Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample112.0ms (2.5%)

Algorithm

1×

intervals

Results

57.0ms	112×	body	1280	valid
23.0ms	24×	body	2560	valid
15.0ms	57×	body	640	valid
5.0ms	23×	body	320	valid
2.0ms	31×	body	80	valid
1.0ms	9×	body	160	valid

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	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: 37.3b

Counts

2 → 1

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 23

Calls

2 calls:

6.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series13.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

simplify49.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5348	268

prune54.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	25	4	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	4	30

Merged error: 0.4b

Counts

30 → 4

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
3.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

7.0ms	(cos (/ (+ x (+ x eps)) 2))
6.0ms	(+ x (+ x eps))
5.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))

series22.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms	(+ x (+ x eps))
6.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify61.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5169	541

prune134.0ms (2.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	43	11	54

Merged error: 0.3b

Counts

54 → 11

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.2b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
3.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

13.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
8.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
7.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series33.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
9.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
8.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))

simplify49.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5064	940

prune195.0ms (4.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	74	10	84

Merged error: 0.3b

Counts

84 → 10

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
0.6b	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
3.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

8.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
7.0ms	(cos (/ (+ x (+ x eps)) 2))
2.0ms	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
2.0ms	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))

series33.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
11.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
5.0ms	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify41.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4924	1255
1	4924	1255

prune217.0ms (4.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Merged error: 0.3b

Counts

107 → 10

regimes179.0ms (3.9%)

Accuracy

Total 0.4b remaining (51.1%)

Threshold costs 0.4b (51.1%)

bsearch65.0ms (1.4%)

Steps

Iters	Range		Point
9	3.157025505158146e-29	4.740471739071633e-22	4.641753169220233e-22
6	-7.919883562745137e-05	-1.057639949449253e-05	-1.0749927920685414e-05

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	38
1	45	38

end0.0ms (0%)

sample3.1s (68.8%)

Algorithm

1×

intervals

Results

1.5s	3290×	body	1280	valid
627.0ms	646×	body	2560	valid
523.0ms	1853×	body	640	valid
150.0ms	767×	body	320	valid
63.0ms	1067×	body	80	valid
48.0ms	377×	body	160	valid

Details

analyze1.0ms (0%)

sample112.0ms (2.5%)

simplify5.0ms (0.1%)

prune6.0ms (0.1%)

localize8.0ms (0.2%)

rewrite11.0ms (0.2%)

series13.0ms (0.3%)

simplify49.0ms (1.1%)

prune54.0ms (1.2%)

localize13.0ms (0.3%)

rewrite19.0ms (0.4%)

series22.0ms (0.5%)

simplify61.0ms (1.3%)

prune134.0ms (2.9%)

localize18.0ms (0.4%)

rewrite37.0ms (0.8%)

series33.0ms (0.7%)

simplify49.0ms (1.1%)

prune195.0ms (4.3%)

localize19.0ms (0.4%)

rewrite22.0ms (0.5%)

series33.0ms (0.7%)

simplify41.0ms (0.9%)

prune217.0ms (4.8%)

regimes179.0ms (3.9%)

bsearch65.0ms (1.4%)

simplify1.0ms (0%)

end0.0ms (0%)

sample3.1s (68.8%)

Profiling