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)

sample26.0ms (1.4%)

Algorithm

1×

intervals

Results

14.0ms	97×	body	1280	valid
4.0ms	131×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify15.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune3.0ms (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: 15.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite5.0ms (0.3%)

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))

series7.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(atan.f64 (+.f64 N 1))
3.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify92.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4925	376
1	4925	376

prune17.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Merged error: 0.2b

Counts

28 → 2

Compiler

Compiled 327 to 217 computations (33.6% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite8.0ms (0.4%)

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:

6.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series7.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(*.f64 N (+.f64 N 1))
2.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify92.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5068	383

prune34.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	32	6	38

Merged error: 0.1b

Counts

38 → 6

Compiler

Compiled 557 to 435 computations (21.9% saved)

localize11.0ms (0.5%)

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)

rewrite12.0ms (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))
2.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)

series62.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
15.0ms	(cbrt.f64 N)
14.0ms	(cbrt.f64 N)
14.0ms	(cbrt.f64 N)

simplify81.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4942	588
1	4942	588

prune61.0ms (3.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	85	6	91

Merged error: 0.1b

Counts

91 → 6

Compiler

Compiled 1673 to 979 computations (41.5% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(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))))))
14.7b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
14.7b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
8×	`swap-sqr_binary64`
6×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`rem-sqrt-square_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(.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))))

series18.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
6.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
3.0ms	(.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	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify83.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5260	1485

prune85.0ms (4.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	2	2
Picked	0	1	1
Done	1	2	3
Total	92	8	100

Merged error: 0.1b

Counts

100 → 8

Compiler

Compiled 1971 to 1622 computations (17.7% saved)

regimes26.0ms (1.3%)

Compiler: Compiled 182 to 153 computations (15.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms (0%)

sample1.2s (60.1%)

Algorithm

1×

intervals

Results

426.0ms	2825×	body	1280	valid
134.0ms	4078×	body	80	valid
71.0ms	584×	body	640	valid
32.0ms	350×	body	320	valid
13.0ms	163×	body	160	valid

Compiler

Compiled 207 to 176 computations (15% saved)

Details

analyze1.0ms (0.1%)

sample26.0ms (1.4%)

simplify15.0ms (0.8%)

prune3.0ms (0.1%)

localize5.0ms (0.3%)

rewrite5.0ms (0.3%)

series7.0ms (0.4%)

simplify92.0ms (4.7%)

prune17.0ms (0.9%)

localize5.0ms (0.3%)

rewrite8.0ms (0.4%)

series7.0ms (0.4%)

simplify92.0ms (4.7%)

prune34.0ms (1.7%)

localize11.0ms (0.5%)

rewrite12.0ms (0.6%)

series62.0ms (3.2%)

simplify81.0ms (4.1%)

prune61.0ms (3.1%)

localize8.0ms (0.4%)

rewrite12.0ms (0.6%)

series18.0ms (0.9%)

simplify83.0ms (4.2%)

prune85.0ms (4.3%)

regimes26.0ms (1.3%)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample1.2s (60.1%)

Profiling