Details

sample548.0ms

Algorithm

intervals

Results

141.0ms	49×	body	2560	valid
65.0ms	88×	body	1280	valid
21.0ms	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

localize10.0ms

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))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

30.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series180.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
60.0ms	(- x (tan x))
43.0ms	(- x (sin x))

simplify153.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune201.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
13.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

11.0ms	(* 27/2800 (pow x 4))
11.0ms	(* 9/40 (pow x 2))
21.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series113.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* 27/2800 (pow x 4))
26.0ms	(* 9/40 (pow x 2))
50.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify44.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315

prune139.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

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))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

25.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series169.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- x (sin x)) (- x (tan x)))
55.0ms	(- x (tan x))
33.0ms	(- x (sin x))

simplify149.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune185.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.2b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

16.0ms	(/ (sin x) (- x (tan x)))
78.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
6.0ms	(- x (tan x))

series358.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (sin x) (- x (tan x)))
185.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
56.0ms	(- x (tan x))
53.0ms	(- x (tan x))

simplify37.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	872
2	5001	872

prune245.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

100% (0.0b remaining)

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

bsearch74.0ms

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	36	21
1	40	21
2	40	21

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1576×	body	2560	valid
1.9s	2742×	body	1280	valid
649.0ms	1897×	body	640	valid
226.0ms	966×	body	320	valid
70.0ms	460×	body	160	valid
38.0ms	359×	body	80	valid