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)

sample36.0ms (1.4%)

Algorithm

1×

intervals

Results

14.0ms	70×	body	2048	valid
9.0ms	133×	body	128	valid
5.0ms	29×	body	1024	valid
2.0ms	16×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify168.0ms (6.5%)

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

Merged error: 14.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
2.1b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1821` `*-un-lft-identity_binary64_1799`
4×	`add-log-exp_binary64_1838`
3×	`add-cube-cbrt_binary64_1834` `cancel-sign-sub-inv_binary64_1765`
2×	`pow1_binary64_1860` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
1×	`sub-neg_binary64_1792` `diff-log_binary64_1891` `flip--_binary64_1774` `diff-atan_binary64_1956` `difference-of-squares_binary64_1768` `flip3--_binary64_1803` `distribute-lft-out--_binary64_1751`

Counts

2 → 24

Calls

2 calls:

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

series33.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

25.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
7.0ms	(atan.f64 (+.f64 N 1))

simplify69.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4971	391
1	4971	391

prune26.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	3	31

Merged error: 0.5b

Counts

31 → 3

Compiler

Compiled 401 to 273 computations (31.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1821` `*-un-lft-identity_binary64_1799`
4×	`pow1_binary64_1860` `add-cube-cbrt_binary64_1834` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837` `associate-r_binary64_1739`
3×	`associate-l_binary64_1740`
2×	`add-log-exp_binary64_1838` `associate-*r/_binary64_1741`
1×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `prod-exp_binary64_1848` `unswap-sqr_binary64_1767` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870` `distribute-lft-out_binary64_1750` `flip3-+_binary64_1802` `flip-+_binary64_1773`

Counts

2 → 30

Calls

2 calls:

7.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series71.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

56.0ms	(*.f64 N (+.f64 N 1))
14.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify79.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4877	383
1	4877	383

prune64.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	34	5	39

Merged error: 0.4b

Counts

39 → 5

Compiler

Compiled 910 to 745 computations (18.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(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))))))
15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1821`
24×	`sqrt-prod_binary64_1815`
21×	`pow1_binary64_1860`
14×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
10×	`pow1/2_binary64_1879` `sqrt-pow1_binary64_1817`
8×	`swap-sqr_binary64_1766`
6×	`associate-l_binary64_1740` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837` `associate-r_binary64_1739`
5×	`pow-prod-up_binary64_1869`
4×	`add-log-exp_binary64_1838` `unswap-sqr_binary64_1767` `rem-sqrt-square_binary64_1812`
3×	`pow-sqr_binary64_1772` `pow-prod-down_binary64_1870`
1×	`pow2_binary64_1880` `sqr-abs_binary64_1814` `prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `sqrt-unprod_binary64_1819` `rem-square-sqrt_binary64_1811` `pow-plus_binary64_1862`

Counts

4 → 83

Calls

4 calls:

8.0ms	(.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))))))
2.0ms	(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))))

series129.0ms (5%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
49.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
17.0ms	(.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))))))
11.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify79.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5111	1475

prune139.0ms (5.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	94	6	100

Merged error: 0.4b

Counts

100 → 6

Compiler

Compiled 2440 to 2019 computations (17.3% saved)

localize12.0ms (0.5%)

Local error

Found 4 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))))))))
15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite33.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`sqrt-pow1_binary64_1817`
45×	`pow1_binary64_1860`
30×	`pow1/2_binary64_1879` `pow-prod-up_binary64_1869`
16×	`add-sqr-sqrt_binary64_1821`
14×	`sqrt-prod_binary64_1815`
9×	`add-cube-cbrt_binary64_1834` `add-cbrt-cube_binary64_1835` `*-un-lft-identity_binary64_1799` `add-exp-log_binary64_1837`
7×	`pow-prod-down_binary64_1870`
6×	`pow-sqr_binary64_1772` `associate-l_binary64_1740`
4×	`add-log-exp_binary64_1838`
3×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `rem-sqrt-square_binary64_1812`
2×	`unswap-sqr_binary64_1767` `sqrt-unprod_binary64_1819` `swap-sqr_binary64_1766`
1×	`-commutative_binary64_1730` `associate-r*_binary64_1739`

Counts

4 → 85

Calls

4 calls:

18.0ms	(.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))))))))
2.0ms	(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)))))

series154.0ms (6%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
44.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
42.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
22.0ms	(.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))))))))

simplify83.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4759	1397
1	4759	1397

prune159.0ms (6.2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	97	6	103

Merged error: 0.4b

Counts

103 → 6

Compiler

Compiled 2826 to 2345 computations (17% saved)

regimes29.0ms (1.1%)

Compiler: Compiled 266 to 226 computations (15% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample1.1s (44.6%)

Algorithm

1×

intervals

Results

451.0ms	2134×	body	2048	valid
185.0ms	4189×	body	128	valid
136.0ms	923×	body	1024	valid
55.0ms	495×	body	512	valid
21.0ms	259×	body	256	valid

Compiler

Compiled 152 to 131 computations (13.8% saved)

Details

analyze1.0ms (0.1%)

sample36.0ms (1.4%)

simplify168.0ms (6.5%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite7.0ms (0.3%)

series33.0ms (1.3%)

simplify69.0ms (2.7%)

prune26.0ms (1%)

localize6.0ms (0.2%)

rewrite10.0ms (0.4%)

series71.0ms (2.7%)

simplify79.0ms (3.1%)

prune64.0ms (2.5%)

localize8.0ms (0.3%)

rewrite19.0ms (0.8%)

series129.0ms (5%)

simplify79.0ms (3.1%)

prune139.0ms (5.4%)

localize12.0ms (0.5%)

rewrite33.0ms (1.3%)

series154.0ms (6%)

simplify83.0ms (3.2%)

prune159.0ms (6.2%)

regimes29.0ms (1.1%)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample1.1s (44.6%)

Profiling