Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample28.0ms (1.1%)

Algorithm

1×

intervals

Results

10.0ms	62×	body	2048	valid
5.0ms	38×	body	1024	valid
4.0ms	135×	body	128	valid
1.0ms	16×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify105.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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

15.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
3×	`add-log-exp_binary64_2504` `cancel-sign-sub-inv_binary64_2431`
2×	`add-cube-cbrt_binary64_2500`
1×	`diff-atan_binary64_2622` `difference-of-squares_binary64_2434` `flip--_binary64_2440` `add-exp-log_binary64_2503` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `add-cbrt-cube_binary64_2501` `diff-log_binary64_2557` `pow1_binary64_2526` `flip3--_binary64_2469`

Counts

1 → 17

Calls

2 calls:

4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series18.0ms (0.7%)

Counts

1 → 3

Calls

1 calls:

18.0ms

(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 42 to 36 computations (14.3% saved)

simplify75.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4992	306
1	4992	306

prune231.0ms (8.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	2	21

Error

0.6b

Counts

21 → 2

Compiler

Compiled 267 to 174 computations (34.8% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64_2465` `add-log-exp_binary64_2504` `add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-sqr-sqrt_binary64_2487` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`

Counts

1 → 7

Calls

2 calls:

1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series14.0ms (0.5%)

Counts

1 → 3

Calls

1 calls:

14.0ms

(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 54 to 48 computations (11.1% saved)

simplify185.0ms (7.1%)

Algorithm

1×	egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 0 (178.0ms)

Iter	Nodes	Cost
0	4793	162
1	4793	162

prune19.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	7	3	10
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	8	4	12

Error

0.6b

Counts

12 → 4

Compiler

Compiled 201 to 167 computations (16.9% saved)

localize9.0ms (0.3%)

Local error

Found 8 expressions with local error:

13.8b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
13.8b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.8b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_2487`
6×	`*-un-lft-identity_binary64_2465` `sqrt-prod_binary64_2481` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
4×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
2×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`

Counts

4 → 40

Calls

8 calls:

1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))

series96.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
31.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
16.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
15.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

Compiler

Compiled 504 to 432 computations (14.3% saved)

simplify85.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4906	862
1	4906	862

prune85.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	52	4	56

Error

0.6b

Counts

56 → 4

Compiler

Compiled 1422 to 1171 computations (17.7% saved)

localize12.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
0.2b	(.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))))
0.0b	(sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
0.0b	(sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
13.8b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.8b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.8b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2487`
9×	`sqrt-prod_binary64_2481`
7×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
4×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`

Counts

4 → 46

Calls

8 calls:

1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.0ms	(.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))))

series119.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
33.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
33.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
18.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

Compiler

Compiled 816 to 696 computations (14.7% saved)

simplify84.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4906	969
1	4906	969

prune120.0ms (4.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	57	5	62

Error

0.6b

Counts

62 → 5

Compiler

Compiled 2258 to 1875 computations (17% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	400
1	48	400

regimes29.0ms (1.1%)

Compiler: Compiled 263 to 228 computations (13.3% saved)

bsearch0.0ms (0%)

regimes16.0ms (0.6%)

Accuracy

Total 0.1b remaining (11.3%)

Threshold costs 0.1b (11.3%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch54.0ms (2.1%)

Steps

Iters	Range		Point
9	4.37501655153618e+74	2.636693488533328e+83	9.549103444578948e+76
9	-1.4822660537427165e+83	-8.041719324610898e+76	-9.337312749146761e+76

Compiler

Compiled 22 to 21 computations (4.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	29
1	21	29

end0.0ms (0%)

sample1.2s (44.5%)

Algorithm

1×

intervals

Results

362.0ms	2093×	body	2048	valid
139.0ms	4130×	body	128	valid
119.0ms	1014×	body	1024	valid
44.0ms	506×	body	512	valid
16.0ms	257×	body	256	valid

Compiler

Compiled 300 to 263 computations (12.3% saved)

Pareto

0.18236828049887832

Details

analyze1.0ms (0.1%)

sample28.0ms (1.1%)

simplify105.0ms (4.1%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite5.0ms (0.2%)

series18.0ms (0.7%)

simplify75.0ms (2.9%)

prune231.0ms (8.9%)

localize7.0ms (0.3%)

rewrite1.0ms (0.1%)

series14.0ms (0.5%)

simplify185.0ms (7.1%)

prune19.0ms (0.7%)

localize9.0ms (0.3%)

rewrite7.0ms (0.3%)

series96.0ms (3.7%)

simplify85.0ms (3.3%)

prune85.0ms (3.3%)

localize12.0ms (0.4%)

rewrite9.0ms (0.4%)

series119.0ms (4.6%)

simplify84.0ms (3.3%)

prune120.0ms (4.6%)

simplify6.0ms (0.2%)

regimes29.0ms (1.1%)

bsearch0.0ms (0%)

regimes16.0ms (0.6%)

bsearch54.0ms (2.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (44.5%)

Profiling