Details

analyze367.0ms (6.6%)

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
0%	99.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	37.5%	12.6%	7
50%	37.5%	12.6%	8
50%	31.2%	18.8%	9
50%	31.2%	18.8%	10
50%	28.1%	22%	11
50%	28.1%	22%	12
50%	26.5%	23.5%	13
50%	26.5%	23.5%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample88.0ms (1.6%)

Algorithm

1×

intervals

Results

32.0ms	76×	body	1024	valid
21.0ms	67×	body	1024	invalid
8.0ms	134×	body	128	valid
7.0ms	33×	body	512	valid
4.0ms	20×	body	512	invalid
2.0ms	29×	body	128	invalid
2.0ms	13×	body	256	valid
1.0ms	10×	body	256	invalid

Compiler

Compiled 23 to 23 computations (0% saved)

simplify264.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4881	18
1	4881	18

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: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64_809` `add-cbrt-cube_binary64_784` `*-un-lft-identity_binary64_751` `add-exp-log_binary64_786`
4×	`add-log-exp_binary64_787` `associate-r_binary64_693`
3×	`prod-exp_binary64_797` `add-cube-cbrt_binary64_783` `pow-prod-down_binary64_819` `cbrt-unprod_binary64_781` `add-sqr-sqrt_binary64_772`
2×	`distribute-lft-out_binary64_704` `flip3-+_binary64_754` `associate-*r/_binary64_695` `flip-+_binary64_725`
1×	`+-commutative_binary64_683` `distribute-lft-in_binary64_702` `-commutative_binary64_684` `sum-log_binary64_839` `associate-l*_binary64_694` `distribute-rgt-in_binary64_703`

Counts

2 → 35

Calls

2 calls:

11.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
6.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series156.0ms (2.8%)

Counts

2 → 6

Calls

2 calls:

124.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
32.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4994	713
1	4994	713

prune37.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Merged error: 0b

Counts

42 → 3

Compiler

Compiled 705 to 284 computations (59.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im)))
0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im))
0.0b	(/.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_784`
9×	`add-exp-log_binary64_786`
8×	`pow1_binary64_809`
6×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
5×	`add-log-exp_binary64_787`
4×	`prod-exp_binary64_797` `cbrt-unprod_binary64_781`
3×	`associate-/r_binary64_697` `pow-prod-down_binary64_819` `times-frac_binary64_757` `associate-r*_binary64_693`
2×	`div-inv_binary64_748` `cbrt-undiv_binary64_782` `div-exp_binary64_799`
1×	`distribute-lft-out_binary64_704` `+-commutative_binary64_683` `flip3-+_binary64_754` `-commutative_binary64_684` `sum-log_binary64_839` `frac-2neg_binary64_762` `associate-l_binary64_694` `clear-num_binary64_750` `associate-/l_binary64_698` `flip-+_binary64_725`

Counts

3 → 51

Calls

3 calls:

9.0ms	(+.f64 (/.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im)))
9.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im))
6.0ms	(/.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im))

series306.0ms (5.5%)

Counts

3 → 9

Calls

3 calls:

153.0ms	(+.f64 (/.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im)))
86.0ms	(/.f64 (*.f64 1/2 (cos.f64 re)) (exp.f64 im))
66.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (exp.f64 im))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5028	959

prune56.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	60	3	63

Merged error: 0b

Counts

63 → 3

Compiler

Compiled 1157 to 591 computations (48.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 (exp.f64 im)) (*.f64 1/2 (exp.f64 im)))
0.0b	(.f64 (cos.f64 re) (+.f64 (/.f64 1/2 (exp.f64 im)) (.f64 1/2 (exp.f64 im))))
0.0b	(/.f64 1/2 (exp.f64 im))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_772`
13×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
9×	`times-frac_binary64_757`
7×	`add-cbrt-cube_binary64_784`
6×	`add-exp-log_binary64_786`
5×	`pow1_binary64_809` `add-log-exp_binary64_787`
4×	`associate-r_binary64_693`
3×	`associate-/r_binary64_697` `div-inv_binary64_748` `associate-l_binary64_694` `associate-/l_binary64_698`
2×	`distribute-lft-out_binary64_704` `flip3-+_binary64_754` `associate-*r/_binary64_695` `flip-+_binary64_725`
1×	`prod-exp_binary64_797` `+-commutative_binary64_683` `unswap-sqr_binary64_719` `distribute-lft-in_binary64_702` `pow-prod-down_binary64_819` `*-commutative_binary64_684` `cbrt-undiv_binary64_782` `sum-log_binary64_839` `frac-2neg_binary64_762` `cbrt-unprod_binary64_781` `clear-num_binary64_750` `distribute-rgt-in_binary64_703` `div-exp_binary64_799`

Counts

3 → 62

Calls

3 calls:

12.0ms	(.f64 (cos.f64 re) (+.f64 (/.f64 1/2 (exp.f64 im)) (.f64 1/2 (exp.f64 im))))
8.0ms	(+.f64 (/.f64 1/2 (exp.f64 im)) (*.f64 1/2 (exp.f64 im)))
5.0ms	(/.f64 1/2 (exp.f64 im))

series240.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

125.0ms	(.f64 (cos.f64 re) (+.f64 (/.f64 1/2 (exp.f64 im)) (.f64 1/2 (exp.f64 im))))
75.0ms	(+.f64 (/.f64 1/2 (exp.f64 im)) (*.f64 1/2 (exp.f64 im)))
40.0ms	(/.f64 1/2 (exp.f64 im))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4885	1136
1	4885	1136

prune64.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	71	3	74

Merged error: 0b

Counts

74 → 3

Compiler

Compiled 1248 to 604 computations (51.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 im) 2)
0.3b	(/.f64 (.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
5.0b	(-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))
5.0b	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_772`
17×	`*-un-lft-identity_binary64_751`
15×	`difference-of-squares_binary64_720`
13×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
10×	`unpow-prod-down_binary64_827`
9×	`add-cube-cbrt_binary64_783`
8×	`sqr-pow_binary64_723` `add-log-exp_binary64_787`
5×	`associate-/r*_binary64_697` `pow1_binary64_809` `times-frac_binary64_757`
4×	`distribute-lft-out--_binary64_705` `unpow2_binary64_813` `flip--_binary64_726` `pow-pow_binary64_820` `flip3--_binary64_755`
3×	`prod-exp_binary64_797` `exp-prod_binary64_800` `cbrt-undiv_binary64_782` `cbrt-unprod_binary64_781` `pow-unpow_binary64_825` `div-exp_binary64_799`
2×	`associate-/l/_binary64_700` `associate-/r/_binary64_699` `associate-*r/_binary64_695` `diff-log_binary64_840` `sub-neg_binary64_744`
1×	`pow-to-exp_binary64_817` `pow-exp_binary64_816` `div-inv_binary64_748` `frac-2neg_binary64_762` `clear-num_binary64_750` `associate-/l*_binary64_698`

Counts

4 → 89

Calls

4 calls:

21.0ms	(/.f64 (.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
10.0ms	(-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))
7.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
4.0ms	(pow.f64 (exp.f64 im) 2)

series609.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

434.0ms	(/.f64 (.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
108.0ms	(-.f64 (pow.f64 (exp.f64 im) -2) (pow.f64 (exp.f64 im) 2))
46.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
20.0ms	(pow.f64 (exp.f64 im) 2)

simplify50.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4939	1945
1	4939	1945

prune110.0ms (2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	101	3	104

Merged error: 0b

Counts

104 → 3

Compiler

Compiled 2502 to 1077 computations (57% saved)

regimes114.0ms (2%)

Compiler: Compiled 862 to 649 computations (24.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	24
1	13	24

end0.0ms (0%)

sample2.7s (48.7%)

Algorithm

1×

intervals

Results

882.0ms	2037×	body	1024	valid
543.0ms	1950×	body	1024	invalid
274.0ms	4448×	body	128	valid
208.0ms	977×	body	512	valid
181.0ms	989×	body	512	invalid
69.0ms	534×	body	256	valid
67.0ms	526×	body	256	invalid
48.0ms	702×	body	128	invalid
3.0ms	4×	body	2048	valid

Compiler

Compiled 138 to 105 computations (23.9% saved)

Details

analyze367.0ms (6.6%)

sample88.0ms (1.6%)

simplify264.0ms (4.7%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite20.0ms (0.4%)

series156.0ms (2.8%)

simplify71.0ms (1.3%)

prune37.0ms (0.7%)

localize9.0ms (0.2%)

rewrite30.0ms (0.5%)

series306.0ms (5.5%)

simplify70.0ms (1.2%)

prune56.0ms (1%)

localize9.0ms (0.2%)

rewrite31.0ms (0.6%)

series240.0ms (4.3%)

simplify80.0ms (1.4%)

prune64.0ms (1.1%)

localize15.0ms (0.3%)

rewrite52.0ms (0.9%)

series609.0ms (10.9%)

simplify50.0ms (0.9%)

prune110.0ms (2%)

regimes114.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (48.7%)

Profiling