Details

sample347.0ms

Algorithm

intervals

Results

41.0ms	207×	body	10240	exit
12.0ms	403×	body	80	nan
8.0ms	242×	body	80	valid
1.0ms	15×	body	160	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune4.0ms

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: 3.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.5b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
3.3b	(- (exp (* 2.0 x)) 1.0)
3.4b	(- (exp x) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

9.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series201.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
34.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify128.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4287	1301
3	5003	1293

prune296.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Merged error: 0.5b

Counts

136 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
0.5b	(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
3.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.4b	(- (exp x) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

21.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
14.0ms	(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series561.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
323.0ms	(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify67.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	605	1402
1	2646	1169
2	5001	1151

prune271.0ms

Filtered

101 candidates to 77 candidates (76.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	101	4	105

Merged error: 0.5b

Counts

105 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (cbrt (pow (- (exp x) 1.0) 3)))
0.5b	(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (cbrt (pow (- (exp x) 1.0) 3))))
3.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.4b	(- (exp x) 1.0)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-prod`
40×	`add-sqr-sqrt`
38×	`times-frac`
35×	`*-un-lft-identity`
31×	`sqrt-prod`
19×	`associate-/r*`
17×	`add-cube-cbrt`
15×	`unpow-prod-down` `cube-prod`
11×	`difference-of-squares`
9×	`add-exp-log` `distribute-lft-out--`
8×	`associate-/l/` `add-log-exp`
7×	`flip3--` `add-cbrt-cube` `flip--`
5×	`pow1`
4×	`cube-div` `frac-times` `cbrt-div` `associate-/r/`
3×	`cube-mult` `flip3-+` `unpow3` `flip-+` `sqr-pow`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `div-inv`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`

Counts

4 → 131

Calls

4 calls:

21.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (cbrt (pow (- (exp x) 1.0) 3)))
18.0ms	(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (cbrt (pow (- (exp x) 1.0) 3))))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series560.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (cbrt (pow (- (exp x) 1.0) 3)))
324.0ms	(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (cbrt (pow (- (exp x) 1.0) 3))))
46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify94.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	754	2227
1	3444	1899
2	5002	1875

prune355.0ms

Filtered

143 candidates to 89 candidates (62.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	143	4	147

Merged error: 0.5b

Counts

147 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (exp (* 2.0 x)) 1.0)
3.3b	(- (exp (* 2.0 x)) 1.0)
3.4b	(- (exp x) 1.0)
3.4b	(- (exp x) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

4.0ms	(- (exp (* 2.0 x)) 1.0)
4.0ms	(- (exp (* 2.0 x)) 1.0)
4.0ms	(- (exp x) 1.0)
4.0ms	(- (exp x) 1.0)

series80.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (exp (* 2.0 x)) 1.0)
28.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)
14.0ms	(- (exp x) 1.0)

simplify93.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	139	336
1	321	310
2	893	304
3	2766	304
4	5001	304

prune207.0ms

Filtered

68 candidates to 48 candidates (70.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	68	4	72

Merged error: 0.5b

Counts

72 → 4

regimes35.0ms

Accuracy

95.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 3.7b

bsearch96.0ms

Steps

Iters	Range		Point
9	2.5055192714849007e-19	1.2000045585397406e-10	6.561572677279099e-15
7	-0.002595282603730271	-1.9027306785960326e-05	-0.00022162383544769925

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	44
1	46	44

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	7003×	body	10240	exit
381.0ms	13033×	body	80	nan
233.0ms	7407×	body	80	valid
56.0ms	730×	body	160	valid