Details

analyze646.0ms (7.1%)

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)

sample171.0ms (1.9%)

Algorithm

1×

intervals

Results

64.0ms	39×	body	8192	exit
56.0ms	141×	body	1024	valid
13.0ms	50×	body	1024	nan
11.0ms	50×	body	512	valid
4.0ms	29×	body	256	valid
3.0ms	19×	body	512	nan
3.0ms	32×	body	128	valid
3.0ms	19×	body	256	nan
2.0ms	4×	body	2048	valid
1.0ms	9×	body	128	nan

Compiler

Compiled 21 to 18 computations (14.3% saved)

simplify204.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4785	15
1	4785	15

prune3.0ms (0%)

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: 58.8b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (cos.f64 x))
0.2b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
5.7b	(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 (0.6%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
14.0ms	(sqrt.f64 (cos.f64 x))
7.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4909	953
1	4909	953

prune42.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	3	57

Merged error: 58.8b

Counts

57 → 3

Compiler

Compiled 857 to 187 computations (78.2% 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))
2.8b	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
3.3b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
5.7b	(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)))

series202.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
71.0ms	(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))
8.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4919	1206
1	4919	1206

prune52.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	73	4	77

Merged error: 58.8b

Counts

77 → 4

Compiler

Compiled 1165 to 236 computations (79.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(exp.f64 (cbrt.f64 (pow.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x) 3)))
2.8b	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
3.3b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
5.7b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`exp-prod_binary64_812`
20×	`*-un-lft-identity_binary64_760`
18×	`cbrt-prod_binary64_791`
17×	`add-sqr-sqrt_binary64_782`
11×	`add-cube-cbrt_binary64_795`
8×	`pow1_binary64_821`
6×	`add-log-exp_binary64_799` `distribute-lft-out--_binary64_712` `cube-prod_binary64_788` `unpow-prod-down_binary64_839` `log-prod_binary64_846`
5×	`add-exp-log_binary64_798`
4×	`add-cbrt-cube_binary64_796` `log-pow_binary64_849`
3×	`cancel-sign-sub-inv_binary64_726` `difference-of-squares_binary64_729` `associate--l+_binary64_697`
1×	`cube-mult_binary64_790` `diff-log_binary64_852` `unpow3_binary64_826` `rem-exp-log_binary64_800` `rem-log-exp_binary64_801` `sqr-pow_binary64_732` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 68

Calls

4 calls:

7.0ms	(exp.f64 (cbrt.f64 (pow.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x) 3)))
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 (2.4%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
84.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
23.0ms	(exp.f64 (cbrt.f64 (pow.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x) 3)))
7.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify112.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4903	1278
1	4903	1278

prune73.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	80	4	84

Merged error: 58.8b

Counts

84 → 4

Compiler

Compiled 1573 to 525 computations (66.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.0b	(log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
3.2b	(log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
3.3b	(-.f64 (log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) x)
5.7b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

6.0ms	(-.f64 (log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) x)
2.0ms	(log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
2.0ms	(log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series587.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

251.0ms	(-.f64 (log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) x)
213.0ms	(log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
117.0ms	(log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
6.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4908	1196
1	4908	1196

prune65.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	74	4	78

Merged error: 58.8b

Counts

78 → 4

Compiler

Compiled 1411 to 505 computations (64.2% saved)

regimes43.0ms (0.5%)

Compiler: Compiled 382 to 236 computations (38.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	17
1	19	17

end0.0ms (0%)

sample6.3s (69%)

Algorithm

1×

intervals

Results

2.6s	1536×	body	8192	exit
1.7s	4006×	body	1024	valid
460.0ms	2013×	body	512	valid
425.0ms	1558×	body	1024	nan
143.0ms	760×	body	512	nan
141.0ms	979×	body	256	valid
90.0ms	168×	body	2048	valid
66.0ms	834×	body	128	valid
57.0ms	414×	body	256	nan
29.0ms	407×	body	128	nan

Compiler

Compiled 201 to 127 computations (36.8% saved)

Details

analyze646.0ms (7.1%)

sample171.0ms (1.9%)

simplify204.0ms (2.2%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite9.0ms (0.1%)

series56.0ms (0.6%)

simplify81.0ms (0.9%)

prune42.0ms (0.5%)

localize9.0ms (0.1%)

rewrite16.0ms (0.2%)

series202.0ms (2.2%)

simplify90.0ms (1%)

prune52.0ms (0.6%)

localize11.0ms (0.1%)

rewrite19.0ms (0.2%)

series214.0ms (2.4%)

simplify112.0ms (1.2%)

prune73.0ms (0.8%)

localize14.0ms (0.2%)

rewrite16.0ms (0.2%)

series587.0ms (6.5%)

simplify77.0ms (0.8%)

prune65.0ms (0.7%)

regimes43.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.3s (69%)

Profiling