Details

sample35.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

13.0ms	52×	body	1280	valid
7.0ms	43×	body	640	valid
4.0ms	133×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	11×	body	160	valid

simplify58.0ms

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: 28.5b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
2.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite23.0ms

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:

9.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
9.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series16.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.0ms	(+ 1.0 (exp (* -2.0 x)))
9.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify89.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (19.0ms)

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

prune127.0ms

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	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
2.5b	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
80×	`times-frac`
62×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
24×	`swap-sqr` `distribute-lft-out`
18×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`associate-/r/`
8×	`add-log-exp`
6×	`flip3-+` `flip-+` `difference-of-squares`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`flip3--` `flip--` `associate-/l/`
1×	`+-commutative` `pow2` `frac-times` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 154

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
21.0ms	(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
18.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
11.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series54.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ 1.0 (exp (* -2.0 x)))
30.0ms	(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
10.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
12.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify118.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	722	2489
1	3781	2190
2	5002	2172

prune453.0ms

Filtered

110 candidates to 166 candidates (-50.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	166	3	169

Merged error: 0.0b

Counts

169 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4) (/ (pow 1.0 4) 1)) (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)))
0.0b	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4)
2.4b	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4) (/ (pow 1.0 4) 1))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

398×	`add-sqr-sqrt`
327×	`times-frac`
204×	`*-un-lft-identity`
140×	`difference-of-squares`
128×	`unpow-prod-down`
86×	`add-cube-cbrt`
76×	`sqr-pow`
32×	`associate-/l*`
24×	`swap-sqr`
21×	`add-exp-log` `distribute-lft-out`
18×	`associate-r` `associate-l` `add-cbrt-cube`
12×	`pow1` `associate-/r/`
6×	`flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp`
5×	`cbrt-undiv` `distribute-lft-out--`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `pow-exp` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 310

Calls

4 calls:

45.0ms	(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4) (/ (pow 1.0 4) 1)) (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)))
18.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
7.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4)
28.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4) (/ (pow 1.0 4) 1))

series74.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4) (/ (pow 1.0 4) 1)) (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)))
10.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
11.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4)
15.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4) (/ (pow 1.0 4) 1))

simplify90.0ms

Algorithm

egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1336	7757
1	5002	6789

prune1.3s

Filtered

183 candidates to 322 candidates (-76.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	322	0	322
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	322	3	325

Merged error: 0.0b

Counts

325 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6)) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b	(cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6))
0.1b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6)
2.5b	(- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6)) (* 1.0 1.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt` `*-un-lft-identity`
62×	`times-frac`
48×	`unpow-prod-down`
46×	`cbrt-prod`
36×	`add-cube-cbrt`
30×	`difference-of-squares`
15×	`distribute-lft-out`
9×	`add-exp-log`
8×	`associate-/l*` `sqr-pow`
6×	`associate-/r/` `add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`associate-/r*`
3×	`pow-unpow` `flip3-+` `flip-+` `div-inv`
2×	`flip3--` `div-exp` `pow-exp` `flip--` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `clear-num`

Counts

4 → 141

Calls

4 calls:

21.0ms	(/ (- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6)) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
7.0ms	(cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6))
7.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6)
14.0ms	(- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6)) (* 1.0 1.0))

series63.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6)) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
10.0ms	(cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6))
12.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6)
12.0ms	(- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 6)) (* 1.0 1.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	634	2426
1	2204	2290
2	5001	2258

prune436.0ms

Filtered

108 candidates to 153 candidates (-41.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	153	3	156

Merged error: 0.0b

Counts

156 → 3

regimes485.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 29.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	29
1	43	29

end0.0ms

sample987.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

408.0ms	1635×	body	1280	valid
215.0ms	1265×	body	640	valid
134.0ms	4129×	body	80	valid
74.0ms	634×	body	320	valid
25.0ms	337×	body	160	valid

Details

sample35.0ms

simplify58.0ms

prune3.0ms

localize6.0ms

rewrite23.0ms

series16.0ms

simplify89.0ms

prune127.0ms

localize11.0ms

rewrite60.0ms

series54.0ms

simplify118.0ms

prune453.0ms

localize17.0ms

rewrite123.0ms

series74.0ms

simplify90.0ms

prune1.3s

localize12.0ms

rewrite55.0ms

series63.0ms

simplify72.0ms

prune436.0ms

regimes485.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample987.0ms

Profiling