Details

sample45.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

14.0ms	52×	body	1280	valid
6.0ms	36×	body	640	valid
5.0ms	136×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	30	5
3	52	5
4	114	5
5	322	5
6	1627	5
7	5002	5

prune3.0ms

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: 27.9b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
13×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`associate-/r*`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out--`

Counts

3 → 60

Calls

3 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series16.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify92.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	251	494
1	731	465
2	2771	460
3	5002	460

prune129.0ms

Filtered

50 candidates to 69 candidates (-38.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 0.0b

Counts

70 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.3b	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
3.9b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
28×	`times-frac`
24×	`add-cube-cbrt`
20×	`sqrt-prod`
12×	`difference-of-squares`
11×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
8×	`associate-/r*`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`flip3-+` `associate-l` `flip-+`
4×	`frac-times` `flip3--` `associate-/r/` `flip--` `distribute-lft-out--`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-r/` `div-exp` `associate-l/` `clear-num` `div-inv`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
33.0ms	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
14.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series53.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
29.0ms	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
12.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify61.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	441	1655
1	1929	1488
2	5002	1459

prune370.0ms

Filtered

94 candidates to 138 candidates (-46.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	138	3	141

Merged error: 0.0b

Counts

141 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
3.9b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
12×	`cbrt-prod`
9×	`sqrt-prod`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp` `difference-of-squares`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`times-frac` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 62

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
3.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
3.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
14.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series68.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
18.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
21.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
12.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	233	710
1	632	665
2	1986	656
3	5002	648

prune301.0ms

Filtered

57 candidates to 74 candidates (-29.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Merged error: 0.0b

Counts

77 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x))))))
0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
3.9b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`cbrt-div` `*-un-lft-identity`
9×	`add-exp-log` `sqrt-prod`
8×	`cbrt-prod` `add-cube-cbrt` `flip3-+` `associate-/r/` `flip-+`
7×	`add-cbrt-cube`
6×	`add-log-exp` `difference-of-squares`
5×	`times-frac`
4×	`pow1` `frac-times`
3×	`associate-/l*`
2×	`cbrt-undiv` `pow1/3` `associate-r/` `div-exp` `associate-l/` `distribute-lft-out` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

11.0ms	(/ 2.0 (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x))))))
3.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
3.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
15.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series80.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 2.0 (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x))))))
18.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
17.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
12.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	397	990
1	1220	899
2	4402	875
3	5002	875

prune443.0ms

Filtered

67 candidates to 89 candidates (-32.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	89	3	92

Merged error: 0.0b

Counts

92 → 3

regimes414.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 29.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	53
1	49	53

end0.0ms

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

441.0ms	1701×	body	1280	valid
225.0ms	1259×	body	640	valid
145.0ms	4102×	body	80	valid
80.0ms	641×	body	320	valid
23.0ms	297×	body	160	valid

Details

sample45.0ms

simplify60.0ms

prune3.0ms

localize7.0ms

rewrite20.0ms

series16.0ms

simplify92.0ms

prune129.0ms

localize11.0ms

rewrite63.0ms

series53.0ms

simplify61.0ms

prune370.0ms

localize18.0ms

rewrite24.0ms

series68.0ms

simplify60.0ms

prune301.0ms

localize22.0ms

rewrite35.0ms

series80.0ms

simplify109.0ms

prune443.0ms

regimes414.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling