Details

analyze3.0ms (0.1%)

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)

sample87.0ms (1.8%)

Algorithm

1×

intervals

Results

39.0ms	112×	body	1024	valid
28.0ms	38×	body	2048	valid
8.0ms	41×	body	512	valid
3.0ms	49×	body	128	valid
2.0ms	16×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune8.0ms (0.2%)

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: 38.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.9b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.1b	(sin.f64 (+.f64 x eps))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `diff-sin_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

2 → 23

Calls

2 calls:

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

series95.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

63.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
31.0ms	(sin.f64 (+.f64 x eps))

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4839	426
1	4839	426

prune31.0ms (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: 0.4b

Counts

30 → 3

Compiler

Compiled 404 to 129 computations (68.1% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-cos-mult_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

3 → 41

Calls

3 calls:

9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(+.f64 x (+.f64 x eps))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series141.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

73.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
35.0ms	(+.f64 x (+.f64 x eps))
34.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4886	830
1	4886	830

prune65.0ms (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: 0.4b

Counts

53 → 8

Compiler

Compiled 1170 to 761 computations (35% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cbrt-prod_binary64`
1×	`pow1/3_binary64`

Counts

4 → 32

Calls

4 calls:

8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series244.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
35.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
30.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
28.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify85.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4812	644
1	4812	644

prune85.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	44	8	52

Merged error: 0.4b

Counts

52 → 8

Compiler

Compiled 1885 to 1128 computations (40.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
3.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`

Counts

4 → 40

Calls

4 calls:

8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))

series423.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
131.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
129.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
33.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify74.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4865	689
1	4865	689

prune84.0ms (1.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	52	8	60

Merged error: 0.4b

Counts

60 → 8

Compiler

Compiled 1703 to 1252 computations (26.5% saved)

regimes75.0ms (1.5%)

Compiler: Compiled 378 to 294 computations (22.2% saved)

bsearch70.0ms (1.4%)

Steps

Iters	Range		Point
8	3.390109041812983e-19	1.3346993280289942e-14	1.3134454814789761e-14
7	-3.9092861706778204e-08	-3.3430077415887593e-10	-2.2040410017593036e-08

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	60
1	47	60

end0.0ms (0%)

sample3.1s (61.9%)

Algorithm

1×

intervals

Results

1.3s	3486×	body	1024	valid
911.0ms	1212×	body	2048	valid
288.0ms	1381×	body	512	valid
87.0ms	1322×	body	128	valid
79.0ms	598×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 246 to 192 computations (22% saved)

Details

analyze3.0ms (0.1%)

sample87.0ms (1.8%)

simplify11.0ms (0.2%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

rewrite15.0ms (0.3%)

series95.0ms (1.9%)

simplify77.0ms (1.5%)

prune31.0ms (0.6%)

localize13.0ms (0.3%)

rewrite25.0ms (0.5%)

series141.0ms (2.9%)

simplify81.0ms (1.6%)

prune65.0ms (1.3%)

localize17.0ms (0.3%)

rewrite30.0ms (0.6%)

series244.0ms (4.9%)

simplify85.0ms (1.7%)

prune85.0ms (1.7%)

localize17.0ms (0.3%)

rewrite19.0ms (0.4%)

series423.0ms (8.6%)

simplify74.0ms (1.5%)

prune84.0ms (1.7%)

regimes75.0ms (1.5%)

bsearch70.0ms (1.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.1s (61.9%)

Profiling