

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:

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

series131.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(fma 27/2800 (pow x 4) 1/2)
46.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify143.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

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

prune74.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (- x (sin x)) (- x (tan x)))))
0.5b	(expm1 (/ (- x (sin x)) (- x (tan x))))
1.3b	(- x (tan x))
1.3b	(- x (sin x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
8×	`add-log-exp`
6×	`fma-neg`
5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 78

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (- x (sin x)) (- x (tan x)))))
0.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
7.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series351.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(log1p (expm1 (/ (- x (sin x)) (- x (tan x)))))
106.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
54.0ms	(- x (tan x))
32.0ms	(- x (sin x))

simplify46.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	442	803
1	1633	588
2	5002	580

prune199.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (cos x) 2)
13.9b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
13.9b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
42×	`div-exp`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
14×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow` `frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 144

Calls

4 calls:

3.0ms	(pow (sin x) 2)
3.0ms	(pow (cos x) 2)
17.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
15.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin x) 2)
17.0ms	(pow (cos x) 2)
74.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
61.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	434	1060
1	1839	950
2	5002	950

prune367.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes62.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch69.0ms

Steps

Iters	Range		Point
8	1.317141247235427e-05	0.43775957865898985	0.030711477964933176
9	-3096.4512561506854	-0.0006592480666379122	-0.0237917079813031

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	27	12

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.4s	1576×	body	2560	valid
1.9s	2742×	body	1280	valid
640.0ms	1897×	body	640	valid
222.0ms	966×	body	320	valid
70.0ms	460×	body	160	valid
34.0ms	359×	body	80	valid