Details

sample309.0ms

Algorithm

intervals

Results

16.0ms	411×	body	80	nan
12.0ms	231×	body	80	valid
8.0ms	217×	body	80	overflowed
3.0ms	26×	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: 5.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)

rewrite50.0ms

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:

23.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
11.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series197.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify122.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (107.0ms)

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

prune295.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	5	136

Merged error: 0.0b

Counts

136 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
0.1b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
5.8b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.8b	(- (exp x) 1.0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

18.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
15.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series357.0ms

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))
117.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
17.0ms	(- (exp x) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	481	1464
1	2403	1163
2	5002	1124

prune278.0ms

Filtered

117 candidates to 82 candidates (70.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	116	6	122

Merged error: 0.0b

Counts

122 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

5.8b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.8b	(- (exp x) 1.0)
5.8b	(- (exp x) 1.0)
5.8b	(- (exp x) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series90.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
13.0ms	(- (exp x) 1.0)
14.0ms	(- (exp x) 1.0)
17.0ms	(- (exp x) 1.0)

simplify99.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	156	394
1	399	367
2	1035	363
3	2831	363
4	5002	363

prune215.0ms

Filtered

72 candidates to 49 candidates (68.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 0.0b

Counts

78 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (log (exp (- (exp x) 1.0))))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(log (exp (- (exp x) 1.0)))
5.8b	(- (exp x) 1.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
42×	`log-pow`
35×	`exp-prod`
28×	`add-cube-cbrt`
19×	`distribute-lft-out--` `difference-of-squares`
11×	`pow1`
9×	`associate-/r*`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log-prod` `associate-/l*`
3×	`sub-neg` `flip3--` `flip--`
2×	`diff-log` `exp-sum` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-sub` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 122

Calls

4 calls:

10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (log (exp (- (exp x) 1.0))))
4.0ms	(- (exp (* 2.0 x)) 1.0)
5.0ms	(log (exp (- (exp x) 1.0)))
4.0ms	(- (exp x) 1.0)

series110.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (- (exp (* 2.0 x)) 1.0) (log (exp (- (exp x) 1.0))))
28.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(log (exp (- (exp x) 1.0)))
14.0ms	(- (exp x) 1.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	380	1252
1	1042	1148
2	4117	1107
3	5003	1105

prune246.0ms

Filtered

134 candidates to 87 candidates (64.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	135	5	140

Merged error: 0.0b

Counts

140 → 5

regimes34.0ms

Accuracy

78.9% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.4b

bsearch40.0ms

Steps

Iters	Range		Point
8	-0.019954974243295568	-8.204019314528673e-06	-1.6839714933484727e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample1.4s

Algorithm

intervals

Results

478.0ms	12291×	body	80	nan
312.0ms	7397×	body	80	valid
249.0ms	6568×	body	80	overflowed
76.0ms	734×	body	160	valid