Details

analyze687.0ms (5.9%)

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)

sample229.0ms (2%)

Algorithm

1×

intervals

Results

110.0ms	39×	body	8192	exit
55.0ms	126×	body	1024	valid
17.0ms	68×	body	512	valid
14.0ms	45×	body	1024	nan
6.0ms	30×	body	512	nan
5.0ms	32×	body	256	valid
4.0ms	6×	body	2048	valid
2.0ms	24×	body	128	valid
2.0ms	13×	body	256	nan
1.0ms	10×	body	128	nan

Compiler

Compiled 21 to 18 computations (14.3% saved)

simplify244.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4667	15
1	4667	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: 60.1b

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))
0.7b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
3.7b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_772`
12×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
9×	`times-frac_binary64_757`
5×	`add-cbrt-cube_binary64_784`
4×	`pow1_binary64_809` `add-exp-log_binary64_786`
3×	`associate-/r_binary64_697` `add-log-exp_binary64_787` `sqrt-prod_binary64_766` `associate-/l_binary64_698`
1×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `sqrt-pow1_binary64_768` `div-exp_binary64_799`

Counts

3 → 47

Calls

3 calls:

5.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
2.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series102.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

65.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
25.0ms	(sqrt.f64 (cos.f64 x))
12.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify90.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4794	953
1	4794	953

prune43.0ms (0.4%)

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: 60.1b

Counts

57 → 4

Compiler

Compiled 872 to 195 computations (77.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
2.0b	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
3.0b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
3.7b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_751`
12×	`add-sqr-sqrt_binary64_772`
9×	`log-prod_binary64_834`
8×	`add-cube-cbrt_binary64_783`
7×	`pow1_binary64_809` `add-log-exp_binary64_787`
6×	`exp-prod_binary64_800` `associate--l+_binary64_690`
5×	`add-exp-log_binary64_786`
4×	`distribute-lft-out--_binary64_705` `add-cbrt-cube_binary64_784` `exp-sum_binary64_794`
3×	`log-pow_binary64_837`
2×	`diff-log_binary64_840` `rem-exp-log_binary64_788` `sub-neg_binary64_744` `difference-of-squares_binary64_720`
1×	`rem-log-exp_binary64_789` `flip--_binary64_726` `exp-diff_binary64_796` `flip3--_binary64_755`

Counts

4 → 56

Calls

4 calls:

6.0ms	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
5.0ms	(-.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)))

series359.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
133.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
37.0ms	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
11.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify109.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4820	1152
1	4820	1152

prune50.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 60.1b

Counts

72 → 4

Compiler

Compiled 1080 to 226 computations (79.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
2.0b	(-.f64 (log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) x)
2.2b	(log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
3.7b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`log-prod_binary64_834`
14×	`log-pow_binary64_837`
13×	`*-un-lft-identity_binary64_751`
12×	`add-sqr-sqrt_binary64_772`
10×	`add-cube-cbrt_binary64_783`
9×	`exp-prod_binary64_800` `pow1_binary64_809`
7×	`associate--l+_binary64_690`
5×	`add-log-exp_binary64_787` `add-exp-log_binary64_786`
4×	`add-cbrt-cube_binary64_784`
2×	`distribute-lft-out--_binary64_705` `rem-log-exp_binary64_789`
1×	`flip--_binary64_726` `diff-log_binary64_840` `sub-neg_binary64_744` `flip3--_binary64_755` `difference-of-squares_binary64_720`

Counts

4 → 59

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

series1.0s (8.8%)

Counts

4 → 12

Calls

4 calls:

434.0ms	(-.f64 (log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) x)
369.0ms	(log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
205.0ms	(log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
9.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4880	1181
1	4880	1181

prune57.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	70	5	75

Merged error: 60.1b

Counts

75 → 5

Compiler

Compiled 1210 to 303 computations (75% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (cos.f64 x)))
0.1b	(*.f64 (sqrt.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (sqrt.f64 (cos.f64 x))))
0.7b	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
3.7b	(fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (sqrt.f64 (cos.f64 x)))))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_766`
58×	`add-sqr-sqrt_binary64_772`
36×	`sqrt-pow1_binary64_768`
29×	`pow1_binary64_809`
26×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
18×	`pow1/2_binary64_828`
15×	`swap-sqr_binary64_718`
9×	`unswap-sqr_binary64_719` `pow-prod-up_binary64_818` `times-frac_binary64_757` `associate-l_binary64_694` `associate-r_binary64_693`
8×	`add-cbrt-cube_binary64_784`
7×	`add-exp-log_binary64_786`
5×	`pow-sqr_binary64_724` `pow-prod-down_binary64_819`
4×	`add-log-exp_binary64_787`
3×	`associate-/r_binary64_697` `associate-/l_binary64_698`
2×	`rem-sqrt-square_binary64_764`
1×	`prod-exp_binary64_797` `rem-square-sqrt_binary64_763` `pow-plus_binary64_811` `*-commutative_binary64_684` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `cbrt-unprod_binary64_781` `pow2_binary64_829` `clear-num_binary64_750` `sqrt-unprod_binary64_770` `div-exp_binary64_799`

Counts

4 → 128

Calls

4 calls:

12.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (sqrt.f64 (cos.f64 x))))
4.0ms	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
2.0ms	(sqrt.f64 (sqrt.f64 (cos.f64 x)))
1.0ms	(fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (sqrt.f64 (cos.f64 x)))))

series234.0ms (2%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(sqrt.f64 (sqrt.f64 (cos.f64 x)))
67.0ms	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
29.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (sqrt.f64 (cos.f64 x))))
14.0ms	(fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (sqrt.f64 (cos.f64 x)))))

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5033	1652

prune98.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	140	5	145

Merged error: 60.1b

Counts

145 → 5

Compiler

Compiled 2178 to 438 computations (79.9% saved)

regimes14.0ms (0.1%)

Compiler: Compiled 85 to 54 computations (36.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	21
1	21	21

end0.0ms (0%)

sample8.0s (68.7%)

Algorithm

1×

intervals

Results

4.2s	1550×	body	8192	exit
1.7s	4001×	body	1024	valid
528.0ms	1631×	body	1024	nan
507.0ms	1933×	body	512	valid
176.0ms	1036×	body	256	valid
168.0ms	785×	body	512	nan
89.0ms	149×	body	2048	valid
86.0ms	881×	body	128	valid
60.0ms	406×	body	256	nan
36.0ms	441×	body	128	nan

Compiler

Compiled 106 to 72 computations (32.1% saved)

Details

analyze687.0ms (5.9%)

sample229.0ms (2%)

simplify244.0ms (2.1%)

prune7.0ms (0.1%)

localize7.0ms (0.1%)

rewrite10.0ms (0.1%)

series102.0ms (0.9%)

simplify90.0ms (0.8%)

prune43.0ms (0.4%)

localize9.0ms (0.1%)

rewrite16.0ms (0.1%)

series359.0ms (3.1%)

simplify109.0ms (0.9%)

prune50.0ms (0.4%)

localize11.0ms (0.1%)

rewrite16.0ms (0.1%)

series1.0s (8.8%)

simplify83.0ms (0.7%)

prune57.0ms (0.5%)

localize9.0ms (0.1%)

rewrite32.0ms (0.3%)

series234.0ms (2%)

simplify87.0ms (0.8%)

prune98.0ms (0.8%)

regimes14.0ms (0.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample8.0s (68.7%)

Profiling