Details

analyze1.6s (14.2%)

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
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample117.0ms (1.1%)

Algorithm

1×

intervals

Results

48.0ms	83×	body	1024	invalid
27.0ms	246×	body	128	valid
9.0ms	25×	body	512	invalid
2.0ms	20×	body	128	invalid
2.0ms	7×	body	512	valid
1.0ms	5×	body	256	invalid
1.0ms	2×	body	1024	valid
1.0ms	1×	body	2048	invalid
0.0ms	1×	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

prune12.0ms (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

34.1b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
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)))
34.5b	(cos.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)))

rewrite103.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

34.1b

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×	`cos-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	(cos.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)))
5.0ms	(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)

series635.0ms (5.8%)

Error

19.3b

Counts

4 → 51

Calls

4 calls:

253.0ms	(cos.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)))
143.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
97.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
75.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 5292 to 2678 computations (49.4% saved)

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5151	2028

prune155.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Error

19.3b

Counts

109 → 6

Compiler

Compiled 4509 to 1188 computations (73.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(*.f64 y.re (atan2.f64 x.im x.re))
1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
18.5b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite76.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

19.3b

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 y.re (atan2.f64 x.im x.re))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1851 to 341 computations (81.6% saved)

series464.0ms (4.2%)

Error

2.5b

Counts

4 → 48

Calls

4 calls:

140.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
136.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
71.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
69.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

Compiler

Compiled 3502 to 1849 computations (47.2% saved)

simplify47.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5051	1573

prune117.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	104	8	112

Error

2.5b

Counts

112 → 8

Compiler

Compiled 3268 to 826 computations (74.7% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.1b	(cbrt.f64 (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)))
34.5b	(cos.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)))

rewrite89.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

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

Counts

4 → 49

Calls

4 calls:

6.0ms	(cos.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)))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

Compiler

Compiled 2832 to 332 computations (88.3% saved)

series714.0ms (6.5%)

Error

2.5b

Counts

4 → 48

Calls

4 calls:

240.0ms	(cos.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)))
159.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
150.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
102.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 6363 to 2863 computations (55% saved)

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4945	1884
1	4945	1884

prune152.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Error

2.5b

Counts

105 → 8

Compiler

Compiled 5243 to 1233 computations (76.5% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.2b	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
30.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.5b	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))

rewrite132.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

12×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_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` `unpow-prod-down_binary64` `distribute-lft-out_binary64`
1×	`cos-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
6.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
6.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 2792 to 1167 computations (58.2% saved)

series635.0ms (5.8%)

Error

2.5b

Counts

4 → 51

Calls

4 calls:

234.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
147.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
95.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
81.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 5562 to 3389 computations (39.1% saved)

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5179	2058

prune177.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	109	8	117

Error

2.5b

Counts

117 → 8

Compiler

Compiled 4594 to 1937 computations (57.8% saved)

regimes714.0ms (6.5%)

Accuracy

Total 5.4b remaining (60.3%)

Threshold costs 0b (0%)

Compiler

Compiled 8227 to 4915 computations (40.3% saved)

bsearch228.0ms (2.1%)

Steps

Iters	Range		Point
5	1.936222325848746e-57	4.849363965424576e-57	4.133172358705715e-57
9	4.625355632308386e-167	2.4067730327763433e-159	1.7995269637531557e-165
9	-2.8419842429029937e-306	2.977235608098335e-306	2.03634166149114e-310

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	89	133
1	89	133

end0.0ms (0%)

sample4.5s (40.7%)

Algorithm

1×

intervals

Results

1.2s	2370×	body	1024	invalid
844.0ms	7576×	body	128	valid
343.0ms	993×	body	512	invalid
94.0ms	187×	body	1024	valid
88.0ms	380×	body	256	invalid
69.0ms	586×	body	128	invalid
49.0ms	136×	body	512	valid
33.0ms	40×	body	2048	invalid
20.0ms	87×	body	256	valid
12.0ms	14×	body	2048	valid

Compiler

Compiled 1735 to 1030 computations (40.6% saved)

Details

analyze1.6s (14.2%)

sample117.0ms (1.1%)

simplify65.0ms (0.6%)

prune12.0ms (0.1%)

localize22.0ms (0.2%)

rewrite103.0ms (0.9%)

series635.0ms (5.8%)

simplify69.0ms (0.6%)

prune155.0ms (1.4%)

localize19.0ms (0.2%)

rewrite76.0ms (0.7%)

series464.0ms (4.2%)

simplify47.0ms (0.4%)

prune117.0ms (1.1%)

localize25.0ms (0.2%)

rewrite89.0ms (0.8%)

series714.0ms (6.5%)

simplify101.0ms (0.9%)

prune152.0ms (1.4%)

localize29.0ms (0.3%)

rewrite132.0ms (1.2%)

series635.0ms (5.8%)

simplify71.0ms (0.6%)

prune177.0ms (1.6%)

regimes714.0ms (6.5%)

bsearch228.0ms (2.1%)

simplify5.0ms (0%)

end0.0ms (0%)

sample4.5s (40.7%)

Profiling