Details

sample1.5s

Algorithm

intervals

Results

53.0ms	96×	body	1280	valid
49.0ms	21×	body	2560	valid
33.0ms	72×	body	640	valid
6.0ms	36×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	15×	body	80	valid

simplify268.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 15.2b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.4b	(- x (tan x))
0.4b	(- 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))

series39.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
12.0ms	(- x (tan x))
14.0ms	(- x (sin x))

simplify150.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	684
2	4781	684
3	5001	684

prune107.0ms

Filtered

89 candidates to 63 candidates (29.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
0.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.4b	(- x (tan x))
0.4b	(- x (tan x))

rewrite46.0ms

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:

6.0ms	(/ (sin x) (- x (tan x)))
30.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series65.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ (sin x) (- x (tan x)))
33.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	870
2	5001	870

prune101.0ms

Filtered

106 candidates to 80 candidates (24.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Merged error: 0.0b

Counts

111 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (/ x (- x (tan x))) (* (sin x) (/ 1 (- x (tan x)))))
0.3b	(* (sin x) (/ 1 (- x (tan x))))
0.4b	(- x (tan x))
0.4b	(- x (tan x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`associate-r`
17×	`times-frac`
14×	`add-cube-cbrt`
13×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube`
6×	`pow1`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`flip3--` `prod-exp` `flip--`
3×	`sub-neg` `diff-log` `associate-r/` `associate-l*` `un-div-inv` `unswap-sqr`
2×	`div-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `div-inv` `sub-div`
1×	`cbrt-undiv` `rec-exp` `distribute-rgt-out--` `1-exp` `pow-prod-down` `*-commutative`

Counts

4 → 89

Calls

4 calls:

10.0ms	(- (/ x (- x (tan x))) (* (sin x) (/ 1 (- x (tan x)))))
11.0ms	(* (sin x) (/ 1 (- x (tan x))))
3.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series64.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ x (- x (tan x))) (* (sin x) (/ 1 (- x (tan x)))))
11.0ms	(* (sin x) (/ 1 (- x (tan x))))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))

simplify53.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	443	763
1	1847	693
2	5001	667

prune101.0ms

Filtered

101 candidates to 72 candidates (28.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	100	5	105

Merged error: 0.0b

Counts

105 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (/ x (- x (tan x))) (* (sin x) (/ 1 (- x (tan x)))))
0.3b	(* (sin x) (/ 1 (- x (tan x))))
0.4b	(- x (tan x))
0.4b	(- x (tan x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`associate-r`
17×	`times-frac`
14×	`add-cube-cbrt`
13×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube`
6×	`pow1`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`flip3--` `prod-exp` `flip--`
3×	`sub-neg` `diff-log` `associate-r/` `associate-l*` `un-div-inv` `unswap-sqr`
2×	`div-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `div-inv` `sub-div`
1×	`cbrt-undiv` `rec-exp` `distribute-rgt-out--` `1-exp` `pow-prod-down` `*-commutative`

Counts

4 → 89

Calls

4 calls:

10.0ms	(- (/ x (- x (tan x))) (* (sin x) (/ 1 (- x (tan x)))))
11.0ms	(* (sin x) (/ 1 (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series64.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ x (- x (tan x))) (* (sin x) (/ 1 (- x (tan x)))))
14.0ms	(* (sin x) (/ 1 (- x (tan x))))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))

simplify53.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	443	763
1	1847	693
2	5001	667

prune124.0ms

Filtered

101 candidates to 73 candidates (27.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	101	5	106

Merged error: 0.0b

Counts

106 → 5

regimes49.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 16.6b

bsearch65.0ms

Steps

Iters	Range		Point
7	0.012859339055769341	0.3555464171021314	0.03266468412777142
15	-5.198581744599781	1.0450147493914085e-304	-0.03802303523574156

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	36
1	38	36

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.2s	839×	body	2560	valid
1.4s	2853×	body	1280	valid
523.0ms	2148×	body	640	valid
182.0ms	1096×	body	320	valid
77.0ms	597×	body	160	valid
34.0ms	467×	body	80	valid

Details

sample1.5s

simplify268.0ms

prune4.0ms

localize12.0ms

rewrite21.0ms

series39.0ms

simplify150.0ms

prune107.0ms

localize10.0ms

rewrite46.0ms

series65.0ms

simplify42.0ms

prune101.0ms

localize12.0ms

rewrite30.0ms

series64.0ms

simplify53.0ms

prune101.0ms

localize15.0ms

rewrite30.0ms

series64.0ms

simplify53.0ms

prune124.0ms

regimes49.0ms

bsearch65.0ms

simplify2.0ms

end0.0ms

sample5.7s

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