Details

analyze1.6s (16.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5006	504
0	4	4
1	4	4

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)

sample119.0ms (1.2%)

Algorithm

1×

intervals

Results

46.0ms	78×	body	1024	invalid
28.0ms	242×	body	128	valid
10.0ms	27×	body	512	invalid
4.0ms	4×	body	2048	invalid
3.0ms	15×	body	256	invalid
2.0ms	4×	body	1024	valid
2.0ms	16×	body	128	invalid
2.0ms	5×	body	512	valid
1.0ms	4×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune9.0ms (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

33.8b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.5b	(*.f64 (atan2.f64 x.im x.re) y.re)
30.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.6b	(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)

series301.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(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)))
27.0ms	(*.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)))

simplify105.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4874	1270
1	4874	1270

prune126.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	9	70

Error

17.9b

Counts

70 → 9

Compiler

Compiled 3229 to 976 computations (69.8% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

30.4b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
30.4b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
30.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.6b	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (sqrt.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)))

rewrite58.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
13×	`sqrt-prod_binary64`
10×	`add-sqr-sqrt_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
3×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`sin-sum_binary64`

Counts

4 → 57

Calls

4 calls:

29.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (sqrt.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)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series271.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (sqrt.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)))
23.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
22.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
22.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4899	1357
1	4899	1357

prune158.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	68	10	78

Error

17.9b

Counts

78 → 10

Compiler

Compiled 3922 to 1960 computations (50% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

7.1b	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
30.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.7b	(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 (.f64 (atan2.f64 x.im x.re) y.re)) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re))) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re)))))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

9.0ms	(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 (.f64 (atan2.f64 x.im x.re) y.re)) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re))) (cbrt.f64 (.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)))
2.0ms	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

series380.0ms (4%)

Counts

4 → 12

Calls

4 calls:

247.0ms	(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 (.f64 (atan2.f64 x.im x.re) y.re)) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re))) (cbrt.f64 (.f64 (atan2.f64 x.im x.re) y.re)))))
88.0ms	(cbrt.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
24.0ms	(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)))

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4871	1173
1	4871	1173

prune111.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	59	10	69

Error

17.9b

Counts

69 → 10

Compiler

Compiled 3546 to 921 computations (74% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

30.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.6b	(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)))
33.6b	(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)))
33.6b	(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)))

rewrite34.0ms (0.4%)

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)))
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)))
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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series592.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(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)))
190.0ms	(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)))
184.0ms	(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)))
23.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5056	1579

prune170.0ms (1.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	51	10	61

Error

17.9b

Counts

61 → 10

Compiler

Compiled 4276 to 2177 computations (49.1% saved)

regimes541.0ms (5.7%)

Accuracy

Total 3.8b remaining (16.4%)

Threshold costs 0b (0%)

Compiler

Compiled 4837 to 3130 computations (35.3% saved)

bsearch227.0ms (2.4%)

Steps

Iters	Range	Point
6	-2.115037658840557e-305	-4.6796706520886426e-306	-4.728921531563574e-306
8	-1.1814933291894451e-203	-5.03447289768838e-208	-3.7887581773494374e-206
7	-1.4969844394063253e+23	-1.3261457020650922e+21	-1.4842793389559469e+21

Iters

Range

Point

-2.115037658840557e-305

-4.6796706520886426e-306

-4.728921531563574e-306

-1.1814933291894451e-203

-5.03447289768838e-208

-3.7887581773494374e-206

-1.4969844394063253e+23

-1.3261457020650922e+21

-1.4842793389559469e+21

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	108	299
1	108	299

end0.0ms (0%)

sample4.3s (45.2%)

Algorithm

1×

intervals

Results

1.3s	2569×	body	1024	invalid
882.0ms	7584×	body	128	valid
343.0ms	952×	body	512	invalid
140.0ms	159×	body	2048	invalid
96.0ms	183×	body	1024	valid
82.0ms	349×	body	256	invalid
64.0ms	491×	body	128	invalid
45.0ms	128×	body	512	valid
22.0ms	92×	body	256	valid
10.0ms	13×	body	2048	valid

Compiler

Compiled 1143 to 699 computations (38.8% saved)

Details

analyze1.6s (16.5%)

sample119.0ms (1.2%)

simplify66.0ms (0.7%)

prune9.0ms (0.1%)

localize22.0ms (0.2%)

rewrite28.0ms (0.3%)

series301.0ms (3.1%)

simplify105.0ms (1.1%)

prune126.0ms (1.3%)

localize33.0ms (0.3%)

rewrite58.0ms (0.6%)

series271.0ms (2.8%)

simplify70.0ms (0.7%)

prune158.0ms (1.6%)

localize28.0ms (0.3%)

rewrite26.0ms (0.3%)

series380.0ms (4%)

simplify73.0ms (0.8%)

prune111.0ms (1.2%)

localize35.0ms (0.4%)

rewrite34.0ms (0.4%)

series592.0ms (6.2%)

simplify78.0ms (0.8%)

prune170.0ms (1.8%)

regimes541.0ms (5.7%)

bsearch227.0ms (2.4%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample4.3s (45.2%)

Profiling