Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	58×	body	1280	valid
4.0ms	30×	body	640	valid
4.0ms	141×	body	80	valid
2.0ms	21×	body	320	valid
0.0ms	6×	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

prune2.0ms

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: 27.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
1.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

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

series116.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
78.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	220	413
1	613	391
2	2032	387
3	5001	387

prune102.0ms

Filtered

54 candidates to 40 candidates (74.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	3	55

Merged error: 0.0b

Counts

55 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
1.8b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

388×	`times-frac`
301×	`*-un-lft-identity`
229×	`sqrt-prod`
211×	`add-sqr-sqrt`
187×	`add-cube-cbrt`
56×	`distribute-lft-out`
30×	`associate-/l*`
20×	`sqrt-div` `associate-/r/`
14×	`associate-/r*`
10×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `div-inv`
7×	`difference-of-squares`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

3 → 305

Calls

3 calls:

16.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
6.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
66.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series186.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
67.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
80.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify91.0ms

Algorithm

egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	756	5618
1	2662	4993
2	5002	4840

prune351.0ms

Filtered

314 candidates to 131 candidates (41.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	314	0	314
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	314	3	317

Merged error: 0.0b

Counts

317 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
0.5b	(* 5.551115123125783e-17 (pow x 4))
11.6b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `flip3-+` `unpow3` `sum-log` `flip-+`

Counts

3 → 67

Calls

3 calls:

6.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(* 5.551115123125783e-17 (pow x 4))
4.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series183.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 0.33333333333333337 (pow x 3))
34.0ms	(* 5.551115123125783e-17 (pow x 4))
112.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify45.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	268	323
1	1157	293
2	5001	293

prune132.0ms

Filtered

76 candidates to 47 candidates (61.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	76	3	79

Merged error: 0.0b

Counts

79 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.1b	(exp (log (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
1.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 68

Calls

3 calls:

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

series193.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
76.0ms	(exp (log (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
77.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	265	626
1	683	591
2	2108	571
3	5001	565

prune142.0ms

Filtered

77 candidates to 55 candidates (71.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	77	3	80

Merged error: 0.0b

Counts

80 → 3

regimes222.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	43	27
2	43	27

end0.0ms

sample895.0ms

Algorithm

intervals

Results

368.0ms	1705×	body	1280	valid
179.0ms	1273×	body	640	valid
116.0ms	4024×	body	80	valid
62.0ms	668×	body	320	valid
20.0ms	330×	body	160	valid