Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

sample77.0ms (2.1%)

Algorithm

1×

intervals

Results

61.0ms	184×	body	1280	valid
7.0ms	39×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	7×	body	80	valid

simplify47.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5718	8

prune5.0ms (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: 31.2b

Counts

2 → 1

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
2.6b	(+ (- (exp x) 2.0) (exp (neg x)))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `associate-+l+` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 33

Calls

2 calls:

8.0ms	(+ (- (exp x) 2.0) (exp (neg x)))
4.0ms	(- (exp x) 2.0)

series9.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))
2.0ms	(- (exp x) 2.0)

simplify59.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5310	423

prune74.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	4	40

Merged error: 0.0b

Counts

40 → 4

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(* 1/360 (pow x 6))
0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

7.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))
5.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))

series28.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
8.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5022	849

prune178.0ms (4.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (exp x) 2.0)
0.0b	(- (exp x) 2.0)
0.0b	(pow (exp x) -2)
2.2b	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (pow (exp x) -2))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `sub-neg` `difference-of-squares`
4×	`add-exp-log` `unpow-prod-down` `pow-pow` `add-cbrt-cube`
3×	`pow-unpow` `exp-prod` `flip3--` `diff-log` `flip--`
2×	`associate--l+` `distribute-lft-out--` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp`

Counts

4 → 62

Calls

4 calls:

13.0ms	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (pow (exp x) -2))
4.0ms	(- (exp x) 2.0)
4.0ms	(- (exp x) 2.0)
3.0ms	(pow (exp x) -2)

series23.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (pow (exp x) -2))
5.0ms	(pow (exp x) -2)
2.0ms	(- (exp x) 2.0)
2.0ms	(- (exp x) 2.0)

simplify69.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4986	668
1	4986	668

prune124.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	74	5	79

Merged error: 0.0b

Counts

79 → 5

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (exp x) 2.0))
0.0b	(cbrt (- (exp x) 2.0))
0.0b	(cbrt (- (exp x) 2.0))
4.6b	(+ (* (* (cbrt (- (exp x) 2.0)) (cbrt (- (exp x) 2.0))) (cbrt (- (exp x) 2.0))) (exp (neg x)))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`cbrt-div`
57×	`flip3--` `flip--`
56×	`frac-times`
52×	`frac-add`
28×	`associate-*l/`
26×	`neg-sub0` `exp-neg` `exp-diff`
16×	`associate-*r/`
15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 108

Calls

4 calls:

23.0ms	(+ (* (* (cbrt (- (exp x) 2.0)) (cbrt (- (exp x) 2.0))) (cbrt (- (exp x) 2.0))) (exp (neg x)))
4.0ms	(cbrt (- (exp x) 2.0))
4.0ms	(cbrt (- (exp x) 2.0))
4.0ms	(cbrt (- (exp x) 2.0))

series64.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (- (exp x) 2.0))
18.0ms	(cbrt (- (exp x) 2.0))
18.0ms	(cbrt (- (exp x) 2.0))
10.0ms	(+ (* (* (cbrt (- (exp x) 2.0)) (cbrt (- (exp x) 2.0))) (cbrt (- (exp x) 2.0))) (exp (neg x)))

simplify78.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4905	4003
1	4905	4003

prune369.0ms (9.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	121	4	125

Merged error: 0.0b

Counts

125 → 4

regimes33.0ms (0.9%)

Accuracy

Total 0.6b remaining (90.8%)

Threshold costs 0.6b (90.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	15
1	16	15

end0.0ms (0%)

sample2.3s (61.5%)

Algorithm

1×

intervals

Results

1.8s	5607×	body	1280	valid
233.0ms	1280×	body	640	valid
72.0ms	635×	body	320	valid
22.0ms	298×	body	160	valid
7.0ms	180×	body	80	valid
2.0ms	2×	body	80	invalid

Details

analyze4.0ms (0.1%)

sample77.0ms (2.1%)

simplify47.0ms (1.2%)

prune5.0ms (0.1%)

localize6.0ms (0.2%)

rewrite12.0ms (0.3%)

series9.0ms (0.2%)

simplify59.0ms (1.6%)

prune74.0ms (2%)

localize9.0ms (0.3%)

rewrite24.0ms (0.7%)

series28.0ms (0.8%)

simplify55.0ms (1.5%)

prune178.0ms (4.8%)

localize11.0ms (0.3%)

rewrite26.0ms (0.7%)

series23.0ms (0.6%)

simplify69.0ms (1.8%)

prune124.0ms (3.3%)

localize10.0ms (0.3%)

rewrite42.0ms (1.1%)

series64.0ms (1.7%)

simplify78.0ms (2.1%)

prune369.0ms (9.9%)

regimes33.0ms (0.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.3s (61.5%)

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