Details

analyze2.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample95.0ms (1.6%)

Algorithm

1×

intervals

Results

41.0ms	103×	body	1024	valid
34.0ms	48×	body	2048	valid
8.0ms	37×	body	512	valid
3.0ms	49×	body	128	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify166.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (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: 37.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.9b	(sin.f64 (+.f64 x eps))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1821` `*-un-lft-identity_binary64_1799`
4×	`add-log-exp_binary64_1838`
3×	`add-cube-cbrt_binary64_1834` `cancel-sign-sub-inv_binary64_1765`
2×	`pow1_binary64_1860` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837` `sin-sum_binary64_1932`
1×	`diff-sin_binary64_1949` `sub-neg_binary64_1792` `associate--l+_binary64_1736` `diff-log_binary64_1891` `flip--_binary64_1774` `difference-of-squares_binary64_1768` `flip3--_binary64_1803` `distribute-lft-out--_binary64_1751`

Counts

2 → 26

Calls

2 calls:

8.0ms	(sin.f64 (+.f64 x eps))
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

series95.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

66.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
29.0ms	(sin.f64 (+.f64 x eps))

simplify60.0ms (1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5018	441

prune64.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Merged error: 0.5b

Counts

33 → 3

Compiler

Compiled 872 to 459 computations (47.4% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1799`
8×	`add-log-exp_binary64_1838`
7×	`add-sqr-sqrt_binary64_1821`
5×	`pow1_binary64_1860` `add-cube-cbrt_binary64_1834` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
3×	`sum-log_binary64_1890` `associate-l_binary64_1740` `distribute-lft-out_binary64_1750` `associate-r_binary64_1739`
1×	`+-commutative_binary64_1729` `prod-exp_binary64_1848` `unswap-sqr_binary64_1767` `associate-+r+_binary64_1731` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870` `flip3-+_binary64_1802` `sin-cos-mult_binary64_1955` `flip-+_binary64_1773`

Counts

3 → 41

Calls

3 calls:

8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(+.f64 x (+.f64 x eps))

series147.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

80.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
36.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
30.0ms	(+.f64 x (+.f64 x eps))

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4821	830
1	4821	830

prune154.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	45	8	53

Merged error: 0.5b

Counts

53 → 8

Compiler

Compiled 2610 to 1871 computations (28.3% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (+.f64 x (.f64 eps 1/2))))
3.5b	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1821`
4×	`pow1_binary64_1860` `add-cube-cbrt_binary64_1834` `add-cbrt-cube_binary64_1835` `*-un-lft-identity_binary64_1799` `add-exp-log_binary64_1837`
3×	`associate-l_binary64_1740` `associate-r_binary64_1739`
2×	`add-log-exp_binary64_1838`
1×	`prod-exp_binary64_1848` `unswap-sqr_binary64_1767` `cos-sum_binary64_1933` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870` `sin-cos-mult_binary64_1955`

Counts

2 → 27

Calls

2 calls:

7.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (+.f64 x (.f64 eps 1/2))))
4.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

series114.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

85.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (+.f64 x (.f64 eps 1/2))))
30.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4833	582
1	4833	582

prune130.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	28	5	33
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	34	7	41

Merged error: 0.1b

Counts

41 → 7

Compiler

Compiled 2107 to 1657 computations (21.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2)))
0.1b	(-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2))))
0.2b	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))
0.2b	(.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1821`
10×	`pow1_binary64_1860` `add-cube-cbrt_binary64_1834` `add-cbrt-cube_binary64_1835` `*-un-lft-identity_binary64_1799` `add-exp-log_binary64_1837`
9×	`associate-l_binary64_1740` `associate-r_binary64_1739`
6×	`add-log-exp_binary64_1838`
5×	`cos-mult_binary64_1953` `sin-mult_binary64_1954`
4×	`associate-*r/_binary64_1741`
3×	`sub-neg_binary64_1792` `prod-exp_binary64_1848` `unswap-sqr_binary64_1767` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870` `cancel-sign-sub-inv_binary64_1765`
2×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `flip--_binary64_1774` `flip3--_binary64_1803` `frac-sub_binary64_1808` `sub-div_binary64_1806`
1×	`diff-log_binary64_1891`

Counts

4 → 78

Calls

4 calls:

14.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))))
7.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2))))
6.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))
5.0ms	(.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2)))

series537.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

229.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))))
158.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2))))
80.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))
70.0ms	(.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2)))

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4919	2160
1	4919	2160

prune491.0ms (8.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	87	10	97

Merged error: 0.0b

Counts

97 → 10

Compiler

Compiled 8822 to 6787 computations (23.1% saved)

regimes73.0ms (1.2%)

Compiler: Compiled 836 to 652 computations (22% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	35
1	48	35

end0.0ms (0%)

sample3.3s (57%)

Algorithm

1×

intervals

Results

1.3s	3533×	body	1024	valid
969.0ms	1249×	body	2048	valid
279.0ms	1323×	body	512	valid
85.0ms	1324×	body	128	valid
78.0ms	569×	body	256	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 459 to 362 computations (21.1% saved)

Details

analyze2.0ms (0%)

sample95.0ms (1.6%)

simplify166.0ms (2.8%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite18.0ms (0.3%)

series95.0ms (1.6%)

simplify60.0ms (1%)

prune64.0ms (1.1%)

localize12.0ms (0.2%)

rewrite26.0ms (0.4%)

series147.0ms (2.5%)

simplify86.0ms (1.5%)

prune154.0ms (2.6%)

localize12.0ms (0.2%)

rewrite13.0ms (0.2%)

series114.0ms (1.9%)

simplify75.0ms (1.3%)

prune130.0ms (2.2%)

localize19.0ms (0.3%)

rewrite39.0ms (0.7%)

series537.0ms (9.2%)

simplify84.0ms (1.4%)

prune491.0ms (8.4%)

regimes73.0ms (1.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (57%)

Profiling