Details

analyze657.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample59.0ms

Algorithm

intervals

Results

25.0ms	65×	body	1280	valid
14.0ms	61×	body	640	valid
4.0ms	30×	body	320	valid
4.0ms	88×	body	80	valid
1.0ms	12×	body	160	valid

simplify443.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4920	12
1	4920	12

prune25.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 41.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
3.2b	(- (pow (exp x) 2.0) 1.0)
3.3b	(- (exp x) 1.0)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
87×	`*-un-lft-identity`
71×	`times-frac`
52×	`difference-of-squares`
41×	`sqrt-prod`
31×	`add-cube-cbrt`
28×	`distribute-lft-out--`
12×	`unpow-prod-down` `sqr-pow`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r*` `flip--`
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 → 145

Calls

4 calls:

11.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
11.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
5.0ms	(- (pow (exp x) 2.0) 1.0)
7.0ms	(- (exp x) 1.0)

series44.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
15.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
4.0ms	(- (pow (exp x) 2.0) 1.0)
10.0ms	(- (exp x) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4970	2783
1	4970	2783

prune283.0ms

Filtered

113 candidates to 157 candidates (-38.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	2	158

Merged error: 0.2b

Counts

158 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ x (sqrt 2)))
0.4b	(* x (/ 1/2 (sqrt 2)))
0.5b	(/ x (sqrt 2))
1.0b	(/ 1/2 (sqrt 2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
76×	`times-frac`
62×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-r` `sqrt-prod`
18×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
8×	`pow1`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 162

Calls

4 calls:

8.0ms	(* x (/ x (sqrt 2)))
9.0ms	(* x (/ 1/2 (sqrt 2)))
4.0ms	(/ x (sqrt 2))
4.0ms	(/ 1/2 (sqrt 2))

series21.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(* x (/ x (sqrt 2)))
9.0ms	(* x (/ 1/2 (sqrt 2)))
6.0ms	(/ x (sqrt 2))
0.0ms	(/ 1/2 (sqrt 2))

simplify54.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5017	1302

prune286.0ms

Filtered

109 candidates to 172 candidates (-57.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	172	2	174

Merged error: 0.2b

Counts

174 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1/2 (sqrt 2))
26.8b	(cbrt (* x (/ x (sqrt 2))))
26.8b	(cbrt (* x (/ x (sqrt 2))))
26.8b	(cbrt (* x (/ x (sqrt 2))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
12×	`sqrt-prod`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-r/` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 69

Calls

4 calls:

4.0ms	(/ 1/2 (sqrt 2))
5.0ms	(cbrt (* x (/ x (sqrt 2))))
5.0ms	(cbrt (* x (/ x (sqrt 2))))
5.0ms	(cbrt (* x (/ x (sqrt 2))))

series87.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(/ 1/2 (sqrt 2))
27.0ms	(cbrt (* x (/ x (sqrt 2))))
30.0ms	(cbrt (* x (/ x (sqrt 2))))
30.0ms	(cbrt (* x (/ x (sqrt 2))))

simplify59.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5313	611

prune217.0ms

Filtered

57 candidates to 79 candidates (-38.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	79	2	81

Merged error: 0.2b

Counts

81 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* (/ (- (pow (exp x) 2.0) 1.0) (- (pow (exp x) 2) (* 1.0 1.0))) (+ (exp x) 1.0)))
0.2b	(/ (- (pow (exp x) 2.0) 1.0) (- (pow (exp x) 2) (* 1.0 1.0)))
3.2b	(- (pow (exp x) 2.0) 1.0)
3.2b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
63×	`difference-of-squares`
49×	`times-frac`
38×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`unpow-prod-down` `sqr-pow`
9×	`distribute-lft-out--` `unpow2`
8×	`add-log-exp`
7×	`pow1` `associate-/r` `associate-/l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`sqrt-div`
4×	`flip3--` `flip--`
2×	`frac-times` `sub-neg` `sqrt-pow1` `flip3-+` `diff-log` `associate-*r/` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-sub` `div-exp` `pow-prod-down` `associate-*l/` `clear-num` `sqrt-prod` `div-inv`

Counts

4 → 126

Calls

4 calls:

15.0ms	(sqrt (* (/ (- (pow (exp x) 2.0) 1.0) (- (pow (exp x) 2) (* 1.0 1.0))) (+ (exp x) 1.0)))
14.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (pow (exp x) 2) (* 1.0 1.0)))
5.0ms	(- (pow (exp x) 2.0) 1.0)
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series13.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (* (/ (- (pow (exp x) 2.0) 1.0) (- (pow (exp x) 2) (* 1.0 1.0))) (+ (exp x) 1.0)))
1.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (pow (exp x) 2) (* 1.0 1.0)))
4.0ms	(- (pow (exp x) 2.0) 1.0)
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5307	2587

prune262.0ms

Filtered

101 candidates to 138 candidates (-36.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	138	2	140

Merged error: 0.2b

Counts

140 → 2

regimes33.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.9b

bsearch31.0ms

Steps

Iters	Range		Point
7	-2.914007458358654e-14	-5.583041428544234e-16	-7.284067260085109e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	60
1	38	60

end0.0ms

analyze452.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample1.6s

Algorithm

intervals

Results

822.0ms	2310×	body	1280	valid
376.0ms	1655×	body	640	valid
132.0ms	883×	body	320	valid
121.0ms	2800×	body	80	valid
34.0ms	352×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze657.0ms

sample59.0ms

simplify443.0ms

prune25.0ms

localize12.0ms

rewrite41.0ms

series44.0ms

simplify55.0ms

prune283.0ms

localize10.0ms

rewrite31.0ms

series21.0ms

simplify54.0ms

prune286.0ms

localize16.0ms

rewrite20.0ms

series87.0ms

simplify59.0ms

prune217.0ms

localize12.0ms

rewrite44.0ms

series13.0ms

simplify52.0ms

prune262.0ms

regimes33.0ms

bsearch31.0ms

simplify2.0ms

end0.0ms

analyze452.0ms

sample1.6s

Profiling