Details

analyze638.0ms (7.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0.1%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample192.0ms (2.3%)

Algorithm

1×

intervals

Results

90.0ms	53×	body	8192	exit
43.0ms	113×	body	1024	valid
15.0ms	68×	body	512	valid
13.0ms	51×	body	1024	nan
5.0ms	37×	body	256	valid
5.0ms	28×	body	512	nan
4.0ms	6×	body	2048	valid
3.0ms	32×	body	128	valid
2.0ms	13×	body	256	nan
1.0ms	14×	body	128	nan

Compiler

Compiled 21 to 18 computations (14.3% saved)

simplify199.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4785	15
1	4785	15

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 59.2b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (cos.f64 x))
0.5b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_782`
12×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
9×	`times-frac_binary64_766`
5×	`add-cbrt-cube_binary64_796`
4×	`add-exp-log_binary64_798` `pow1_binary64_821`
3×	`sqrt-prod_binary64_776` `associate-/r_binary64_704` `add-log-exp_binary64_799` `associate-/l_binary64_705`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `pow1/2_binary64_840` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

3 → 47

Calls

3 calls:

4.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
1.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series56.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
15.0ms	(sqrt.f64 (cos.f64 x))
7.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4909	953
1	4909	953

prune44.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	4	57

Merged error: 59.2b

Counts

57 → 4

Compiler

Compiled 868 to 195 computations (77.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
1.0b	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
1.8b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_760`
14×	`add-sqr-sqrt_binary64_782`
10×	`add-cube-cbrt_binary64_795`
9×	`log-prod_binary64_846`
7×	`add-log-exp_binary64_799` `exp-sum_binary64_806` `pow1_binary64_821`
6×	`exp-prod_binary64_812` `cancel-sign-sub-inv_binary64_726` `associate--l+_binary64_697`
5×	`add-exp-log_binary64_798`
4×	`add-cbrt-cube_binary64_796` `distribute-lft-out--_binary64_712`
3×	`log-pow_binary64_849`
2×	`diff-log_binary64_852` `rem-exp-log_binary64_800` `difference-of-squares_binary64_729` `sub-neg_binary64_753`
1×	`exp-diff_binary64_808` `rem-log-exp_binary64_801` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 62

Calls

4 calls:

5.0ms	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
4.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
1.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series199.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
74.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
23.0ms	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
7.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4919	1206
1	4919	1206

prune55.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	73	5	78

Merged error: 59.2b

Counts

78 → 5

Compiler

Compiled 1189 to 239 computations (79.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 E.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
1.0b	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
1.8b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_760`
15×	`add-sqr-sqrt_binary64_782`
11×	`add-cube-cbrt_binary64_795`
9×	`log-prod_binary64_846`
8×	`pow1_binary64_821`
7×	`unpow-prod-up_binary64_838`
6×	`add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726` `associate--l+_binary64_697` `pow-unpow_binary64_837`
5×	`add-log-exp_binary64_799`
4×	`add-cbrt-cube_binary64_796` `distribute-lft-out--_binary64_712`
3×	`log-pow_binary64_849` `unpow-prod-down_binary64_839`
2×	`pow-exp_binary64_828` `difference-of-squares_binary64_729` `sub-neg_binary64_753`
1×	`diff-log_binary64_852` `pow-to-exp_binary64_829` `rem-log-exp_binary64_801` `sqr-pow_binary64_732` `flip--_binary64_735` `pow-pow_binary64_832` `pow-sub_binary64_836` `e-exp-1_binary64_805` `flip3--_binary64_764`

Counts

4 → 68

Calls

4 calls:

6.0ms	(pow.f64 E.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
4.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
1.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series214.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
81.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
25.0ms	(pow.f64 E.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
9.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4921	1449
1	4921	1449

prune57.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	80	5	85

Merged error: 59.2b

Counts

85 → 5

Compiler

Compiled 1386 to 256 computations (81.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64_760` `add-exp-log_binary64_798` `add-cube-cbrt_binary64_795` `pow1_binary64_821` `add-sqr-sqrt_binary64_782`
4×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`log-prod_binary64_846`
1×	`log-pow_binary64_849` `rem-log-exp_binary64_801`

Counts

4 → 33

Calls

4 calls:

1.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series91.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
6.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
6.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
6.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4822	620
1	4822	620

prune48.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	45	5	50

Merged error: 59.2b

Counts

50 → 5

Compiler

Compiled 1706 to 201 computations (88.2% saved)

regimes49.0ms (0.6%)

Compiler: Compiled 478 to 260 computations (45.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample6.2s (73.5%)

Algorithm

1×

intervals

Results

2.7s	1610×	body	8192	exit
1.5s	4006×	body	1024	valid
464.0ms	1990×	body	512	valid
439.0ms	1592×	body	1024	nan
158.0ms	1011×	body	256	valid
152.0ms	815×	body	512	nan
92.0ms	162×	body	2048	valid
70.0ms	831×	body	128	valid
47.0ms	379×	body	256	nan
28.0ms	392×	body	128	nan

Compiler

Compiled 250 to 140 computations (44% saved)

Details

analyze638.0ms (7.5%)

sample192.0ms (2.3%)

simplify199.0ms (2.3%)

prune7.0ms (0.1%)

localize7.0ms (0.1%)

rewrite9.0ms (0.1%)

series56.0ms (0.7%)

simplify79.0ms (0.9%)

prune44.0ms (0.5%)

localize9.0ms (0.1%)

rewrite16.0ms (0.2%)

series199.0ms (2.3%)

simplify89.0ms (1%)

prune55.0ms (0.7%)

localize9.0ms (0.1%)

rewrite17.0ms (0.2%)

series214.0ms (2.5%)

simplify57.0ms (0.7%)

prune57.0ms (0.7%)

localize14.0ms (0.2%)

rewrite6.0ms (0.1%)

series91.0ms (1.1%)

simplify83.0ms (1%)

prune48.0ms (0.6%)

regimes49.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.2s (73.5%)

Profiling