Details

sample118.0ms

Algorithm

intervals

Results

34.0ms	159×	body	80	valid
21.0ms	306×	body	80	nan
9.0ms	28×	body	1280	valid
9.0ms	33×	body	640	valid
8.0ms	24×	body	1280	nan
5.0ms	28×	body	320	valid
4.0ms	16×	body	640	nan
2.0ms	10×	body	320	nan
1.0ms	8×	body	160	valid
1.0ms	7×	body	160	nan

simplify88.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

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: 43.5b

Counts

2 → 1

localize25.0ms

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)
11.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.2b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite53.0ms

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:

17.0ms	(/ (* (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)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
15.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

436.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
41.0ms	(* (sqrt 2.0) t)
223.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify62.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

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

prune292.0ms

Filtered

92 candidates to 65 candidates (70.7%)

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: 8.4b

Counts

93 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

3.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.5b	(/ (pow l 2) x)
8.0b	(/ (pow t 2) x)
26.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite30.0ms

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:

9.0ms	(+ (* 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)))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms	(/ (pow l 2) x)
24.0ms	(/ (pow t 2) x)
167.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	526	1093
1	2235	984
2	5001	978

prune417.0ms

Filtered

142 candidates to 97 candidates (68.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	136	12	148

Merged error: 4.8b

Counts

148 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
3.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
8.0b	(/ (pow t 2) x)
26.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite32.0ms

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)))))
8.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sqrt 2.0) t)
63.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
19.0ms	(/ (pow t 2) x)
167.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (53.0ms)

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

prune338.0ms

Filtered

115 candidates to 80 candidates (69.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	115	12	127

Merged error: 4.8b

Counts

127 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow t 2) (/ l (/ x l)))
3.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
8.0b	(/ (pow t 2) x)
26.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite45.0ms

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))))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (pow t 2) (/ l (/ x l)))
69.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
19.0ms	(/ (pow t 2) x)
172.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (46.0ms)

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

prune314.0ms

Filtered

105 candidates to 76 candidates (72.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	103	14	117

Merged error: 4.8b

Counts

117 → 14

regimes575.0ms

Accuracy

75.4% (5.9b remaining)

Error of 9.8b against oracle of 4.0b and baseline of 27.8b

bsearch673.0ms

Steps

Iters	Range		Point
6	3.535080165719566e+41	3.341288634873774e+42	1.9202685079401505e+42
2	5.3939037819869456e-222	6.219332546703312e-222	5.857671429623004e-222
9	2.245549009883105e-274	1.9115382417649492e-267	3.3397983208009454e-269
9	-6.578304950363068e-253	-2.9774815790151963e-258	-5.306558026339235e-255
7	-9.673551804545756e-187	-1.9685869310215835e-188	-1.6725816241633412e-187
10	-6.792006205197398e+114	-1.923636620968605e+102	-7.668338051009316e+111

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	123
1	77	123

end0.0ms

sample2.6s

Algorithm

intervals

Results

670.0ms	10078×	body	80	nan
350.0ms	5078×	body	80	valid
283.0ms	875×	body	1280	valid
261.0ms	1018×	body	640	valid
185.0ms	574×	body	1280	nan
155.0ms	612×	body	640	nan
124.0ms	655×	body	320	valid
60.0ms	323×	body	320	nan
47.0ms	374×	body	160	valid
24.0ms	174×	body	160	nan

Details

sample118.0ms

simplify88.0ms

prune5.0ms

localize25.0ms

rewrite53.0ms

series1.9s

simplify62.0ms

prune292.0ms

localize16.0ms

rewrite30.0ms

series273.0ms

simplify67.0ms

prune417.0ms

localize15.0ms

rewrite32.0ms

series294.0ms

simplify64.0ms

prune338.0ms

localize22.0ms

rewrite45.0ms

series295.0ms

simplify58.0ms

prune314.0ms

regimes575.0ms

bsearch673.0ms

simplify3.0ms

end0.0ms

sample2.6s

Profiling