Details

sample316.0ms

Algorithm

intervals

Results

14.0ms	353×	body	80	nan
11.0ms	243×	body	80	valid
10.0ms	197×	body	80	overflowed
2.0ms	18×	body	160	valid

simplify71.0ms

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: 4.1b

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)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.2b	(- (exp (* 2.0 x)) 1.0)
4.3b	(- (exp x) 1.0)

rewrite51.0ms

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)))
10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series204.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
64.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify125.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4265	1301
3	5001	1293

prune297.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Merged error: 0.0b

Counts

136 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (exp (* 2.0 x)))
0.5b	(sqrt (exp (* 2.0 x)))
4.3b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.3b	(- (exp x) 1.0)

rewrite17.0ms

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))
5.0ms	(- (exp x) 1.0)

series110.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* 2.0 x)))
22.0ms	(sqrt (exp (* 2.0 x)))
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify105.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	168	382
1	414	365
2	1068	363
3	3163	361
4	5002	361

prune185.0ms

Filtered

74 candidates to 49 candidates (66.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	73	3	76

Merged error: 0b

Counts

76 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp 2.0) (* 1/2 x))
0.5b	(sqrt (exp (* 2.0 x)))
4.3b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.3b	(- (exp x) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

3.0ms	(pow (exp 2.0) (* 1/2 x))
2.0ms	(sqrt (exp (* 2.0 x)))
7.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series122.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (exp 2.0) (* 1/2 x))
22.0ms	(sqrt (exp (* 2.0 x)))
56.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify67.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	243	428
1	686	409
2	2418	406
3	5002	404

prune230.0ms

Filtered

78 candidates to 54 candidates (69.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	78	3	81

Merged error: 0b

Counts

81 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.2b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r` `add-log-exp`
4×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `prod-exp`
3×	`cbrt-undiv` `div-inv`
2×	`frac-times` `pow-to-exp` `flip3--` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 221

Calls

4 calls:

5.0ms	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
25.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
6.0ms	(/ (pow x 2) (sqrt 2.0))
4.0ms	(/ x (sqrt 2.0))

series329.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
72.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
65.0ms	(/ (pow x 2) (sqrt 2.0))
54.0ms	(/ x (sqrt 2.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	607	1712
1	2477	1546
2	5002	1532

prune460.0ms

Filtered

233 candidates to 143 candidates (61.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	233	3	236

Merged error: 0b

Counts

236 → 3

regimes28.0ms

Accuracy

72.1% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch48.0ms

Steps

Iters	Range		Point
7	-2.1715692429689375e-16	-4.9708941443212345e-18	-1.6685537623511625e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	27
1	38	27

end0.0ms

sample1.5s

Algorithm

intervals

Results

492.0ms	12490×	body	80	nan
323.0ms	7391×	body	80	valid
247.0ms	6727×	body	80	overflowed
74.0ms	744×	body	160	valid

Details

sample316.0ms

simplify71.0ms

prune4.0ms

localize11.0ms

rewrite51.0ms

series204.0ms

simplify125.0ms

prune297.0ms

localize16.0ms

rewrite17.0ms

series110.0ms

simplify105.0ms

prune185.0ms

localize19.0ms

rewrite18.0ms

series122.0ms

simplify67.0ms

prune230.0ms

localize13.0ms

rewrite51.0ms

series329.0ms

simplify75.0ms

prune460.0ms

regimes28.0ms

bsearch48.0ms

simplify2.0ms

end0.0ms

sample1.5s

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