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)

sample34.0ms (1.2%)

Algorithm

1×

intervals

Results

17.0ms	64×	body	2048	valid
6.0ms	140×	body	128	valid
4.0ms	32×	body	1024	valid
1.0ms	12×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify11.0ms (0.4%)

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: 14.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-atan_binary64`

Counts

2 → 21

Calls

2 calls:

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

series31.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

23.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
7.0ms	(atan.f64 (+.f64 N 1))

simplify89.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5609	376

prune21.0ms (0.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	1	28

Merged error: 0.3b

Counts

28 → 1

Compiler

Compiled 327 to 217 computations (33.6% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-l_binary64`
2×	`add-log-exp_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

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))))

series68.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

53.0ms	(*.f64 N (+.f64 N 1))
14.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify89.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4880	383
1	4880	383

prune39.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	30	6	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	7	37

Merged error: 0.2b

Counts

37 → 7

Compiler

Compiled 585 to 459 computations (21.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (*.f64 N (+.f64 1 N))))
15.0b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
15.0b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
15.0b	(cbrt.f64 (*.f64 N (+.f64 1 N)))

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*r/_binary64`
18×	`cbrt-div_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (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)))
5.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))

series258.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (*.f64 N (+.f64 1 N))))
63.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
61.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
59.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))

simplify62.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5485	1373

prune133.0ms (4.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Merged error: 0.2b

Counts

91 → 7

Compiler

Compiled 2497 to 1921 computations (23.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)

series634.0ms (22.4%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
151.0ms	(cbrt.f64 N)
149.0ms	(cbrt.f64 N)
147.0ms	(cbrt.f64 N)

simplify66.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4957	563
1	4957	563

prune84.0ms (3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	85	7	92

Merged error: 0.2b

Counts

92 → 7

Compiler

Compiled 1584 to 910 computations (42.6% saved)

regimes16.0ms (0.6%)

Compiler: Compiled 129 to 107 computations (17.1% 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%)

sample1.1s (38.7%)

Algorithm

1×

intervals

Results

408.0ms	2079×	body	2048	valid
179.0ms	4202×	body	128	valid
136.0ms	975×	body	1024	valid
56.0ms	516×	body	512	valid
17.0ms	228×	body	256	valid

Compiler

Compiled 154 to 130 computations (15.6% saved)

Details

analyze1.0ms (0.1%)

sample34.0ms (1.2%)

simplify11.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite6.0ms (0.2%)

series31.0ms (1.1%)

simplify89.0ms (3.1%)

prune21.0ms (0.7%)

localize8.0ms (0.3%)

rewrite9.0ms (0.3%)

series68.0ms (2.4%)

simplify89.0ms (3.2%)

prune39.0ms (1.4%)

localize10.0ms (0.3%)

rewrite30.0ms (1%)

series258.0ms (9.1%)

simplify62.0ms (2.2%)

prune133.0ms (4.7%)

localize9.0ms (0.3%)

rewrite16.0ms (0.6%)

series634.0ms (22.4%)

simplify66.0ms (2.3%)

prune84.0ms (3%)

regimes16.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (38.7%)

Profiling