Details

sample338.0ms

Algorithm

intervals

Results

39.0ms	187×	body	10240	exit
19.0ms	243×	body	80	valid
11.0ms	358×	body	80	nan
1.0ms	17×	body	160	valid

simplify75.0ms

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: 3.9b

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)))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.7b	(- (exp (* 2.0 x)) 1.0)
3.8b	(- (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	(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)

series213.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
38.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify127.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (108.0ms)

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

prune291.0ms

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: 0.2b

Counts

136 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp (* 2.0 x)))
0.3b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
3.8b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.8b	(- (exp x) 1.0)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

2.0ms	(sqrt (exp (* 2.0 x)))
18.0ms	(/ (* (+ (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)

series279.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (exp (* 2.0 x)))
185.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
49.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
18.0ms	(- (exp x) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	418	958
1	1889	760
2	5001	736

prune226.0ms

Filtered

94 candidates to 66 candidates (70.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	94	4	98

Merged error: 0.2b

Counts

98 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))) (- (exp x) 1.0))
0.3b	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
3.8b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.8b	(- (exp x) 1.0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

24.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))) (- (exp x) 1.0))
8.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series295.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))) (- (exp x) 1.0))
52.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
48.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	457	1277
1	2285	1074
2	5001	1063

prune272.0ms

Filtered

114 candidates to 71 candidates (62.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	114	4	118

Merged error: 0.2b

Counts

118 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.3b	(cbrt (pow (sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))) 3))
3.7b	(- (exp (* 2.0 x)) 1.0)
3.8b	(- (exp x) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt` `*-un-lft-identity`
75×	`times-frac`
74×	`cbrt-prod`
62×	`sqrt-prod`
41×	`add-cube-cbrt`
34×	`unpow-prod-down` `cube-prod` `distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r` `associate-/l`
4×	`pow1`
3×	`div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `cube-div` `cube-mult` `cbrt-div` `frac-2neg` `pow1/3` `sqrt-div` `unpow3` `div-sub` `div-exp` `clear-num` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 164

Calls

4 calls:

10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
17.0ms	(cbrt (pow (sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))) 3))
4.0ms	(- (exp (* 2.0 x)) 1.0)
4.0ms	(- (exp x) 1.0)

series192.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
92.0ms	(cbrt (pow (sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))) 3))
25.0ms	(- (exp (* 2.0 x)) 1.0)
15.0ms	(- (exp x) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	713	2034
1	2090	1939
2	5003	1917

prune306.0ms

Filtered

176 candidates to 94 candidates (53.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	176	4	180

Merged error: 0.2b

Counts

180 → 4

regimes83.0ms

Accuracy

72.6% (0.9b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 3.5b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	38
1	45	38

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6438×	body	10240	exit
392.0ms	12360×	body	80	nan
255.0ms	7366×	body	80	valid
62.0ms	752×	body	160	valid