Details

analyze1.4s (12.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample242.0ms (2.2%)

Algorithm

1×

intervals

Results

141.0ms	58×	body	2560	valid
63.0ms	87×	body	1280	valid
19.0ms	55×	body	640	valid
5.0ms	25×	body	320	valid
2.0ms	12×	body	160	valid
2.0ms	19×	body	80	valid

simplify469.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

prune7.0ms (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: 31.7b

Counts

2 → 1

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.8b	(- x (sin x))
1.0b	(- x (tan x))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 78

Calls

3 calls:

17.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series38.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

20.0ms	(- x (tan x))
13.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune112.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) 9/40)
0.3b	(* 27/2800 (pow x 4))
13.1b	(- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

9.0ms	(- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2))
5.0ms	(* (* x x) 9/40)
5.0ms	(* 27/2800 (pow x 4))

series12.0ms (0.1%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2))
4.0ms	(* 27/2800 (pow x 4))
3.0ms	(* (* x x) 9/40)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4961	578
1	4961	578

prune122.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	65	5	70

Merged error: 0.0b

Counts

70 → 5

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

13.1b	(- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2))
15.3b	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
15.3b	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
15.3b	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3`
2×	`diff-log`
1×	`sub-neg` `sum-log` `associate--r+`

Counts

4 → 52

Calls

4 calls:

9.0ms	(- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2))
9.0ms	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
9.0ms	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
9.0ms	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))

series53.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
16.0ms	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
14.0ms	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
5.0ms	(- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2))

simplify41.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5904	1358

prune273.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	64	5	69

Merged error: 0.0b

Counts

69 → 5

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

15.3b	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
15.3b	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
22.9b	(/ (cbrt (- (* (pow x 6) 729/64000) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3))) (cbrt (+ (* (pow x 4) 81/1600) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2))))))
25.4b	(- (* (pow x 6) 729/64000) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`cbrt-prod`
36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-div`
6×	`add-exp-log` `associate-/r` `associate-/l` `add-log-exp`
4×	`pow1` `flip3--` `add-cbrt-cube` `flip--`
2×	`pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

16.0ms	(/ (cbrt (- (* (pow x 6) 729/64000) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3))) (cbrt (+ (* (pow x 4) 81/1600) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2))))))
10.0ms	(- (* (pow x 6) 729/64000) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3))
8.0ms	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
8.0ms	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))

series65.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (cbrt (- (* (pow x 6) 729/64000) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3))) (cbrt (+ (* (pow x 4) 81/1600) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2))))))
14.0ms	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
14.0ms	(cbrt (- (* (* x x) 9/40) (+ (* 27/2800 (pow x 4)) 1/2)))
10.0ms	(- (* (pow x 6) 729/64000) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3))

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5006	5844

prune1.1s (10.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	113	5	118

Merged error: 0.0b

Counts

118 → 5

regimes95.0ms (0.9%)

Accuracy

Total 0.0b remaining (10.8%)

Threshold costs 0.0b (10.8%)

bsearch42.0ms (0.4%)

Steps

Iters	Range		Point
8	0.014178460367165312	142.67258068776127	0.02856113453362911
10	-86.26200852349665	-2.2673774106756e-10	-0.02779748745899354

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	31
1	86	31

end0.0ms (0%)

sample6.5s (59.5%)

Algorithm

1×

intervals

Results

3.9s	1603×	body	2560	valid
1.7s	2739×	body	1280	valid
530.0ms	1882×	body	640	valid
188.0ms	972×	body	320	valid
63.0ms	477×	body	160	valid
26.0ms	327×	body	80	valid

Details

analyze1.4s (12.6%)

sample242.0ms (2.2%)

simplify469.0ms (4.3%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite30.0ms (0.3%)

series38.0ms (0.3%)

simplify65.0ms (0.6%)

prune112.0ms (1%)

localize9.0ms (0.1%)

rewrite21.0ms (0.2%)

series12.0ms (0.1%)

simplify26.0ms (0.2%)

prune122.0ms (1.1%)

localize14.0ms (0.1%)

rewrite36.0ms (0.3%)

series53.0ms (0.5%)

simplify41.0ms (0.4%)

prune273.0ms (2.5%)

localize33.0ms (0.3%)

rewrite46.0ms (0.4%)

series65.0ms (0.6%)

simplify65.0ms (0.6%)

prune1.1s (10.4%)

regimes95.0ms (0.9%)

bsearch42.0ms (0.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.5s (59.5%)

Profiling