Details

analyze1.5s (16.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample114.0ms (1.2%)

Algorithm

1×

intervals

Results

41.0ms	76×	body	1024	invalid
29.0ms	246×	body	128	valid
9.0ms	24×	body	512	invalid
6.0ms	7×	body	2048	invalid
3.0ms	6×	body	1024	valid
2.0ms	20×	body	128	invalid
2.0ms	9×	body	256	invalid
1.0ms	1×	body	2048	valid
0.0ms	2×	body	256	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify165.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune8.0ms (0.1%)

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

Error

33.3b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(*.f64 (atan2.f64 x.im x.re) y.re)
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

8.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

series295.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
29.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
25.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4874	1270
1	4874	1270

prune118.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Error

20.9b

Counts

70 → 8

Compiler

Compiled 3150 to 920 computations (70.8% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
31.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
31.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sin-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 39

Calls

4 calls:

7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
6.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
6.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series570.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
180.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
179.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
21.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5056	1579

prune176.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	51	8	59

Error

20.9b

Counts

59 → 8

Compiler

Compiled 4525 to 2335 computations (48.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(*.f64 y.re (atan2.f64 x.im x.re))
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

6.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

series252.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
25.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
21.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
14.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

simplify101.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4874	1270
1	4874	1270

prune105.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	67	9	76

Error

20.8b

Counts

76 → 9

Compiler

Compiled 3011 to 840 computations (72.1% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.3b	(*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.6b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)))))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`associate-r_binary64` `add-exp-log_binary64` `sqrt-prod_binary64`
5×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `cbrt-prod_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `sin-sum_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 60

Calls

4 calls:

8.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)))))
5.0ms	(*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series341.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

235.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)))))
54.0ms	(*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))
27.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
25.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4883	1389
1	4883	1389

prune96.0ms (1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	72	9	81

Error

20.8b

Counts

81 → 9

Compiler

Compiled 3374 to 742 computations (78% saved)

regimes497.0ms (5.4%)

Accuracy

Total 3.0b remaining (13.3%)

Threshold costs 0b (0%)

Compiler

Compiled 5602 to 3600 computations (35.7% saved)

bsearch106.0ms (1.1%)

Steps

Iters	Range		Point
10	-2.3585987502932996e-298	1.2644505533430413e-307	-5.29893804714451e-309

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	130
1	86	130

end0.0ms (0%)

sample4.3s (46.7%)

Algorithm

1×

intervals

Results

1.3s	2560×	body	1024	invalid
858.0ms	7584×	body	128	valid
321.0ms	917×	body	512	invalid
161.0ms	186×	body	2048	invalid
93.0ms	171×	body	1024	valid
84.0ms	344×	body	256	invalid
62.0ms	521×	body	128	invalid
51.0ms	142×	body	512	valid
20.0ms	86×	body	256	valid
14.0ms	17×	body	2048	valid

Compiler

Compiled 1208 to 760 computations (37.1% saved)

Details

analyze1.5s (16.2%)

sample114.0ms (1.2%)

simplify165.0ms (1.8%)

prune8.0ms (0.1%)

localize23.0ms (0.2%)

rewrite28.0ms (0.3%)

series295.0ms (3.2%)

simplify103.0ms (1.1%)

prune118.0ms (1.3%)

localize36.0ms (0.4%)

rewrite31.0ms (0.3%)

series570.0ms (6.2%)

simplify76.0ms (0.8%)

prune176.0ms (1.9%)

localize20.0ms (0.2%)

rewrite24.0ms (0.3%)

series252.0ms (2.7%)

simplify101.0ms (1.1%)

prune105.0ms (1.1%)

localize25.0ms (0.3%)

rewrite28.0ms (0.3%)

series341.0ms (3.7%)

simplify71.0ms (0.8%)

prune96.0ms (1%)

regimes497.0ms (5.4%)

bsearch106.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.3s (46.7%)

Profiling