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)

sample76.0ms (1.3%)

Algorithm

1×

intervals

Results

31.0ms	128×	body	1024	valid
29.0ms	63×	body	2048	valid
6.0ms	39×	body	512	valid
2.0ms	17×	body	256	valid
1.0ms	9×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify105.0ms (1.8%)

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: 40.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.7b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.3b	(cos.f64 (+.f64 x eps))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`add-log-exp_binary64_117`
3×	`add-cube-cbrt_binary64_113` `cancel-sign-sub-inv_binary64_44`
2×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `cos-sum_binary64_212` `pow1_binary64_139`
1×	`distribute-lft-out--_binary64_30` `flip3--_binary64_82` `diff-log_binary64_170` `diff-cos_binary64_229` `flip--_binary64_53` `difference-of-squares_binary64_47` `associate--l-_binary64_16` `sub-neg_binary64_71`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

series144.0ms (2.5%)

Counts

2 → 24

Calls

2 calls:

102.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
42.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 419 to 341 computations (18.6% saved)

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4916	794
1	4916	794

prune50.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	8	51

Merged error: 0.2b

Counts

51 → 8

Compiler

Compiled 794 to 333 computations (58.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_78`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
9×	`add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117`
7×	`add-cube-cbrt_binary64_113`
6×	`associate-l_binary64_19`
4×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-r_binary64_18` `pow-prod-down_binary64_149`
3×	`distribute-lft-out_binary64_29` `sum-log_binary64_169`
2×	`*-commutative_binary64_9` `sin-mult_binary64_233`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `associate-+r+_binary64_10` `unswap-sqr_binary64_46` `associate-*r/_binary64_20` `flip3-+_binary64_81`

Counts

4 → 60

Calls

4 calls:

13.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
12.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series428.0ms (7.3%)

Counts

4 → 48

Calls

4 calls:

161.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
149.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
61.0ms	(+.f64 x (+.f64 x eps))
57.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Compiler

Compiled 1244 to 1127 computations (9.4% saved)

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4972	2087
1	4972	2087

prune124.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	105	11	116

Merged error: 0.2b

Counts

116 → 11

Compiler

Compiled 2295 to 1562 computations (31.9% saved)

localize18.0ms (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)))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_109`
7×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `pow1_binary64_139`
3×	`pow1/3_binary64_160`

Counts

4 → 40

Calls

4 calls:

7.0ms	(sin.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)))

series339.0ms (5.8%)

Counts

4 → 24

Calls

4 calls:

95.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
89.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
89.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
66.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Compiler

Compiled 1288 to 1110 computations (13.8% saved)

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5525	860

prune122.0ms (2.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	63	12	75

Merged error: 0.2b

Counts

75 → 12

Compiler

Compiled 2302 to 1721 computations (25.2% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))))
0.6b	(cbrt.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))))
0.6b	(cbrt.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`cbrt-prod_binary64_109`
10×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `pow1_binary64_139`
3×	`pow1/3_binary64_160`

Counts

4 → 49

Calls

4 calls:

8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))))
3.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))))
3.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))))

series380.0ms (6.5%)

Counts

4 → 24

Calls

4 calls:

107.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))))
99.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))))
99.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))))
75.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Compiler

Compiled 1822 to 1570 computations (13.8% saved)

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4998	1127
1	4998	1127

prune186.0ms (3.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	73	12	85

Merged error: 0.2b

Counts

85 → 12

Compiler

Compiled 3486 to 2728 computations (21.7% saved)

regimes251.0ms (4.3%)

Compiler: Compiled 1695 to 1333 computations (21.4% saved)

bsearch81.0ms (1.4%)

Steps

Iters	Range		Point
11	1.3604158820995664e-19	879013.2230478316	0.003293292867343906
10	-831345150.1956456	-0.0002568586196256804	-0.0030418061005483

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	125	96
1	125	96

end0.0ms (0%)

sample3.2s (53.9%)

Algorithm

1×

intervals

Results

1.1s	2108×	body	2048	valid
958.0ms	3835×	body	1024	valid
214.0ms	1265×	body	512	valid
76.0ms	542×	body	256	valid
15.0ms	247×	body	128	valid
3.0ms	3×	body	4096	valid

Compiler

Compiled 606 to 466 computations (23.1% saved)

Details

analyze2.0ms (0%)

sample76.0ms (1.3%)

simplify105.0ms (1.8%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite12.0ms (0.2%)

series144.0ms (2.5%)

simplify58.0ms (1%)

prune50.0ms (0.9%)

localize12.0ms (0.2%)

rewrite43.0ms (0.7%)

series428.0ms (7.3%)

simplify79.0ms (1.3%)

prune124.0ms (2.1%)

localize18.0ms (0.3%)

rewrite18.0ms (0.3%)

series339.0ms (5.8%)

simplify53.0ms (0.9%)

prune122.0ms (2.1%)

localize20.0ms (0.3%)

rewrite23.0ms (0.4%)

series380.0ms (6.5%)

simplify76.0ms (1.3%)

prune186.0ms (3.2%)

regimes251.0ms (4.3%)

bsearch81.0ms (1.4%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.2s (53.9%)

Profiling