Details

analyze1.6s (13.7%)

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%)

Algorithm

1×

intervals

Results

40.0ms	77×	body	1024	invalid
28.0ms	244×	body	128	valid
16.0ms	31×	body	512	invalid
3.0ms	6×	body	1024	valid
3.0ms	3×	body	2048	invalid
2.0ms	8×	body	256	invalid
2.0ms	15×	body	128	invalid
1.0ms	4×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify65.0ms (0.6%)

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

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

32.0b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.2b	(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)))

rewrite102.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

31.9b

Rules

12×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `associate-r_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`
1×	`sin-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_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)))
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series743.0ms (6.3%)

Error

18.6b

Counts

4 → 61

Calls

4 calls:

311.0ms	(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)))
145.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
141.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
70.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 6435 to 3289 computations (48.9% saved)

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4949	2415
1	4949	2415

prune177.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	110	7	117
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	8	118

Error

18.6b

Counts

118 → 8

Compiler

Compiled 5039 to 1393 computations (72.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(*.f64 y.re (atan2.f64 x.im x.re))
1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
19.9b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
28.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite79.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

18.6b

Rules

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

Counts

4 → 58

Calls

4 calls:

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.im)
3.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
1.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1851 to 341 computations (81.6% saved)

series463.0ms (3.9%)

Error

8.3b

Counts

4 → 47

Calls

4 calls:

143.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
134.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
72.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
68.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3474 to 1820 computations (47.6% saved)

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5051	1533

prune122.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	100	5	105
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	102	11	113

Error

8.3b

Counts

113 → 11

Compiler

Compiled 3324 to 866 computations (73.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

19.9b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
19.9b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
19.9b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
28.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite59.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

8.3b

Rules

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

Counts

4 → 36

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
2.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
2.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
2.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1803 to 225 computations (87.5% saved)

series627.0ms (5.3%)

Error

8.3b

Counts

4 → 51

Calls

4 calls:

145.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
145.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
140.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
138.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 6171 to 2327 computations (62.3% saved)

simplify48.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5036	1503

prune128.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	85	13	98

Error

8.3b

Counts

98 → 13

Compiler

Compiled 4408 to 903 computations (79.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
19.9b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
21.9b	(cbrt.f64 (pow.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) 3))
28.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite90.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

8.3b

Rules

13×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-prod_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `associate-l_binary64` `associate-r_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `pow1/3_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `rem-cbrt-cube_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 61

Calls

4 calls:

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.im)
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) 3))
2.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 2218 to 548 computations (75.3% saved)

series539.0ms (4.6%)

Error

8.3b

Counts

4 → 49

Calls

4 calls:

143.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
136.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
134.0ms	(cbrt.f64 (pow.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) 3))
74.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3975 to 2243 computations (43.6% saved)

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4975	1823
1	4975	1823

prune117.0ms (1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	110	13	123

Error

8.3b

Counts

123 → 13

Compiler

Compiled 3441 to 935 computations (72.8% saved)

regimes934.0ms (8%)

Accuracy

Total 9.1b remaining (44.9%)

Threshold costs 0b (0%)

Compiler

Compiled 8577 to 5140 computations (40.1% saved)

bsearch539.0ms (4.6%)

Steps

Iters	Range		Point
9	3.9114342229993193e+34	4.086884602139325e+40	1.940140996050804e+35
11	2.6004801754656126e-27	5.6835582021404e-07	2.8096680029547107e-08
8	5.854082601081246e-207	1.3353555378181721e-202	9.796633468730483e-206
6	1.8763441476998993e-234	2.769153309692791e-233	8.893872608083424e-234
9	3.7878786117665445e-280	2.3184505065112856e-273	5.999233792908306e-275
9	-1.9389857324274015e-298	-1.0908876198779331e-303	-2.2880081199411094e-302
5	-2.6265830174837794e+155	-9.298603617485253e+154	-9.423511434206789e+154

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	145	491
1	145	491

end0.0ms (0%)

sample4.8s (41.3%)

Algorithm

1×

intervals

Results

1.3s	2455×	body	1024	invalid
882.0ms	7554×	body	128	valid
339.0ms	925×	body	512	invalid
155.0ms	175×	body	2048	invalid
104.0ms	188×	body	1024	valid
72.0ms	310×	body	256	invalid
72.0ms	549×	body	128	invalid
59.0ms	156×	body	512	valid
22.0ms	91×	body	256	valid
9.0ms	11×	body	2048	valid

Compiler

Compiled 1987 to 1109 computations (44.2% saved)

Details

analyze1.6s (13.7%)

sample119.0ms (1%)

simplify65.0ms (0.6%)

prune8.0ms (0.1%)

localize27.0ms (0.2%)

rewrite102.0ms (0.9%)

series743.0ms (6.3%)

simplify91.0ms (0.8%)

prune177.0ms (1.5%)

localize18.0ms (0.2%)

rewrite79.0ms (0.7%)

series463.0ms (3.9%)

simplify64.0ms (0.5%)

prune122.0ms (1%)

localize23.0ms (0.2%)

rewrite59.0ms (0.5%)

series627.0ms (5.3%)

simplify48.0ms (0.4%)

prune128.0ms (1.1%)

localize20.0ms (0.2%)

rewrite90.0ms (0.8%)

series539.0ms (4.6%)

simplify75.0ms (0.6%)

prune117.0ms (1%)

regimes934.0ms (8%)

bsearch539.0ms (4.6%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample4.8s (41.3%)

Profiling