Details

analyze508.0ms (7.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample157.0ms (2.4%)

Algorithm

1×

intervals

Results

81.0ms	58×	body	2560	valid
42.0ms	78×	body	1280	valid
19.0ms	76×	body	640	valid
5.0ms	26×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	8×	body	80	valid

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	229	7
1	229	7

prune6.0ms (0.1%)

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: 32.1b

Counts

2 → 1

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.8b	(- 1.0 (cos x))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series12.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

simplify36.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5058	605

prune132.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	45	12	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	12	58

Merged error: 0.2b

Counts

58 → 12

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
0.1b	(* 1/240 (pow x 5))
0.1b	(* 1/24 (pow x 3))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

8.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
6.0ms	(* 1/24 (pow x 3))
5.0ms	(* 1/240 (pow x 5))

series14.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
5.0ms	(* 1/240 (pow x 5))
4.0ms	(* 1/24 (pow x 3))

simplify43.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5093	704

prune187.0ms (2.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	78	12	90

Merged error: 0.2b

Counts

90 → 12

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ 1.0 (cos x)))
0.3b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
0.6b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

13.0ms	(- (pow 1.0 3) (pow (cos x) 3))
6.0ms	(* (cos x) (+ 1.0 (cos x)))
4.0ms	(+ 1.0 (cos x))
2.0ms	(pow (cos x) 3)

series18.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (pow 1.0 3) (pow (cos x) 3))
5.0ms	(pow (cos x) 3)
4.0ms	(* (cos x) (+ 1.0 (cos x)))
2.0ms	(+ 1.0 (cos x))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5011	963

prune261.0ms (4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	101	14	115

Merged error: 0.2b

Counts

115 → 14

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
0.6b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
0.8b	(log (exp (pow (cos x) 3)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`log-pow`
12×	`add-cube-cbrt` `exp-prod`
7×	`pow1` `unpow-prod-down` `cube-prod` `add-log-exp`
6×	`log-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`difference-of-squares`
3×	`pow-unpow` `associate--r+` `sqr-pow`
2×	`cube-mult` `unpow3` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 79

Calls

4 calls:

15.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
4.0ms	(log (exp (pow (cos x) 3)))
4.0ms	(+ 1.0 (cos x))
2.0ms	(pow (cos x) 3)

series18.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
5.0ms	(log (exp (pow (cos x) 3)))
5.0ms	(pow (cos x) 3)
2.0ms	(+ 1.0 (cos x))

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5204	653

prune207.0ms (3.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	89	16	105

Merged error: 0.1b

Counts

105 → 16

regimes107.0ms (1.6%)

Accuracy

Total 0.3b remaining (63.5%)

Threshold costs 0.3b (63.5%)

bsearch36.0ms (0.5%)

Steps

Iters	Range		Point
10	6.515877835829287e-05	18669351.880964175	0.0237498496172468
7	-0.027740174261797323	-0.001582594379722933	-0.02393634628213539

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	89
1	81	89

end0.0ms (0%)

sample4.6s (69.8%)

Algorithm

1×

intervals

Results

2.3s	1619×	body	2560	valid
1.4s	2822×	body	1280	valid
468.0ms	1824×	body	640	valid
153.0ms	882×	body	320	valid
64.0ms	476×	body	160	valid
37.0ms	9×	body	5120	valid
31.0ms	368×	body	80	valid

Details

analyze508.0ms (7.7%)

sample157.0ms (2.4%)

simplify10.0ms (0.2%)

prune6.0ms (0.1%)

localize7.0ms (0.1%)

rewrite11.0ms (0.2%)

series12.0ms (0.2%)

simplify36.0ms (0.6%)

prune132.0ms (2%)

localize10.0ms (0.2%)

rewrite21.0ms (0.3%)

series14.0ms (0.2%)

simplify43.0ms (0.7%)

prune187.0ms (2.8%)

localize15.0ms (0.2%)

rewrite28.0ms (0.4%)

series18.0ms (0.3%)

simplify52.0ms (0.8%)

prune261.0ms (4%)

localize19.0ms (0.3%)

rewrite27.0ms (0.4%)

series18.0ms (0.3%)

simplify45.0ms (0.7%)

prune207.0ms (3.1%)

regimes107.0ms (1.6%)

bsearch36.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.6s (69.8%)

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