Details

analyze1.5s (8.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

Compiler

Compiled 51 to 41 computations (19.6% saved)

sample269.0ms (1.5%)

Algorithm

1×

intervals

Results

143.0ms	92×	body	1024	valid
62.0ms	53×	body	512	valid
28.0ms	86×	body	128	valid
17.0ms	24×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 101 to 83 computations (17.8% saved)

simplify238.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4940	77
1	4940	77

prune16.0ms (0.1%)

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: 0.3b

Counts

2 → 2

Compiler

Compiled 146 to 116 computations (20.5% saved)

localize60.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.7b	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.8b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite113.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`cancel-sign-sub-inv_binary64_4136`
44×	`add-sqr-sqrt_binary64_4192`
35×	`*-un-lft-identity_binary64_4170`
30×	`distribute-lft-in_binary64_4119` `distribute-rgt-in_binary64_4120`
29×	`add-cube-cbrt_binary64_4205`
19×	`times-frac_binary64_4176`
11×	`pow1_binary64_4231` `add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206`
9×	`associate-l_binary64_4111`
8×	`sqrt-prod_binary64_4186` `add-log-exp_binary64_4209` `sub-neg_binary64_4163`
7×	`associate-r_binary64_4110`
6×	`associate-*r/_binary64_4112`
5×	`difference-of-squares_binary64_4139`
4×	`flip3--_binary64_4174` `prod-exp_binary64_4219` `cbrt-unprod_binary64_4203` `pow-prod-down_binary64_4241` `flip--_binary64_4145`
3×	`distribute-lft-out--_binary64_4122`
2×	`diff-log_binary64_4262` `div-inv_binary64_4167` `*-commutative_binary64_4101` `unswap-sqr_binary64_4138`
1×	`diff-cos_binary64_4321`

Counts

4 → 128

Calls

4 calls:

28.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
25.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
10.0ms	(-.f64 3 (sqrt.f64 5))
10.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series243.0ms (1.3%)

Counts

4 → 10

Calls

4 calls:

99.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
74.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
70.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))

simplify98.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5119	2405

prune704.0ms (3.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	131	9	140

Merged error: 0.1b

Counts

140 → 9

Compiler

Compiled 7799 to 5210 computations (33.2% saved)

localize66.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.8b	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (+.f64 -1 (sqrt.f64 5))) (sqrt.f64 3/2)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.8b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite102.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_4192`
35×	`cancel-sign-sub-inv_binary64_4136`
32×	`*-un-lft-identity_binary64_4170`
26×	`add-cube-cbrt_binary64_4205`
19×	`times-frac_binary64_4176`
15×	`pow1_binary64_4231` `add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206`
14×	`distribute-lft-in_binary64_4119` `distribute-rgt-in_binary64_4120`
12×	`associate-l_binary64_4111`
11×	`sqrt-prod_binary64_4186`
8×	`add-log-exp_binary64_4209`
7×	`prod-exp_binary64_4219` `cbrt-unprod_binary64_4203` `associate-r_binary64_4110` `pow-prod-down_binary64_4241`
6×	`associate-*r/_binary64_4112`
5×	`difference-of-squares_binary64_4139`
4×	`sub-neg_binary64_4163`
3×	`flip3--_binary64_4174` `distribute-lft-out--_binary64_4122` `flip--_binary64_4145`
2×	`diff-log_binary64_4262` `associate-l/_binary64_4113` `div-inv_binary64_4167` `-commutative_binary64_4101` `unswap-sqr_binary64_4138`
1×	`diff-cos_binary64_4321` `flip-+_binary64_4144` `flip3-+_binary64_4173`

Counts

4 → 118

Calls

4 calls:

24.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
22.0ms	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (+.f64 -1 (sqrt.f64 5))) (sqrt.f64 3/2)))
8.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
8.0ms	(-.f64 3 (sqrt.f64 5))

series284.0ms (1.5%)

Counts

4 → 10

Calls

4 calls:

111.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
102.0ms	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (+.f64 -1 (sqrt.f64 5))) (sqrt.f64 3/2)))
70.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5352	2267

prune653.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	128	9	137

Merged error: 0.1b

Counts

137 → 9

Compiler

Compiled 7739 to 5352 computations (30.8% saved)

localize72.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (+.f64 -1 (sqrt.f64 5))) (sqrt.f64 3/2)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.8b	(-.f64 (cos.f64 x) (cos.f64 y))
3.1b	(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))))

rewrite102.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`cancel-sign-sub-inv_binary64_4136`
31×	`log-prod_binary64_4256`
30×	`add-sqr-sqrt_binary64_4192`
28×	`*-un-lft-identity_binary64_4170` `exp-sum_binary64_4216`
24×	`add-cube-cbrt_binary64_4205`
18×	`times-frac_binary64_4176`
14×	`distribute-lft-in_binary64_4119` `distribute-rgt-in_binary64_4120` `pow1_binary64_4231`
13×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206`
9×	`add-log-exp_binary64_4209`
7×	`sqrt-prod_binary64_4186`
6×	`associate-l_binary64_4111` `prod-exp_binary64_4219` `cbrt-unprod_binary64_4203` `pow-prod-down_binary64_4241`
4×	`associate-*r/_binary64_4112` `sub-neg_binary64_4163`
3×	`log-pow_binary64_4259` `difference-of-squares_binary64_4139`
2×	`flip3--_binary64_4174` `diff-log_binary64_4262` `associate-*l/_binary64_4113` `div-inv_binary64_4167` `distribute-lft-out--_binary64_4122` `flip--_binary64_4145`
1×	`diff-cos_binary64_4321` `exp-prod_binary64_4222` `rem-log-exp_binary64_4211` `flip-+_binary64_4144` `associate-r_binary64_4110` `flip3-+_binary64_4173` `*-commutative_binary64_4101` `exp-to-pow_binary64_4232`

Counts

4 → 105

Calls

4 calls:

27.0ms	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (+.f64 -1 (sqrt.f64 5))) (sqrt.f64 3/2)))
15.0ms	(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))))
10.0ms	(-.f64 3 (sqrt.f64 5))
10.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series416.0ms (2.3%)

Counts

4 → 10

Calls

4 calls:

254.0ms	(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))))
101.0ms	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (+.f64 -1 (sqrt.f64 5))) (sqrt.f64 3/2)))
60.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))

simplify92.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5014	1958

prune641.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	115	9	124

Merged error: 0.1b

Counts

124 → 9

Compiler

Compiled 7050 to 4935 computations (30% saved)

localize69.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))
0.7b	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.8b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite117.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`distribute-lft-in_binary64_4119` `distribute-rgt-in_binary64_4120`
57×	`cancel-sign-sub-inv_binary64_4136`
30×	`add-sqr-sqrt_binary64_4192`
28×	`*-un-lft-identity_binary64_4170` `associate-+l+_binary64_4103`
24×	`add-cube-cbrt_binary64_4205`
20×	`associate-*r/_binary64_4112`
16×	`sqrt-prod_binary64_4186` `associate-+r+_binary64_4102`
14×	`sub-neg_binary64_4163`
10×	`add-log-exp_binary64_4209`
9×	`pow1_binary64_4231` `add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206`
7×	`flip3--_binary64_4174` `flip--_binary64_4145`
4×	`frac-add_binary64_4178`
3×	`associate-l_binary64_4111` `prod-exp_binary64_4219` `cbrt-unprod_binary64_4203` `difference-of-squares_binary64_4139` `pow-prod-down_binary64_4241`
2×	`diff-log_binary64_4262` `distribute-lft-out--_binary64_4122`
1×	`diff-cos_binary64_4321` `flip-+_binary64_4144` `associate-r_binary64_4110` `+-commutative_binary64_4100` `flip3-+_binary64_4173` `*-commutative_binary64_4101` `sum-log_binary64_4261`

Counts

4 → 132

Calls

4 calls:

29.0ms	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))
17.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
8.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
8.0ms	(-.f64 3 (sqrt.f64 5))

series414.0ms (2.3%)

Counts

4 → 10

Calls

4 calls:

267.0ms	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))
76.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
70.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
0.0ms	(-.f64 3 (sqrt.f64 5))

simplify111.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4947	3062
1	4947	3062

prune686.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	142	9	151

Merged error: 0.1b

Counts

151 → 9

Compiler

Compiled 8309 to 5605 computations (32.5% saved)

regimes690.0ms (3.8%)

Compiler: Compiled 5468 to 4366 computations (20.2% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	96	84
1	96	84

end0.0ms (0%)

sample10.5s (57.1%)

Algorithm

1×

intervals

Results

5.5s	3440×	body	1024	valid
1.5s	1349×	body	512	valid
908.0ms	2603×	body	128	valid
421.0ms	595×	body	256	valid
39.0ms	13×	body	2048	valid

Compiler

Compiled 1891 to 1511 computations (20.1% saved)

Details

analyze1.5s (8.2%)

sample269.0ms (1.5%)

simplify238.0ms (1.3%)

prune16.0ms (0.1%)

localize60.0ms (0.3%)

rewrite113.0ms (0.6%)

series243.0ms (1.3%)

simplify98.0ms (0.5%)

prune704.0ms (3.8%)

localize66.0ms (0.4%)

rewrite102.0ms (0.6%)

series284.0ms (1.5%)

simplify101.0ms (0.5%)

prune653.0ms (3.6%)

localize72.0ms (0.4%)

rewrite102.0ms (0.6%)

series416.0ms (2.3%)

simplify92.0ms (0.5%)

prune641.0ms (3.5%)

localize69.0ms (0.4%)

rewrite117.0ms (0.6%)

series414.0ms (2.3%)

simplify111.0ms (0.6%)

prune686.0ms (3.7%)

regimes690.0ms (3.8%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample10.5s (57.1%)

Profiling