Details

analyze1.5s (14.8%)

Algorithm

1×

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)

sample130.0ms (1.3%)

Algorithm

1×

intervals

Results

51.0ms	84×	body	1024	invalid
29.0ms	236×	body	128	valid
13.0ms	33×	body	512	invalid
5.0ms	13×	body	512	valid
4.0ms	15×	body	256	invalid
3.0ms	5×	body	1024	valid
2.0ms	2×	body	2048	valid
2.0ms	2×	body	2048	invalid
2.0ms	13×	body	128	invalid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify169.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

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

Merged error: 34.8b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.7b	(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 (atan2.f64 x.im x.re) y.re)))

rewrite29.0ms (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:

9.0ms	(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.im)

series292.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(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)))
26.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
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)))

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4884	1270
1	4884	1270

prune128.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	9	69

Merged error: 22.1b

Counts

69 → 9

Compiler

Compiled 3216 to 969 computations (69.9% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

7.0b	(cbrt.f64 (atan2.f64 x.im x.re))
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.7b	(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 (atan2.f64 x.im x.re) y.re)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_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×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow1/3_binary64` `sin-sum_binary64`

Counts

4 → 49

Calls

4 calls:

7.0ms	(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)))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

series290.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(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)))
45.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
22.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
21.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4870	1162
1	4870	1162

prune110.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	61	9	70

Merged error: 22.1b

Counts

70 → 9

Compiler

Compiled 3557 to 940 computations (73.6% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.7b	(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)))
33.7b	(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)))
33.7b	(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)))

rewrite36.0ms (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)))

series591.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(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)))
189.0ms	(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)))
183.0ms	(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)))
27.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5056	1579

prune185.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	50	10	60

Merged error: 22.1b

Counts

60 → 10

Compiler

Compiled 4673 to 2441 computations (47.8% saved)

localize40.0ms (0.4%)

Local error

Found 4 expressions with local error:

33.7b	(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)))
33.7b	(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)))
33.7b	(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)))
33.7b	(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)))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 32

Calls

4 calls:

9.0ms	(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)))
8.0ms	(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)))

series729.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(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)))
188.0ms	(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)))
177.0ms	(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)))
171.0ms	(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)))

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4848	1720
1	4848	1720

prune220.0ms (2.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	43	11	54

Merged error: 22.1b

Counts

54 → 11

Compiler

Compiled 5532 to 2846 computations (48.6% saved)

regimes471.0ms (4.7%)

Compiler: Compiled 6342 to 3995 computations (37% saved)

bsearch110.0ms (1.1%)

Steps

Iters	Range		Point
9	-2.1011816564682988e-303	2.5244069345529946e-304	-1.1308612178617e-310

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	118	151
1	118	151

end0.0ms (0%)

sample4.5s (45%)

Algorithm

1×

intervals

Results

1.4s	2563×	body	1024	invalid
911.0ms	7547×	body	128	valid
341.0ms	903×	body	512	invalid
170.0ms	186×	body	2048	invalid
84.0ms	331×	body	256	invalid
82.0ms	153×	body	1024	valid
70.0ms	535×	body	128	invalid
66.0ms	171×	body	512	valid
29.0ms	120×	body	256	valid
8.0ms	9×	body	2048	valid

Compiler

Compiled 1366 to 844 computations (38.2% saved)

Details

analyze1.5s (14.8%)

sample130.0ms (1.3%)

simplify169.0ms (1.7%)

prune8.0ms (0.1%)

localize23.0ms (0.2%)

rewrite29.0ms (0.3%)

series292.0ms (2.9%)

simplify102.0ms (1%)

prune128.0ms (1.3%)

localize25.0ms (0.3%)

rewrite26.0ms (0.3%)

series290.0ms (2.9%)

simplify79.0ms (0.8%)

prune110.0ms (1.1%)

localize34.0ms (0.3%)

rewrite36.0ms (0.4%)

series591.0ms (5.9%)

simplify74.0ms (0.7%)

prune185.0ms (1.8%)

localize40.0ms (0.4%)

rewrite41.0ms (0.4%)

series729.0ms (7.3%)

simplify94.0ms (0.9%)

prune220.0ms (2.2%)

regimes471.0ms (4.7%)

bsearch110.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.5s (45%)

Profiling