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)

sample29.0ms (1.2%)

Algorithm

1×

intervals

Results

13.0ms	75×	body	2048	valid
4.0ms	125×	body	128	valid
4.0ms	32×	body	1024	valid
2.0ms	19×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify100.0ms (4%)

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

Error

15.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize10.0ms (0.4%)

Local error

Found 1 expressions with local error:

0.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
3×	`add-log-exp_binary64_2504` `cancel-sign-sub-inv_binary64_2431`
2×	`add-cube-cbrt_binary64_2500`
1×	`diff-atan_binary64_2622` `difference-of-squares_binary64_2434` `flip--_binary64_2440` `add-exp-log_binary64_2503` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `add-cbrt-cube_binary64_2501` `diff-log_binary64_2557` `pow1_binary64_2526` `flip3--_binary64_2469`

Counts

1 → 17

Calls

1 calls:

4.0ms

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

series22.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

22.0ms

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

Compiler

Compiled 42 to 36 computations (14.3% saved)

simplify70.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4992	306
1	4992	306

prune16.0ms (0.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	1	21

Error

0.4b

Counts

21 → 1

Compiler

Compiled 250 to 161 computations (35.6% saved)

localize6.0ms (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×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
4×	`add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526` `associate-r_binary64_2405`
3×	`associate-l_binary64_2406`
2×	`add-log-exp_binary64_2504` `associate-*r/_binary64_2407`
1×	`flip3-+_binary64_2468` `distribute-lft-in_binary64_2414` `*-commutative_binary64_2396` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `distribute-rgt-in_binary64_2415` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416` `cbrt-unprod_binary64_2498`

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))))

series54.0ms (2.2%)

Counts

2 → 9

Calls

2 calls:

40.0ms	(*.f64 N (+.f64 N 1))
13.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 127 to 115 computations (9.4% saved)

simplify73.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4927	392
1	4927	392

prune37.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	5	40

Error

0.4b

Counts

40 → 5

Compiler

Compiled 564 to 441 computations (21.8% saved)

localize8.0ms (0.3%)

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))))))
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)))))

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2487`
24×	`sqrt-prod_binary64_2481`
21×	`pow1_binary64_2526`
14×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
10×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483`
8×	`swap-sqr_binary64_2432`
6×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `associate-r_binary64_2405` `associate-l_binary64_2406`
5×	`pow-prod-up_binary64_2535`
4×	`add-log-exp_binary64_2504` `unswap-sqr_binary64_2433` `rem-sqrt-square_binary64_2478`
3×	`pow-prod-down_binary64_2536` `pow-sqr_binary64_2438`
1×	`sqr-abs_binary64_2480` `*-commutative_binary64_2396` `pow-plus_binary64_2528` `sqrt-unprod_binary64_2485` `rem-square-sqrt_binary64_2477` `pow2_binary64_2546` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`

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))))

series91.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
29.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
16.0ms	(.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))))))
15.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

Compiler

Compiled 432 to 372 computations (13.9% saved)

simplify77.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5103	1475

prune119.0ms (4.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	93	7	100

Error

0.4b

Counts

100 → 7

Compiler

Compiled 2129 to 1756 computations (17.5% saved)

localize11.0ms (0.4%)

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)))))

rewrite32.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`sqrt-pow1_binary64_2483`
45×	`pow1_binary64_2526`
30×	`pow1/2_binary64_2545` `pow-prod-up_binary64_2535`
16×	`add-sqr-sqrt_binary64_2487`
14×	`sqrt-prod_binary64_2481`
9×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
7×	`pow-prod-down_binary64_2536`
6×	`pow-sqr_binary64_2438` `associate-l_binary64_2406`
4×	`add-log-exp_binary64_2504`
3×	`rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
2×	`swap-sqr_binary64_2432` `sqrt-unprod_binary64_2485` `unswap-sqr_binary64_2433`
1×	`-commutative_binary64_2396` `associate-r*_binary64_2405`

Counts

4 → 85

Calls

4 calls:

19.0ms	(.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))))))))
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	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

series126.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
35.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
35.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
19.0ms	(.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))))))))

Compiler

Compiled 666 to 570 computations (14.4% saved)

simplify82.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4894	1397
1	4894	1397

prune148.0ms (6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	96	8	104

Error

0.3b

Counts

104 → 8

Compiler

Compiled 2677 to 2218 computations (17.1% saved)

regimes65.0ms (2.6%)

Accuracy

Total 0.1b remaining (10.9%)

Threshold costs 0.1b (10.9%)

Compiler

Compiled 764 to 660 computations (13.6% 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%)

sample1.3s (51%)

Algorithm

1×

intervals

Results

367.0ms	2145×	body	2048	valid
144.0ms	4111×	body	128	valid
124.0ms	1029×	body	1024	valid
46.0ms	486×	body	512	valid
15.0ms	229×	body	256	valid

Compiler

Compiled 401 to 348 computations (13.2% saved)

Details

analyze1.0ms (0.1%)

sample29.0ms (1.2%)

simplify100.0ms (4%)

prune2.0ms (0.1%)

localize10.0ms (0.4%)

rewrite6.0ms (0.2%)

series22.0ms (0.9%)

simplify70.0ms (2.8%)

prune16.0ms (0.6%)

localize6.0ms (0.2%)

rewrite9.0ms (0.4%)

series54.0ms (2.2%)

simplify73.0ms (2.9%)

prune37.0ms (1.5%)

localize8.0ms (0.3%)

rewrite18.0ms (0.7%)

series91.0ms (3.7%)

simplify77.0ms (3.1%)

prune119.0ms (4.8%)

localize11.0ms (0.4%)

rewrite32.0ms (1.3%)

series126.0ms (5.1%)

simplify82.0ms (3.3%)

prune148.0ms (6%)

regimes65.0ms (2.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (51%)

Profiling