Details

analyze375.0ms (8.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	68.6%	31.4%	5
0%	65.5%	34.5%	6
0%	59.2%	40.8%	7
0%	51.4%	48.6%	8
0%	41.3%	58.7%	9
0%	28.4%	71.6%	10
2.3%	22.3%	75.4%	11
2.3%	21%	76.7%	12
2.7%	18%	79.3%	13
2.7%	16.4%	80.8%	14

sample46.0ms (1%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	80	valid
9.0ms	147×	body	80	nan

simplify104.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5198	16

prune17.0ms (0.4%)

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: 0.1b

Counts

2 → 2

localize20.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))
0.1b	(+ (log z) (- (* (- a 0.5) (log t)) t))
0.2b	(* (- a 0.5) (log t))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity`
19×	`log-prod`
15×	`add-sqr-sqrt`
13×	`distribute-lft-out`
12×	`pow1`
11×	`add-cube-cbrt`
10×	`add-log-exp`
8×	`associate-+r+`
7×	`associate-+l+` `sum-log` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
5×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`associate-r`
3×	`associate-+r-` `flip3-+` `flip-+`
2×	`+-commutative` `associate-+l-` `log-div` `diff-log` `associate-*l/`
1×	`sub-neg` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

14.0ms	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))
9.0ms	(+ (log z) (- (* (- a 0.5) (log t)) t))
7.0ms	(* (- a 0.5) (log t))

series81.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))
19.0ms	(+ (log z) (- (* (- a 0.5) (log t)) t))
9.0ms	(* (- a 0.5) (log t))

simplify29.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5177	1268

prune177.0ms (3.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 0.0b

Counts

92 → 8

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(* (- a 0.5) (log (cbrt t)))
0.3b	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
0.6b	(cbrt t)
0.6b	(cbrt t)

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`log-prod`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`cbrt-prod`
28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt` `associate-+l+`
12×	`associate-+r+`
10×	`associate-*l/`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `associate-r` `associate-l` `flip--`
4×	`frac-add`
3×	`pow1/3`
2×	`log-pow`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

13.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
7.0ms	(* (- a 0.5) (log (cbrt t)))
3.0ms	(cbrt t)
1.0ms	(cbrt t)

series105.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
24.0ms	(* (- a 0.5) (log (cbrt t)))
21.0ms	(cbrt t)
21.0ms	(cbrt t)

simplify81.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4936	1252
1	4936	1252

prune228.0ms (5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	123	7	130

Merged error: 0b

Counts

130 → 7

localize29.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(* (- a 0.5) (log (pow t 1/3)))
0.3b	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (pow t 1/3))))
0.6b	(cbrt t)
5.1b	(pow t 1/3)

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`log-prod`
38×	`distribute-rgt-in` `distribute-lft-in`
29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
24×	`associate-+l+`
15×	`cbrt-prod` `unpow-prod-down`
14×	`associate-+r+`
10×	`associate-*l/`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
5×	`flip3--` `associate-l` `flip--` `sqr-pow`
4×	`associate-r` `frac-add`
3×	`pow-unpow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `flip3-+` `unpow1/3` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

15.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (pow t 1/3))))
8.0ms	(* (- a 0.5) (log (pow t 1/3)))
2.0ms	(pow t 1/3)
1.0ms	(cbrt t)

series110.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (pow t 1/3))))
24.0ms	(cbrt t)
20.0ms	(* (- a 0.5) (log (pow t 1/3)))
19.0ms	(pow t 1/3)

simplify67.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4906	1258
1	4906	1258

prune253.0ms (5.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	134	5	139

Merged error: 0b

Counts

139 → 5

localize31.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(* (- a 0.5) (log (pow t (/ 1/3 2))))
0.3b	(+ (* (- a 0.5) (* (log t) 5/6)) (* (- a 0.5) (log (pow t (/ 1/3 2)))))
0.3b	(* (log t) 5/6)
4.1b	(pow t (/ 1/3 2))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`log-prod`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
14×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
13×	`pow-unpow`
10×	`pow1` `associate-*l/`
9×	`add-exp-log` `times-frac` `associate-l`
8×	`add-cbrt-cube`
7×	`associate-r`
6×	`add-log-exp`
5×	`flip3--` `flip--` `sqr-pow`
4×	`frac-add`
2×	`pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `sum-log` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 113

Calls

4 calls:

12.0ms	(+ (* (- a 0.5) (* (log t) 5/6)) (* (- a 0.5) (log (pow t (/ 1/3 2)))))
8.0ms	(* (- a 0.5) (log (pow t (/ 1/3 2))))
4.0ms	(* (log t) 5/6)
4.0ms	(pow t (/ 1/3 2))

series96.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* (- a 0.5) (* (log t) 5/6)) (* (- a 0.5) (log (pow t (/ 1/3 2)))))
20.0ms	(* (- a 0.5) (log (pow t (/ 1/3 2))))
19.0ms	(pow t (/ 1/3 2))
12.0ms	(* (log t) 5/6)

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4989	1256
1	4989	1256

prune255.0ms (5.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	125	5	130

Merged error: 0b

Counts

130 → 5

regimes920.0ms (20.4%)

Accuracy

Total 0.3b remaining (86.6%)

Threshold costs 0.3b (86.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	27
1	49	27

end0.0ms (0%)

sample1.3s (28.3%)

Algorithm

1×

intervals

Results

602.0ms	8000×	body	80	valid
297.0ms	4353×	body	80	nan
3.0ms	35×	body	80	invalid

Details

analyze375.0ms (8.3%)

sample46.0ms (1%)

simplify104.0ms (2.3%)

prune17.0ms (0.4%)

localize20.0ms (0.4%)

rewrite32.0ms (0.7%)

series81.0ms (1.8%)

simplify29.0ms (0.6%)

prune177.0ms (3.9%)

localize21.0ms (0.5%)

rewrite29.0ms (0.7%)

series105.0ms (2.3%)

simplify81.0ms (1.8%)

prune228.0ms (5%)

localize29.0ms (0.6%)

rewrite31.0ms (0.7%)

series110.0ms (2.4%)

simplify67.0ms (1.5%)

prune253.0ms (5.6%)

localize31.0ms (0.7%)

rewrite31.0ms (0.7%)

series96.0ms (2.1%)

simplify62.0ms (1.4%)

prune255.0ms (5.7%)

regimes920.0ms (20.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (28.3%)

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