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)

sample96.0ms (1.6%)

Algorithm

1×

intervals

Results

41.0ms	103×	body	1024	valid
34.0ms	48×	body	2048	valid
9.0ms	37×	body	512	valid
3.0ms	49×	body	128	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify167.0ms (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))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2165` `*-un-lft-identity_binary64_2143`
4×	`add-log-exp_binary64_2182`
3×	`add-cube-cbrt_binary64_2178` `cancel-sign-sub-inv_binary64_2109`
2×	`pow1_binary64_2204` `sin-sum_binary64_2276` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
1×	`diff-log_binary64_2235` `flip--_binary64_2118` `sub-neg_binary64_2136` `distribute-lft-out--_binary64_2095` `diff-sin_binary64_2293` `flip3--_binary64_2147` `associate--l+_binary64_2080` `difference-of-squares_binary64_2112`

Counts

2 → 26

Calls

2 calls:

8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

series94.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

64.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
30.0ms	(sin.f64 (+.f64 x eps))

simplify60.0ms (1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (48.0ms)

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))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_2143`
8×	`add-log-exp_binary64_2182`
7×	`add-sqr-sqrt_binary64_2165`
5×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cube-cbrt_binary64_2178` `add-cbrt-cube_binary64_2179`
3×	`associate-r_binary64_2083` `sum-log_binary64_2234` `associate-l_binary64_2084` `distribute-lft-out_binary64_2094`
1×	`+-commutative_binary64_2073` `sin-cos-mult_binary64_2299` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `associate-+r+_binary64_2075` `unswap-sqr_binary64_2111` `flip3-+_binary64_2146` `flip-+_binary64_2117` `*-commutative_binary64_2074`

Counts

3 → 41

Calls

3 calls:

8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(+.f64 x (+.f64 x eps))

series157.0ms (2.7%)

Counts

3 → 9

Calls

3 calls:

86.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
37.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
34.0ms	(+.f64 x (+.f64 x eps))

simplify92.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4821	830
1	4821	830

prune156.0ms (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_2165`
4×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143` `add-cbrt-cube_binary64_2179`
3×	`associate-r_binary64_2083` `associate-l_binary64_2084`
2×	`add-log-exp_binary64_2182`
1×	`sin-cos-mult_binary64_2299` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `unswap-sqr_binary64_2111` `cos-sum_binary64_2277` `*-commutative_binary64_2074`

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)))

series111.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

78.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (+.f64 x (.f64 eps 1/2))))
33.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4833	582
1	4833	582

prune131.0ms (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)

localize18.0ms (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)))))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_2165`
10×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143` `add-cbrt-cube_binary64_2179`
9×	`associate-r_binary64_2083` `associate-l_binary64_2084`
6×	`add-log-exp_binary64_2182`
5×	`cos-mult_binary64_2297` `sin-mult_binary64_2298`
4×	`associate-*r/_binary64_2085`
3×	`sub-neg_binary64_2136` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `unswap-sqr_binary64_2111` `cancel-sign-sub-inv_binary64_2109` `*-commutative_binary64_2074`
2×	`sub-div_binary64_2150` `flip--_binary64_2118` `distribute-rgt-in_binary64_2093` `flip3--_binary64_2147` `frac-sub_binary64_2152` `distribute-lft-in_binary64_2092`
1×	`diff-log_binary64_2235`

Counts

4 → 78

Calls

4 calls:

15.0ms	(.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)))

series535.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(.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)))))
154.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2))))
80.0ms	(.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2)))
75.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4919	2160
1	4919	2160

prune494.0ms (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)

regimes76.0ms (1.3%)

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

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	35
1	48	35

end0.0ms (0%)

sample3.3s (56.7%)

Algorithm

1×

intervals

Results

1.3s	3533×	body	1024	valid
962.0ms	1249×	body	2048	valid
298.0ms	1323×	body	512	valid
91.0ms	1324×	body	128	valid
84.0ms	569×	body	256	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 459 to 362 computations (21.1% saved)

Details

analyze2.0ms (0%)

sample96.0ms (1.6%)

simplify167.0ms (2.8%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite17.0ms (0.3%)

series94.0ms (1.6%)

simplify60.0ms (1%)

prune64.0ms (1.1%)

localize12.0ms (0.2%)

rewrite24.0ms (0.4%)

series157.0ms (2.7%)

simplify92.0ms (1.6%)

prune156.0ms (2.6%)

localize12.0ms (0.2%)

rewrite13.0ms (0.2%)

series111.0ms (1.9%)

simplify80.0ms (1.4%)

prune131.0ms (2.2%)

localize18.0ms (0.3%)

rewrite42.0ms (0.7%)

series535.0ms (9.1%)

simplify87.0ms (1.5%)

prune494.0ms (8.4%)

regimes76.0ms (1.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.3s (56.7%)

Profiling