Details

sample2.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 43.75%

Guaranteed chance to sample good point: 36.458333%

Results

12.0ms	166×	body	80	valid
11.0ms	25×	body	1280	nan
9.0ms	26×	body	1280	valid
9.0ms	32×	body	640	valid
5.0ms	20×	body	640	nan
5.0ms	24×	body	320	valid
3.0ms	50×	body	80	nan
2.0ms	11×	body	320	nan
1.0ms	9×	body	160	nan
1.0ms	8×	body	160	valid

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	14
1	93	14
2	193	14
3	414	14
4	718	14
5	1192	14
6	2816	14
7	5001	14

prune4.0ms

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: 44.6b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
12.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.8b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

19.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
12.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
56.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
194.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify58.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	417	1207
1	2051	1099
2	5002	1094

prune215.0ms

Filtered

65 candidates to 92 candidates (-41.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 4.1b

Counts

93 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.4b	(/ (pow l 2) x)
11.3b	(/ (pow t 2) x)
29.9b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

11.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms	(/ (pow l 2) x)
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
3.0ms	(/ (pow l 2) x)
3.0ms	(/ (pow t 2) x)
25.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	526	1067
1	2113	984
2	5001	978

prune384.0ms

Filtered

97 candidates to 142 candidates (-46.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	136	12	148

Merged error: 3.0b

Counts

148 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
11.3b	(/ (pow t 2) x)
29.9b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-r/` `add-cbrt-cube` `associate-/l`
7×	`pow1` `sqrt-prod`
6×	`associate-l` `add-log-exp`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`associate-+r+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 103

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
15.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
3.0ms	(/ (pow t 2) x)
27.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	477	917
1	2140	851
2	5001	848

prune280.0ms

Filtered

80 candidates to 115 candidates (-43.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	115	12	127

Merged error: 3.0b

Counts

127 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow t 2) (/ l (/ x l)))
3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
11.3b	(/ (pow t 2) x)
29.9b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity` `times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-r/` `associate-/l` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 93

Calls

4 calls:

21.0ms	(+ (pow t 2) (/ l (/ x l)))
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (pow t 2) (/ l (/ x l)))
14.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
3.0ms	(/ (pow t 2) x)
25.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	453	932
1	1835	862
2	5001	859

prune311.0ms

Filtered

76 candidates to 105 candidates (-38.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	103	14	117

Merged error: 3.0b

Counts

117 → 14

regimes788.0ms

Accuracy

77.1% (5.5b remaining)

Error of 9.0b against oracle of 3.5b and baseline of 27.5b

bsearch117.0ms

Steps

Iters	Range		Point
7	1.304297190455883e+88	4.0578969142307515e+89	6.1818169122754946e+88
6	-1.7808041198503912e+86	-3.438105017121717e+85	-1.3966866900389786e+86

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	64
1	65	64

end0.0ms

sample4.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 43.75%

Guaranteed chance to sample good point: 36.458333%

Results

382.0ms	5142×	body	80	valid
302.0ms	888×	body	1280	valid
263.0ms	954×	body	640	valid
199.0ms	567×	body	1280	nan
165.0ms	626×	body	640	nan
133.0ms	641×	body	320	valid
104.0ms	1450×	body	80	nan
68.0ms	340×	body	320	nan
56.0ms	375×	body	160	valid
33.0ms	218×	body	160	nan

Details

sample2.3s

simplify79.0ms

prune4.0ms

localize16.0ms

rewrite50.0ms

series348.0ms

simplify58.0ms

prune215.0ms

localize17.0ms

rewrite32.0ms

series46.0ms

simplify62.0ms

prune384.0ms

localize17.0ms

rewrite29.0ms

series49.0ms

simplify63.0ms

prune280.0ms

localize21.0ms

rewrite44.0ms

series52.0ms

simplify55.0ms

prune311.0ms

regimes788.0ms

bsearch117.0ms

simplify2.0ms

end0.0ms

sample4.3s

Profiling