Details

analyze2.0ms (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)

sample33.0ms (1.2%)

Algorithm

1×

intervals

Results

14.0ms	67×	body	2048	valid
6.0ms	136×	body	128	valid
5.0ms	34×	body	1024	valid
1.0ms	13×	body	512	valid
0.0ms	6×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify173.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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: 16.1b

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))
2.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_2120` `add-log-exp_binary64_2135` `*-un-lft-identity_binary64_2099`
2×	`add-cube-cbrt_binary64_2131` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-exp-log_binary64_2134`
1×	`difference-of-squares_binary64_2068` `sub-neg_binary64_2092` `flip3--_binary64_2103` `flip--_binary64_2074` `diff-atan_binary64_2253` `distribute-lft-out--_binary64_2053` `diff-log_binary64_2188`

Counts

2 → 21

Calls

2 calls:

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

series32.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

24.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
7.0ms	(atan.f64 (+.f64 N 1))

simplify89.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5609	376

prune23.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Merged error: 0.5b

Counts

28 → 3

Compiler

Compiled 344 to 230 computations (33.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_2120` `*-un-lft-identity_binary64_2099`
5×	`add-cube-cbrt_binary64_2131` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-log-exp_binary64_2135` `add-exp-log_binary64_2134`
4×	`associate-r_binary64_2041`
3×	`associate-l_binary64_2042`
2×	`associate-*r/_binary64_2043` `flip3-+_binary64_2102` `distribute-rgt-in_binary64_2051` `distribute-lft-in_binary64_2050` `flip-+_binary64_2073` `associate-+r+_binary64_2033`
1×	`distribute-lft-out_binary64_2052` `*-commutative_binary64_2032` `sum-log_binary64_2187` `prod-exp_binary64_2145` `+-commutative_binary64_2031` `pow-prod-down_binary64_2167` `unswap-sqr_binary64_2067` `cbrt-unprod_binary64_2129`

Counts

3 → 43

Calls

3 calls:

7.0ms	(*.f64 N (+.f64 N 1))
4.0ms	(+.f64 1 (*.f64 N (+.f64 N 1)))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series275.0ms (10.3%)

Counts

3 → 9

Calls

3 calls:

201.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
57.0ms	(*.f64 N (+.f64 N 1))
16.0ms	(+.f64 1 (*.f64 N (+.f64 N 1)))

simplify90.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4899	599
1	4899	599

prune56.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	48	7	55

Merged error: 0.5b

Counts

55 → 7

Compiler

Compiled 798 to 626 computations (21.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64_2135`
6×	`*-un-lft-identity_binary64_2099`
4×	`sum-log_binary64_2187`
3×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-exp-log_binary64_2134`
2×	`flip3-+_binary64_2102` `+-commutative_binary64_2031` `flip-+_binary64_2073`
1×	`distribute-lft-out_binary64_2052` `distribute-lft1-in_binary64_2056` `distribute-rgt-out_binary64_2054` `associate-+r+_binary64_2033`

Counts

3 → 34

Calls

3 calls:

7.0ms	(+.f64 1 (+.f64 (*.f64 N N) N))
5.0ms	(+.f64 (*.f64 N N) N)
1.0ms	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

series86.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

54.0ms	(+.f64 (*.f64 N N) N)
19.0ms	(+.f64 1 (+.f64 (*.f64 N N) N))
13.0ms	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

simplify81.0ms (3%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4888	549
1	4888	549

prune36.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	43	7	50

Merged error: 0.5b

Counts

50 → 7

Compiler

Compiled 669 to 381 computations (43% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (.f64 N (+.f64 1 N)))) (cbrt.f64 (*.f64 N (+.f64 1 N))))))
15.4b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
15.4b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
15.4b	(cbrt.f64 (*.f64 N (+.f64 1 N)))

rewrite20.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cbrt-div_binary64_2128` `associate-*r/_binary64_2043`
4×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-log-exp_binary64_2135` `*-un-lft-identity_binary64_2099` `add-exp-log_binary64_2134`
3×	`flip3-+_binary64_2102` `pow1/3_binary64_2178` `cbrt-prod_binary64_2127` `flip-+_binary64_2073`

Counts

4 → 40

Calls

4 calls:

5.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
5.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
5.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
1.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (.f64 N (+.f64 1 N)))) (cbrt.f64 (*.f64 N (+.f64 1 N))))))

series217.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
65.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
59.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
26.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (.f64 N (+.f64 1 N)))) (cbrt.f64 (*.f64 N (+.f64 1 N))))))

simplify63.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4876	846
1	4876	846

prune76.0ms (2.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	51	8	59

Merged error: 0.5b

Counts

59 → 8

Compiler

Compiled 1456 to 1095 computations (24.8% saved)

regimes35.0ms (1.3%)

Compiler: Compiled 302 to 252 computations (16.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	10	13

end0.0ms (0%)

sample1.2s (45.3%)

Algorithm

1×

intervals

Results

466.0ms	2173×	body	2048	valid
182.0ms	4145×	body	128	valid
147.0ms	946×	body	1024	valid
57.0ms	499×	body	512	valid
22.0ms	237×	body	256	valid

Compiler

Compiled 170 to 143 computations (15.9% saved)

Details

analyze2.0ms (0.1%)

sample33.0ms (1.2%)

simplify173.0ms (6.5%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite7.0ms (0.3%)

series32.0ms (1.2%)

simplify89.0ms (3.4%)

prune23.0ms (0.9%)

localize6.0ms (0.2%)

rewrite14.0ms (0.5%)

series275.0ms (10.3%)

simplify90.0ms (3.4%)

prune56.0ms (2.1%)

localize6.0ms (0.2%)

rewrite15.0ms (0.5%)

series86.0ms (3.2%)

simplify81.0ms (3%)

prune36.0ms (1.4%)

localize12.0ms (0.4%)

rewrite20.0ms (0.8%)

series217.0ms (8.2%)

simplify63.0ms (2.4%)

prune76.0ms (2.9%)

regimes35.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (45.3%)

Profiling