Details

analyze368.0ms (7.3%)

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
25%	74.9%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
62.4%	31.2%	6.3%	7
62.4%	31.2%	6.3%	8
62.4%	28.1%	9.5%	9
62.4%	28.1%	9.5%	10
62.4%	26.5%	11%	11
62.4%	26.5%	11%	12
62.4%	25.8%	11.8%	13
62.4%	25.8%	11.8%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample109.0ms (2.2%)

Algorithm

1×

intervals

Results

29.0ms	53×	body	1280	valid
17.0ms	48×	body	1280	invalid
12.0ms	48×	body	640	invalid
11.0ms	132×	body	80	valid
10.0ms	35×	body	640	valid
5.0ms	82×	body	80	invalid
4.0ms	20×	body	320	valid
4.0ms	21×	body	320	invalid
2.0ms	16×	body	160	valid
2.0ms	13×	body	160	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify146.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	5417	18

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: 0.3b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.2b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `flip-+_binary64`
1×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 35

Calls

2 calls:

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

series19.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

16.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
3.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

simplify96.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5334	719

prune40.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0.2b

Counts

42 → 4

Compiler

Compiled 731 to 304 computations (58.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 im))
0.0b	(+.f64 (/.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (sin.f64 re)) (exp.f64 im)))
0.3b	(/.f64 (*.f64 1/2 (sin.f64 re)) (exp.f64 im))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `associate-r*_binary64` `times-frac_binary64`
2×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 51

Calls

3 calls:

9.0ms	(+.f64 (/.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (sin.f64 re)) (exp.f64 im)))
7.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 im))
6.0ms	(/.f64 (*.f64 1/2 (sin.f64 re)) (exp.f64 im))

series42.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

22.0ms	(+.f64 (/.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 im)) (.f64 (*.f64 1/2 (sin.f64 re)) (exp.f64 im)))
10.0ms	(/.f64 (*.f64 1/2 (sin.f64 re)) (exp.f64 im))
9.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 im))

simplify89.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4945	984
1	4945	984

prune45.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	60	4	64

Merged error: 0.0b

Counts

64 → 4

Compiler

Compiled 1188 to 609 computations (48.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 1/2 (sqrt.f64 (exp.f64 im))) (/.f64 (sin.f64 re) (sqrt.f64 (exp.f64 im)))) (.f64 (*.f64 1/2 (sin.f64 re)) (exp.f64 im)))
0.0b	(/.f64 (sin.f64 re) (sqrt.f64 (exp.f64 im)))
0.2b	(sqrt.f64 (exp.f64 im))
0.2b	(sqrt.f64 (exp.f64 im))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64` `sqrt-prod_binary64`
8×	`sqrt-pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-prod_binary64`
3×	`associate-/l*_binary64`
2×	`pow1/2_binary64` `rem-sqrt-square_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 82

Calls

4 calls:

14.0ms	(+.f64 (.f64 (/.f64 1/2 (sqrt.f64 (exp.f64 im))) (/.f64 (sin.f64 re) (sqrt.f64 (exp.f64 im)))) (.f64 (*.f64 1/2 (sin.f64 re)) (exp.f64 im)))
6.0ms	(/.f64 (sin.f64 re) (sqrt.f64 (exp.f64 im)))
2.0ms	(sqrt.f64 (exp.f64 im))
2.0ms	(sqrt.f64 (exp.f64 im))

series42.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(+.f64 (.f64 (/.f64 1/2 (sqrt.f64 (exp.f64 im))) (/.f64 (sin.f64 re) (sqrt.f64 (exp.f64 im)))) (.f64 (*.f64 1/2 (sin.f64 re)) (exp.f64 im)))
15.0ms	(/.f64 (sin.f64 re) (sqrt.f64 (exp.f64 im)))
3.0ms	(sqrt.f64 (exp.f64 im))
3.0ms	(sqrt.f64 (exp.f64 im))

simplify58.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5076	1421

prune63.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	94	4	98

Merged error: 0.0b

Counts

98 → 4

Compiler

Compiled 2363 to 940 computations (60.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1/2 (exp.f64 im))
0.0b	(+.f64 (/.f64 1/2 (exp.f64 im)) (*.f64 1/2 (exp.f64 im)))
0.2b	(.f64 (sin.f64 re) (+.f64 (/.f64 1/2 (exp.f64 im)) (.f64 1/2 (exp.f64 im))))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`associate-r_binary64`
3×	`associate-/r_binary64` `associate-l_binary64` `associate-/l_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 62

Calls

3 calls:

11.0ms	(.f64 (sin.f64 re) (+.f64 (/.f64 1/2 (exp.f64 im)) (.f64 1/2 (exp.f64 im))))
7.0ms	(+.f64 (/.f64 1/2 (exp.f64 im)) (*.f64 1/2 (exp.f64 im)))
4.0ms	(/.f64 1/2 (exp.f64 im))

series30.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

17.0ms	(.f64 (sin.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)))
4.0ms	(/.f64 1/2 (exp.f64 im))

simplify131.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4827	1142
1	4827	1142

prune41.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	71	4	75

Merged error: 0.0b

Counts

75 → 4

Compiler

Compiled 1231 to 602 computations (51.1% saved)

regimes118.0ms (2.3%)

Compiler: Compiled 268 to 212 computations (20.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	24
1	13	24

end0.0ms (0%)

sample3.5s (68.6%)

Algorithm

1×

intervals

Results

856.0ms	1540×	body	1280	valid
539.0ms	1486×	body	1280	invalid
376.0ms	1234×	body	640	valid
320.0ms	1276×	body	640	invalid
276.0ms	4292×	body	80	valid
159.0ms	2413×	body	80	invalid
121.0ms	610×	body	320	valid
113.0ms	621×	body	320	invalid
41.0ms	324×	body	160	valid
40.0ms	325×	body	160	invalid

Compiler

Compiled 91 to 72 computations (20.9% saved)

Details

analyze368.0ms (7.3%)

sample109.0ms (2.2%)

simplify146.0ms (2.9%)

prune7.0ms (0.1%)

localize15.0ms (0.3%)

rewrite17.0ms (0.3%)

series19.0ms (0.4%)

simplify96.0ms (1.9%)

prune40.0ms (0.8%)

localize10.0ms (0.2%)

rewrite24.0ms (0.5%)

series42.0ms (0.8%)

simplify89.0ms (1.8%)

prune45.0ms (0.9%)

localize13.0ms (0.3%)

rewrite27.0ms (0.5%)

series42.0ms (0.8%)

simplify58.0ms (1.2%)

prune63.0ms (1.2%)

localize10.0ms (0.2%)

rewrite25.0ms (0.5%)

series30.0ms (0.6%)

simplify131.0ms (2.6%)

prune41.0ms (0.8%)

regimes118.0ms (2.3%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.5s (68.6%)

Profiling