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)

sample98.0ms (1.9%)

Algorithm

1×

intervals

Results

41.0ms	103×	body	1024	valid
35.0ms	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)

simplify177.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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 (0.2%)

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))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_2120` `add-log-exp_binary64_2135` `*-un-lft-identity_binary64_2099`
2×	`add-cube-cbrt_binary64_2131` `sin-sum_binary64_2229` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-exp-log_binary64_2134`
1×	`difference-of-squares_binary64_2068` `sub-neg_binary64_2092` `associate--l+_binary64_2038` `diff-sin_binary64_2246` `flip3--_binary64_2103` `flip--_binary64_2074` `distribute-lft-out--_binary64_2053` `diff-log_binary64_2188`

Counts

2 → 23

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

series96.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

65.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
31.0ms	(sin.f64 (+.f64 x eps))

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4839	426
1	4839	426

prune30.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.5b

Counts

30 → 3

Compiler

Compiled 404 to 129 computations (68.1% 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))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_2099`
8×	`add-log-exp_binary64_2135`
7×	`add-sqr-sqrt_binary64_2120`
5×	`add-cube-cbrt_binary64_2131` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-exp-log_binary64_2134`
3×	`associate-l_binary64_2042` `distribute-lft-out_binary64_2052` `sum-log_binary64_2187` `associate-r_binary64_2041`
1×	`flip3-+_binary64_2102` `*-commutative_binary64_2032` `prod-exp_binary64_2145` `sin-cos-mult_binary64_2252` `+-commutative_binary64_2031` `pow-prod-down_binary64_2167` `unswap-sqr_binary64_2067` `flip-+_binary64_2073` `cbrt-unprod_binary64_2129` `associate-+r+_binary64_2033`

Counts

3 → 41

Calls

3 calls:

9.0ms	(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))

series148.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

82.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
35.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
31.0ms	(+.f64 x (+.f64 x eps))

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4886	830
1	4886	830

prune69.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	8	53

Merged error: 0.5b

Counts

53 → 8

Compiler

Compiled 1164 to 756 computations (35.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.4b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
3.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_2127`
24×	`add-sqr-sqrt_binary64_2120`
15×	`add-cube-cbrt_binary64_2131` `-un-lft-identity_binary64_2099` `associate-r*_binary64_2041`
10×	`unpow-prod-down_binary64_2175` `cube-prod_binary64_2124`
7×	`pow1_binary64_2157` `add-exp-log_binary64_2134`
6×	`add-cbrt-cube_binary64_2132`
5×	`unswap-sqr_binary64_2067`
4×	`sqr-pow_binary64_2071` `add-log-exp_binary64_2135`
3×	`associate-l_binary64_2042` `unpow3_binary64_2162` `pow-unpow_binary64_2173` `cube-mult_binary64_2126`
1×	`pow1/3_binary64_2178` `pow-exp_binary64_2164` `*-commutative_binary64_2032` `pow-pow_binary64_2168` `rem-cube-cbrt_binary64_2121` `pow-to-exp_binary64_2165` `prod-exp_binary64_2145` `pow-prod-down_binary64_2167` `rem-cbrt-cube_binary64_2122` `cbrt-unprod_binary64_2129`

Counts

4 → 85

Calls

4 calls:

10.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

series257.0ms (5%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
82.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
33.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
31.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4829	1942
1	4829	1942

prune139.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	94	11	105

Merged error: 0.4b

Counts

105 → 11

Compiler

Compiled 2503 to 1668 computations (33.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (.f64 eps 1/2))) 3)))
0.4b	(cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3))
0.5b	(pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3)
3.5b	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_2127`
24×	`add-sqr-sqrt_binary64_2120`
15×	`add-cube-cbrt_binary64_2131` `-un-lft-identity_binary64_2099` `associate-r*_binary64_2041`
10×	`unpow-prod-down_binary64_2175` `cube-prod_binary64_2124`
7×	`pow1_binary64_2157` `add-exp-log_binary64_2134`
6×	`add-cbrt-cube_binary64_2132`
5×	`unswap-sqr_binary64_2067`
4×	`sqr-pow_binary64_2071` `add-log-exp_binary64_2135`
3×	`associate-l_binary64_2042` `unpow3_binary64_2162` `pow-unpow_binary64_2173` `cube-mult_binary64_2126`
1×	`pow1/3_binary64_2178` `pow-exp_binary64_2164` `*-commutative_binary64_2032` `pow-pow_binary64_2168` `rem-cube-cbrt_binary64_2121` `pow-to-exp_binary64_2165` `prod-exp_binary64_2145` `pow-prod-down_binary64_2167` `rem-cbrt-cube_binary64_2122` `cos-sum_binary64_2230` `cbrt-unprod_binary64_2129`

Counts

4 → 86

Calls

4 calls:

13.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (.f64 eps 1/2))) 3)))
5.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))
4.0ms	(pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3))

series242.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3)
77.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (.f64 eps 1/2))) 3)))
31.0ms	(cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3))
31.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4822	1676
1	4822	1676

prune133.0ms (2.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	6	3	9
Picked	1	0	1
Done	0	1	1
Total	99	10	109

Merged error: 0.1b

Counts

109 → 10

Compiler

Compiled 2040 to 1640 computations (19.6% saved)

regimes53.0ms (1%)

Compiler: Compiled 428 to 364 computations (15% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	40
1	51	40

end0.0ms (0%)

sample3.3s (62.9%)

Algorithm

1×

intervals

Results

1.3s	3533×	body	1024	valid
978.0ms	1249×	body	2048	valid
285.0ms	1323×	body	512	valid
85.0ms	1324×	body	128	valid
77.0ms	569×	body	256	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 258 to 221 computations (14.3% saved)

Details

analyze2.0ms (0%)

sample98.0ms (1.9%)

simplify177.0ms (3.4%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite13.0ms (0.3%)

series96.0ms (1.9%)

simplify78.0ms (1.5%)

prune30.0ms (0.6%)

localize12.0ms (0.2%)

rewrite25.0ms (0.5%)

series148.0ms (2.9%)

simplify83.0ms (1.6%)

prune69.0ms (1.3%)

localize15.0ms (0.3%)

rewrite32.0ms (0.6%)

series257.0ms (5%)

simplify78.0ms (1.5%)

prune139.0ms (2.7%)

localize14.0ms (0.3%)

rewrite32.0ms (0.6%)

series242.0ms (4.7%)

simplify80.0ms (1.5%)

prune133.0ms (2.6%)

regimes53.0ms (1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.3s (62.9%)

Profiling