Details

analyze1.6s (13%)

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)

sample134.0ms (1.1%)

Algorithm

1×

intervals

Results

49.0ms	93×	body	1024	invalid
28.0ms	245×	body	128	valid
14.0ms	38×	body	512	invalid
3.0ms	6×	body	1024	valid
3.0ms	11×	body	256	invalid
2.0ms	16×	body	128	invalid
2.0ms	2×	body	2048	invalid
1.0ms	3×	body	512	valid
1.0ms	2×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify65.0ms (0.5%)

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

33.6b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.8b	(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)))
31.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite106.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

33.6b

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:

6.0ms	(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)))
6.0ms	(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.im)

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series833.0ms (6.6%)

Error

20.8b

Counts

4 → 63

Calls

4 calls:

381.0ms	(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)))
158.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
146.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
69.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 6763 to 3449 computations (49% saved)

simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5187	2549

prune176.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	112	7	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	7	120

Error

20.7b

Counts

120 → 7

Compiler

Compiled 5193 to 1436 computations (72.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 y.re (atan2.f64 x.im x.re))
1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
17.6b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
31.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite86.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

20.7b

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:

5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
2.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1851 to 341 computations (81.6% saved)

series439.0ms (3.5%)

Error

10.8b

Counts

4 → 45

Calls

4 calls:

134.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
117.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
73.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
72.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

Compiler

Compiled 3282 to 1722 computations (47.5% saved)

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5145	1456

prune123.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	100	10	110

Error

10.8b

Counts

110 → 10

Compiler

Compiled 3253 to 843 computations (74.1% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y.re)
1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
17.6b	(sin.f64 (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))))
31.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite76.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

10.8b

Rules

11×	`add-sqr-sqrt_binary64`
8×	`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` `associate-l_binary64` `associate-r_binary64` `cbrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64` `pow1/3_binary64`

Counts

4 → 51

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

Compiler

Compiled 2010 to 333 computations (83.4% saved)

series473.0ms (3.8%)

Error

10.8b

Counts

4 → 39

Calls

4 calls:

145.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
131.0ms	(sin.f64 (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))))
79.0ms	(cbrt.f64 y.re)
76.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3423 to 1736 computations (49.3% saved)

simplify67.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5083	1231

prune118.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	89	11	100

Error

10.8b

Counts

100 → 11

Compiler

Compiled 3439 to 867 computations (74.8% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.2b	(cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
7.2b	(cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
17.7b	(sin.f64 (.f64 (.f64 (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re))) (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))
31.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite70.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

10.8b

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` `pow1/3_binary64` `cbrt-prod_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 40

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
3.0ms	(sin.f64 (.f64 (.f64 (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re))) (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))
2.0ms	(cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
2.0ms	(cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1970 to 248 computations (87.4% saved)

series967.0ms (7.7%)

Error

10.8b

Counts

4 → 45

Calls

4 calls:

326.0ms	(cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
313.0ms	(cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
141.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
132.0ms	(sin.f64 (.f64 (.f64 (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re))) (cbrt.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))

Compiler

Compiled 4893 to 2204 computations (55% saved)

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4935	1286
1	4935	1286

prune97.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	85	11	96

Error

10.8b

Counts

96 → 11

Compiler

Compiled 3434 to 561 computations (83.7% saved)

regimes1.2s (9.4%)

Accuracy

Total 8.9b remaining (45.3%)

Threshold costs 0b (0%)

Compiler

Compiled 9242 to 5350 computations (42.1% saved)

bsearch705.0ms (5.6%)

Steps

Iters	Range		Point
8	1.1182618949267123e+145	1.1929559298970641e+148	5.905307583074926e+146
5	2.6376617726070884e-58	5.424033909004746e-58	3.287617321062957e-58
8	3.985627347714119e-169	1.8175795982312556e-166	8.616224543200037e-169
7	3.834187091881292e-207	1.0594976835327752e-205	9.081701895702835e-207
8	1.1788081924383744e-213	5.781029999030482e-210	8.860112327650189e-212
11	1.5155716933371553e-254	5.356592157488738e-232	2.3749711864456892e-232
7	-1.5408341641200606e-226	-7.722454440360218e-228	-5.812317682129375e-227
9	-3.204395359645437e-194	-1.682052795700937e-199	-3.302271378437987e-195
9	-7.318643800929273e+160	-4.038947428262442e+154	-4.0934041149708724e+154

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	208	623
1	208	623

end0.0ms (0%)

sample4.9s (38.9%)

Algorithm

1×

intervals

Results

1.3s	2442×	body	1024	invalid
876.0ms	7599×	body	128	valid
335.0ms	943×	body	512	invalid
149.0ms	166×	body	2048	invalid
94.0ms	182×	body	1024	valid
87.0ms	350×	body	256	invalid
62.0ms	525×	body	128	invalid
47.0ms	134×	body	512	valid
17.0ms	72×	body	256	valid
11.0ms	13×	body	2048	valid

Compiler

Compiled 2188 to 1184 computations (45.9% saved)

Details

analyze1.6s (13%)

sample134.0ms (1.1%)

simplify65.0ms (0.5%)

prune8.0ms (0.1%)

localize23.0ms (0.2%)

rewrite106.0ms (0.8%)

series833.0ms (6.6%)

simplify79.0ms (0.6%)

prune176.0ms (1.4%)

localize18.0ms (0.1%)

rewrite86.0ms (0.7%)

series439.0ms (3.5%)

simplify66.0ms (0.5%)

prune123.0ms (1%)

localize26.0ms (0.2%)

rewrite76.0ms (0.6%)

series473.0ms (3.8%)

simplify67.0ms (0.5%)

prune118.0ms (0.9%)

localize24.0ms (0.2%)

rewrite70.0ms (0.6%)

series967.0ms (7.7%)

simplify80.0ms (0.6%)

prune97.0ms (0.8%)

regimes1.2s (9.4%)

bsearch705.0ms (5.6%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample4.9s (38.9%)

Profiling