Details

analyze95.0ms (4.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11
0	1	1
1	1	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 (1.3%)

Algorithm

1×

intervals

Results

11.0ms	63×	body	2048	valid
5.0ms	39×	body	1024	valid
4.0ms	131×	body	128	valid
1.0ms	10×	body	512	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify10.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune6.0ms (0.3%)

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

15.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.8b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`add-log-exp_binary64_1822`
3×	`add-cube-cbrt_binary64_1818` `cancel-sign-sub-inv_binary64_1749`
2×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
1×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `diff-atan_binary64_1940` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

2 → 24

Calls

2 calls:

4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms	(atan.f64 (+.f64 N 1))

series16.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

12.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms	(atan.f64 (+.f64 N 1))

simplify72.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4998	391
1	4998	391

prune21.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	2	31

Error

0.4b

Counts

31 → 2

Compiler

Compiled 351 to 229 computations (34.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `associate-r_binary64_1723` `pow1_binary64_1844`
3×	`associate-l_binary64_1724`
2×	`associate-*r/_binary64_1725` `add-log-exp_binary64_1822`
1×	`distribute-lft-in_binary64_1732` `distribute-lft-out_binary64_1734` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`

Counts

2 → 30

Calls

2 calls:

6.0ms	(*.f64 N (+.f64 N 1))
0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series36.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

28.0ms	(*.f64 N (+.f64 N 1))
8.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify72.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4927	383
1	4927	383

prune34.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	34	4	38

Error

0.4b

Counts

38 → 4

Compiler

Compiled 541 to 424 computations (21.6% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b	(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))))))
14.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
14.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite19.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1805`
24×	`sqrt-prod_binary64_1799`
21×	`pow1_binary64_1844`
14×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
8×	`swap-sqr_binary64_1750`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `associate-l_binary64_1724` `associate-r_binary64_1723`
5×	`pow-prod-up_binary64_1853`
4×	`unswap-sqr_binary64_1751` `rem-sqrt-square_binary64_1796` `add-log-exp_binary64_1822`
3×	`pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
1×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `pow-plus_binary64_1846` `*-commutative_binary64_1714` `rem-square-sqrt_binary64_1795` `sqr-abs_binary64_1798` `pow2_binary64_1864`

Counts

4 → 83

Calls

4 calls:

7.0ms	(.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))))))
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))))

series67.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
23.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
10.0ms	(.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))))))
7.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify80.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5103	1475

prune117.0ms (5.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	94	5	99

Error

0.3b

Counts

99 → 5

Compiler

Compiled 2078 to 1711 computations (17.7% saved)

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
14.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
14.3b	(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_1805`
6×	`add-cube-cbrt_binary64_1818` `sqrt-prod_binary64_1799` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-log-exp_binary64_1822`
2×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`

Counts

4 → 40

Calls

4 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))))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

series58.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
22.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
7.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
6.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify82.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4906	862
1	4906	862

prune82.0ms (3.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	52	5	57

Error

0.3b

Counts

57 → 5

Compiler

Compiled 1552 to 1313 computations (15.4% saved)

regimes50.0ms (2.3%)

Accuracy

Total 0.0b remaining (13.3%)

Threshold costs 0.0b (13.3%)

Compiler

Compiled 530 to 454 computations (14.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample1.2s (53.8%)

Algorithm

1×

intervals

Results

393.0ms	2217×	body	2048	valid
145.0ms	4087×	body	128	valid
122.0ms	1002×	body	1024	valid
42.0ms	458×	body	512	valid
15.0ms	236×	body	256	valid

Compiler

Compiled 284 to 245 computations (13.7% saved)

Details

analyze95.0ms (4.4%)

sample28.0ms (1.3%)

simplify10.0ms (0.5%)

prune6.0ms (0.3%)

localize6.0ms (0.3%)

rewrite6.0ms (0.3%)

series16.0ms (0.7%)

simplify72.0ms (3.3%)

prune21.0ms (1%)

localize5.0ms (0.2%)

rewrite9.0ms (0.4%)

series36.0ms (1.7%)

simplify72.0ms (3.3%)

prune34.0ms (1.6%)

localize11.0ms (0.5%)

rewrite19.0ms (0.9%)

series67.0ms (3.1%)

simplify80.0ms (3.7%)

prune117.0ms (5.4%)

localize13.0ms (0.6%)

rewrite7.0ms (0.3%)

series58.0ms (2.7%)

simplify82.0ms (3.8%)

prune82.0ms (3.8%)

regimes50.0ms (2.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (53.8%)

Profiling