Details

analyze808.0ms (12.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

sample70.0ms (1.1%)

Algorithm

1×

intervals

Results

12.0ms	163×	body	80	valid
10.0ms	30×	body	1280	valid
9.0ms	31×	body	640	valid
7.0ms	27×	body	640	nan
6.0ms	17×	body	1280	nan
5.0ms	22×	body	320	valid
3.0ms	40×	body	80	nan
2.0ms	12×	body	320	nan
1.0ms	10×	body	160	valid
1.0ms	4×	body	160	nan

simplify35.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5225	27

prune15.0ms (0.2%)

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: 44.7b

Counts

2 → 2

localize18.0ms (0.3%)

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)
12.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite49.0ms (0.8%)

Algorithm

1×	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 → 79

Calls

4 calls:

17.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ 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)))
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
4.0ms	(* (sqrt 2.0) t)

series340.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))
92.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
56.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
4.0ms	(* (sqrt 2.0) t)

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5044	2021

prune253.0ms (4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	89	4	93

Merged error: 3.0b

Counts

93 → 4

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ t (/ x t))
0.4b	(* (sqrt 2.0) t)
4.4b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.8b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

10.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
5.0ms	(/ t (/ x t))
4.0ms	(* (sqrt 2.0) t)

series49.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))
17.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
4.0ms	(* (sqrt 2.0) t)
3.0ms	(/ t (/ x t))

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4968	1904
1	4968	1904

prune449.0ms (7.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	130	10	140

Merged error: 2.9b

Counts

140 → 10

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(* t (cbrt (sqrt 2.0)))
0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
4.4b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.8b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`pow1`
18×	`add-exp-log`
16×	`add-sqr-sqrt`
11×	`add-cbrt-cube`
10×	`associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`cbrt-prod` `associate-*r/`
7×	`sqrt-prod`
6×	`add-log-exp`
4×	`flip3-+` `sqrt-div` `associate-l` `frac-add` `flip-+`
3×	`unswap-sqr`
2×	`associate-+r+` `*-commutative`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 80

Calls

4 calls:

12.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
9.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))
5.0ms	(* t (cbrt (sqrt 2.0)))

series70.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(* t (cbrt (sqrt 2.0)))
24.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))
15.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
4.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5035	1397

prune316.0ms (5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	91	11	102

Merged error: 2.9b

Counts

102 → 11

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(* t (sqrt (sqrt 2.0)))
0.3b	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
4.4b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.8b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-prod`
19×	`add-sqr-sqrt`
12×	`pow1` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-r`
8×	`associate-*r/`
6×	`add-log-exp`
4×	`flip3-+` `sqrt-div` `pow-prod-down` `frac-add` `prod-exp` `cbrt-unprod` `flip-+`
3×	`unswap-sqr`
2×	`associate-+r+` `*-commutative`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 82

Calls

4 calls:

10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
9.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))
9.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
6.0ms	(* t (sqrt (sqrt 2.0)))

series50.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))
15.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
6.0ms	(* t (sqrt (sqrt 2.0)))
4.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4994	1409
1	4994	1409

prune248.0ms (3.9%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	93	12	105

Merged error: 2.9b

Counts

105 → 12

regimes710.0ms (11.2%)

Accuracy

Total 5.6b remaining (56.8%)

Threshold costs 0b (0%)

bsearch433.0ms (6.9%)

Steps

Iters	Range		Point
10	3.730194580565081e+41	4.698640247924842e+54	4.633595256269455e+54
8	9.472984164457177e-165	4.863465518416841e-160	9.737845307435373e-165
10	1.0554483519623456e-221	3.309682420602759e-204	3.219152109280772e-204
10	-2.135230378654967e+63	-9.97479881903036e+45	-2.0889904105457687e+63

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	130	116
1	130	116

end0.0ms (0%)

sample2.0s (31.8%)

Algorithm

1×

intervals

Results

385.0ms	5156×	body	80	valid
301.0ms	839×	body	1280	valid
283.0ms	1029×	body	640	valid
217.0ms	639×	body	1280	nan
167.0ms	613×	body	640	nan
129.0ms	608×	body	320	valid
98.0ms	1396×	body	80	nan
68.0ms	340×	body	320	nan
53.0ms	368×	body	160	valid
24.0ms	166×	body	160	nan

Details

analyze808.0ms (12.8%)

sample70.0ms (1.1%)

simplify35.0ms (0.5%)

prune15.0ms (0.2%)

localize18.0ms (0.3%)

rewrite49.0ms (0.8%)

series340.0ms (5.4%)

simplify45.0ms (0.7%)

prune253.0ms (4%)

localize20.0ms (0.3%)

rewrite33.0ms (0.5%)

series49.0ms (0.8%)

simplify60.0ms (0.9%)

prune449.0ms (7.1%)

localize22.0ms (0.4%)

rewrite38.0ms (0.6%)

series70.0ms (1.1%)

simplify58.0ms (0.9%)

prune316.0ms (5%)

localize20.0ms (0.3%)

rewrite38.0ms (0.6%)

series50.0ms (0.8%)

simplify54.0ms (0.9%)

prune248.0ms (3.9%)

regimes710.0ms (11.2%)

bsearch433.0ms (6.9%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (31.8%)

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