Details

sample495.0ms

Algorithm

intervals

Results

129.0ms	57×	body	2560	valid
47.0ms	91×	body	1280	valid
17.0ms	58×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	12×	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

prune25.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.2b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (tan x))
1.4b	(- x (sin x))

rewrite21.0ms

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:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series119.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- x (sin x)) (- x (tan x)))
42.0ms	(- x (tan x))
31.0ms	(- x (sin x))

simplify146.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	351	716
1	1106	683
2	4690	682
3	5001	682

prune250.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	6	90

Merged error: 0.2b

Counts

90 → 6

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x 11/10) 3/4)
0.0b	(- (* x (- (* x 11/10) 3/4)) 1/2)
0.1b	(* x (- (* x 11/10) 3/4))
0.5b	(* x 11/10)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
6×	`sub-neg` `associate-r` `associate-l`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
3×	`flip3--` `flip--`
2×	`diff-log` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

4.0ms	(- (* x 11/10) 3/4)
9.0ms	(- (* x (- (* x 11/10) 3/4)) 1/2)
6.0ms	(* x (- (* x 11/10) 3/4))
3.0ms	(* x 11/10)

series121.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* x 11/10) 3/4)
23.0ms	(- (* x (- (* x 11/10) 3/4)) 1/2)
50.0ms	(* x (- (* x 11/10) 3/4))
14.0ms	(* x 11/10)

simplify111.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	224	319
1	786	291
2	3956	286
3	5002	286

prune175.0ms

Filtered

82 candidates to 52 candidates (63.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	80	8	88

Merged error: 0.2b

Counts

88 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)) (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)))
15.4b	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))
15.4b	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))
15.4b	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

16.0ms	(* (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)) (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)))
6.0ms	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))
6.0ms	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))
8.0ms	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))

series254.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)) (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)))
63.0ms	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))
60.0ms	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))
65.0ms	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))

simplify139.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	318	1360
1	996	1277
2	4650	1198
3	5001	1191

prune330.0ms

Filtered

99 candidates to 75 candidates (75.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	99	8	107

Merged error: 0.2b

Counts

107 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)) 6)
13.7b	(cbrt (pow (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)) 6))
15.4b	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))
15.4b	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`cbrt-div` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`flip3--` `pow-pow` `flip--` `sqr-pow`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 65

Calls

4 calls:

8.0ms	(pow (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)) 6)
9.0ms	(cbrt (pow (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)) 6))
9.0ms	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))
6.0ms	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))

series325.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(pow (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)) 6)
65.0ms	(cbrt (pow (cbrt (- (* x (- (* x 11/10) 3/4)) 1/2)) 6))
63.0ms	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))
60.0ms	(cbrt (- (* x (- (* x 11/10) 3/4)) 1/2))

simplify49.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	399	925
1	1357	862
2	5001	814

prune250.0ms

Filtered

77 candidates to 55 candidates (71.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	76	9	85

Merged error: 0.2b

Counts

85 → 9

regimes165.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 31.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	26
1	27	26

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.1s	1642×	body	2560	valid
1.5s	2745×	body	1280	valid
487.0ms	1871×	body	640	valid
159.0ms	938×	body	320	valid
53.0ms	451×	body	160	valid
25.0ms	353×	body	80	valid

Details

sample495.0ms

simplify11.0ms

prune25.0ms

localize12.0ms

rewrite21.0ms

series119.0ms

simplify146.0ms

prune250.0ms

localize6.0ms

rewrite24.0ms

series121.0ms

simplify111.0ms

prune175.0ms

localize11.0ms

rewrite40.0ms

series254.0ms

simplify139.0ms

prune330.0ms

localize13.0ms

rewrite34.0ms

series325.0ms

simplify49.0ms

prune250.0ms

regimes165.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample6.6s

Profiling