Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

sample416.0ms (4.1%)

Algorithm

1×

intervals

Results

245.0ms	92×	body	1280	valid
147.0ms	88×	body	2560	valid
9.0ms	44×	body	640	valid
4.0ms	256×	pre	80	true
3.0ms	23×	body	320	valid
1.0ms	9×	body	160	valid

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	220	8
1	220	8

prune5.0ms (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: 60.4b

Counts

2 → 1

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.9b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 49

Calls

2 calls:

13.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))
4.0ms	(/ 1.0 (tan x))

series31.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

21.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))
10.0ms	(/ 1.0 (tan x))

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4916	556
1	4916	556

prune89.0ms (0.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	1	56

Merged error: 0.3b

Counts

56 → 1

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))

rewrite24.0ms (0.2%)

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:

9.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
6.0ms	(* 0.022222222222222223 (pow x 3))
5.0ms	(* 0.0021164021164021165 (pow x 5))

series14.0ms (0.1%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(* 0.0021164021164021165 (pow x 5))
4.0ms	(* 0.022222222222222223 (pow x 3))

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4943	707
1	4943	707

prune173.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	6	79

Merged error: 0.2b

Counts

79 → 6

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

21.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

series82.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
20.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
19.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
19.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

simplify36.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	4987	3186
1	4987	3186

prune673.0ms (6.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	91	14	105

Merged error: 0.1b

Counts

105 → 14

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.6b	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
0.6b	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
0.6b	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`cbrt-prod`
14×	`cbrt-div`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 61

Calls

4 calls:

11.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
9.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
9.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

series94.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
24.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
24.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
20.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

simplify32.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5554	2389

prune739.0ms (7.3%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	72	15	87

Merged error: 0.1b

Counts

87 → 15

regimes126.0ms (1.2%)

Accuracy

Total 0.2b remaining (44.2%)

Threshold costs 0.2b (44.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms (0%)

sample7.4s (72.3%)

Algorithm

1×

intervals

Results

5.4s	3235×	body	2560	valid
1.3s	2566×	body	1280	valid
238.0ms	1250×	body	640	valid
131.0ms	8000×	pre	80	true
66.0ms	577×	body	320	valid
26.0ms	322×	body	160	valid
2.0ms	50×	body	80	valid

Details

analyze6.0ms (0.1%)

sample416.0ms (4.1%)

simplify11.0ms (0.1%)

prune5.0ms (0%)

localize5.0ms (0.1%)

rewrite19.0ms (0.2%)

series31.0ms (0.3%)

simplify53.0ms (0.5%)

prune89.0ms (0.9%)

localize10.0ms (0.1%)

rewrite24.0ms (0.2%)

series14.0ms (0.1%)

simplify60.0ms (0.6%)

prune173.0ms (1.7%)

localize14.0ms (0.1%)

rewrite45.0ms (0.4%)

series82.0ms (0.8%)

simplify36.0ms (0.4%)

prune673.0ms (6.6%)

localize21.0ms (0.2%)

rewrite38.0ms (0.4%)

series94.0ms (0.9%)

simplify32.0ms (0.3%)

prune739.0ms (7.3%)

regimes126.0ms (1.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample7.4s (72.3%)

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