Details

analyze2.2s (12.5%)

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

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample134.0ms (0.8%)

Algorithm

1×

intervals

Results

47.0ms	85×	body	1024	invalid
28.0ms	241×	body	128	valid
12.0ms	34×	body	512	invalid
4.0ms	16×	body	256	invalid
3.0ms	8×	body	512	valid
3.0ms	6×	body	1024	valid
2.0ms	15×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify111.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune20.0ms (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

37.6b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize44.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
32.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.7b	(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)))

rewrite207.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

37.6b

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×	`cos-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

14.0ms	(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)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2420 to 343 computations (85.8% saved)

series1.1s (6.6%)

Error

22.9b

Counts

4 → 47

Calls

4 calls:

567.0ms	(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)))
209.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
152.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
138.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 4209 to 2373 computations (43.6% saved)

simplify127.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5151	1930

prune256.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	5	104

Error

23.0b

Counts

104 → 5

Compiler

Compiled 3209 to 971 computations (69.7% saved)

localize76.0ms (0.4%)

Local error

Found 4 expressions with local error:

32.7b	(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)))))))
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)))))))
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)))))))

rewrite339.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

23.0b

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×	`cos-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 39

Calls

4 calls:

13.0ms	(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)))))))
12.0ms	(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)))))))
12.0ms	(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)))))))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3487 to 1729 computations (50.4% saved)

series2.5s (14.2%)

Error

22.9b

Counts

4 → 54

Calls

4 calls:

614.0ms	(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)))))))
600.0ms	(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)))))))
590.0ms	(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)))))))
415.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 10820 to 6570 computations (39.3% saved)

simplify136.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5200	2604

prune517.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	90	8	98

Error

22.9b

Counts

98 → 8

Compiler

Compiled 6062 to 3130 computations (48.4% saved)

localize79.0ms (0.5%)

Local error

Found 4 expressions with local error:

32.7b	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
32.7b	(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)))))))
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)))))))

rewrite337.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

22.9b

Rules

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

Counts

4 → 48

Calls

4 calls:

19.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
14.0ms	(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)))))))
12.0ms	(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)))))))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3501 to 1521 computations (56.6% saved)

series1.5s (8.7%)

Error

22.9b

Counts

4 → 48

Calls

4 calls:

583.0ms	(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)))))))
520.0ms	(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)))))))
233.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
73.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))

Compiler

Compiled 7931 to 4589 computations (42.1% saved)

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4959	2260
1	4959	2260

prune258.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	96	8	104

Error

22.9b

Counts

104 → 8

Compiler

Compiled 5191 to 2376 computations (54.2% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

16.7b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
32.7b	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
32.7b	(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)))))))

rewrite152.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

22.9b

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_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`

Counts

4 → 47

Calls

4 calls:

9.0ms	(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)))))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 2826 to 917 computations (67.6% saved)

series1.5s (8.5%)

Error

22.9b

Counts

4 → 48

Calls

4 calls:

567.0ms	(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)))))))
360.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
322.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
153.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))

Compiler

Compiled 6183 to 3222 computations (47.9% saved)

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5063	1872

prune168.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	95	8	103

Error

22.9b

Counts

103 → 8

Compiler

Compiled 3843 to 1313 computations (65.8% saved)

regimes1.5s (8.4%)

Accuracy

Total 13.4b remaining (78%)

Threshold costs 0b (0%)

Compiler

Compiled 13572 to 8380 computations (38.3% saved)

bsearch226.0ms (1.3%)

Steps

Iters	Range		Point
7	1.9213200085579265e-22	1.389030224858017e-20	6.98163160565977e-21
10	-3.1584447776007537e-186	-1.6197667539098375e-200	-2.196245806719985e-193
7	-1.6891185572949009e-43	-9.698996020711577e-45	-1.8917662554192892e-44
8	-0.00417977297077719	-1.3147659207728952e-07	-1.8408802784809857e-05

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	65	82
1	65	82

end3.0ms (0%)

Compiler: Compiled 45 to 33 computations (26.7% saved)

sample3.8s (21.7%)

Algorithm

1×

intervals

Results

1.2s	2377×	body	1024	invalid
855.0ms	7556×	body	128	valid
366.0ms	995×	body	512	invalid
100.0ms	195×	body	1024	valid
89.0ms	392×	body	256	invalid
72.0ms	551×	body	128	invalid
56.0ms	152×	body	512	valid
31.0ms	36×	body	2048	invalid
19.0ms	83×	body	256	valid
11.0ms	14×	body	2048	valid

Compiler

Compiled 514 to 336 computations (34.6% saved)

Details

analyze2.2s (12.5%)

sample134.0ms (0.8%)

simplify111.0ms (0.6%)

prune20.0ms (0.1%)

localize44.0ms (0.3%)

rewrite207.0ms (1.2%)

series1.1s (6.6%)

simplify127.0ms (0.7%)

prune256.0ms (1.5%)

localize76.0ms (0.4%)

rewrite339.0ms (1.9%)

series2.5s (14.2%)

simplify136.0ms (0.8%)

prune517.0ms (3%)

localize79.0ms (0.5%)

rewrite337.0ms (1.9%)

series1.5s (8.7%)

simplify88.0ms (0.5%)

prune258.0ms (1.5%)

localize39.0ms (0.2%)

rewrite152.0ms (0.9%)

series1.5s (8.5%)

simplify68.0ms (0.4%)

prune168.0ms (1%)

regimes1.5s (8.4%)

bsearch226.0ms (1.3%)

simplify4.0ms (0%)

end3.0ms (0%)

sample3.8s (21.7%)

Profiling