Details

sample367.0ms

Algorithm

intervals

Results

59.0ms	240×	body	10240	exit
15.0ms	421×	body	80	nan
9.0ms	237×	body	80	valid
2.0ms	25×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 4.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.2b	(- (exp (* 2.0 x)) 1.0)
5.3b	(- (exp x) 1.0)

rewrite33.0ms

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

series202.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
56.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
34.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify127.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (110.0ms)

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

prune330.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	129	6	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	6	136

Merged error: 0b

Counts

136 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(sqrt (exp (* 2.0 x)))
5.3b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.3b	(- (exp x) 1.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `sqrt-prod`
10×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-pow1`
5×	`difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `exp-prod` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `flip--`

Counts

4 → 62

Calls

4 calls:

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

series105.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (exp (* 2.0 x)))
21.0ms	(sqrt (exp (* 2.0 x)))
48.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify106.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	168	382
1	414	365
2	1068	363
3	3163	361
4	5001	361

prune229.0ms

Filtered

74 candidates to 49 candidates (66.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Merged error: 0b

Counts

80 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
5.3b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.3b	(- (exp x) 1.0)
7.5b	(log (sqrt (exp (* 2.0 x))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
12×	`sqrt-prod`
10×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`log-prod` `sqrt-pow1`
5×	`add-exp-log` `log-pow` `difference-of-squares`
4×	`add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `flip--`
1×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 66

Calls

4 calls:

2.0ms	(sqrt (exp (* 2.0 x)))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)
3.0ms	(log (sqrt (exp (* 2.0 x))))

series215.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* 2.0 x)))
45.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)
133.0ms	(log (sqrt (exp (* 2.0 x))))

simplify49.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	204	445
1	552	414
2	1448	412
3	5002	409

prune263.0ms

Filtered

78 candidates to 51 candidates (65.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 0b

Counts

83 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (sqrt (exp (* 2.0 x))) 3))
0.1b	(pow (sqrt (exp (* 2.0 x))) 3)
5.3b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.3b	(- (exp x) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`cbrt-prod` `sqrt-prod`
14×	`add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod`
9×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log` `pow-pow` `add-cbrt-cube` `difference-of-squares`
3×	`pow-unpow` `sqrt-pow1` `distribute-lft-out--`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `sqr-pow`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow1/2` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 93

Calls

4 calls:

4.0ms	(cbrt (pow (sqrt (exp (* 2.0 x))) 3))
4.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series132.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt (pow (sqrt (exp (* 2.0 x))) 3))
44.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
49.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	287	596
1	992	559
2	5001	547

prune264.0ms

Filtered

105 candidates to 54 candidates (51.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	105	5	110

Merged error: 0b

Counts

110 → 5

regimes33.0ms

Accuracy

81.1% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.6b

bsearch2.0ms

Steps

Iters	Range		Point
0	-1.4365382038701608e-08	-1.394695875033139e-08	-1.41561703945165e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	24
1	38	24

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	6812×	body	10240	exit
408.0ms	12826×	body	80	nan
248.0ms	7417×	body	80	valid
58.0ms	721×	body	160	valid