Details

analyze772.0ms

Algorithm: search

sample62.0ms

Algorithm

intervals

Results

11.0ms	168×	body	80	valid
9.0ms	37×	body	640	valid
8.0ms	24×	body	1280	nan
6.0ms	19×	body	1280	valid
6.0ms	14×	body	640	nan
3.0ms	17×	body	320	valid
2.0ms	35×	body	80	nan
2.0ms	15×	body	160	valid
1.0ms	7×	body	320	nan
1.0ms	6×	body	160	nan

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: 42.6b

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))))
0.5b	(* (sqrt 2.0) t)
11.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.5b	(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:

17.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
7.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
13.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (* (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)
58.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
321.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify57.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (45.0ms)

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

prune199.0ms

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: 4.4b

Counts

93 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

4.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.9b	(/ (pow l 2) x)
9.2b	(/ (pow t 2) x)
27.2b	(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:

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)))))

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)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (48.0ms)

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

prune337.0ms

Filtered

97 candidates to 142 candidates (-46.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	138	10	148

Merged error: 2.7b

Counts

148 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
4.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.2b	(/ (pow t 2) x)
27.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite28.0ms

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:

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

series46.0ms

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 (/ l x)))))
3.0ms	(/ (pow t 2) x)
24.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	478	914
1	2189	851
2	5001	848

prune254.0ms

Filtered

78 candidates to 115 candidates (-47.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	109	6	115
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	113	12	125

Merged error: 2.6b

Counts

125 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
4.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.2b	(/ (pow t 2) x)
27.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

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

series46.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
15.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
3.0ms	(/ (pow t 2) x)
24.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	518	986
1	2185	891
2	5001	884

prune260.0ms

Filtered

80 candidates to 117 candidates (-46.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	115	14	129

Merged error: 2.6b

Counts

129 → 14

regimes882.0ms

Accuracy

78.5% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 28.2b

bsearch3.6s

Steps

Iters	Range		Point
9	3.9873898331644507e+145	1.103847078732604e+151	4.5609212906017924e+145
9	2.180738320820095e-227	1.8126891460255522e-221	1.1616535065145012e-223
8	3.089895348979833e-271	8.515322333924791e-268	1.13394788847948e-268
11	-9.604497779418962e-228	-2.733446660044372e-247	-1.2689972051154065e-237
10	-9.675539285698247e-173	-8.298209885675474e-184	-1.998253187068954e-175
10	-1.9510482852813132e+102	-3.76574775793078e+90	-3.3550726730889666e+98

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	105
1	72	105
2	75	105
3	75	105

end0.0ms

analyze786.0ms

Algorithm: search

sample1.9s

Algorithm

intervals

Results

363.0ms	5120×	body	80	valid
265.0ms	805×	body	1280	valid
264.0ms	1033×	body	640	valid
192.0ms	603×	body	1280	nan
154.0ms	604×	body	640	nan
127.0ms	655×	body	320	valid
96.0ms	1409×	body	80	nan
70.0ms	357×	body	320	nan
51.0ms	387×	body	160	valid
24.0ms	188×	body	160	nan

Details

analyze772.0ms

sample62.0ms

simplify79.0ms

prune4.0ms

localize16.0ms

rewrite50.0ms

series471.0ms

simplify57.0ms

prune199.0ms

localize17.0ms

rewrite32.0ms

series46.0ms

simplify61.0ms

prune337.0ms

localize18.0ms

rewrite28.0ms

series46.0ms

simplify68.0ms

prune254.0ms

localize18.0ms

rewrite34.0ms

series46.0ms

simplify68.0ms

prune260.0ms

regimes882.0ms

bsearch3.6s

simplify3.0ms

end0.0ms

analyze786.0ms

sample1.9s

Profiling