Details

analyze813.0ms (5.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample193.0ms (1.3%)

Algorithm

1×

intervals

Results

86.0ms	52×	body	2048	valid
65.0ms	103×	body	1024	valid
11.0ms	33×	body	512	valid
5.0ms	7×	body	1024	invalid
4.0ms	53×	body	128	valid
3.0ms	1×	body	4096	valid
2.0ms	14×	body	256	valid
2.0ms	6×	body	512	invalid
2.0ms	16×	body	128	invalid
1.0ms	1×	body	2048	invalid
1.0ms	3×	body	256	invalid
1.0ms	12×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify221.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4939	22
1	4939	22

prune3.0ms (0%)

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: 49.8b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.6b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.7b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
9.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite186.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_3525`
486×	`add-sqr-sqrt_binary64_3541`
367×	`*-un-lft-identity_binary64_3519`
225×	`add-cube-cbrt_binary64_3554`
174×	`associate-r_binary64_3459`
168×	`difference-of-squares_binary64_3488`
88×	`unpow-prod-down_binary64_3598`
85×	`sqr-pow_binary64_3491`
84×	`difference-of-sqr-1_binary64_3489`
29×	`div-inv_binary64_3516`
28×	`distribute-lft-out--_binary64_3471`
19×	`add-exp-log_binary64_3557`
18×	`add-cbrt-cube_binary64_3555`
13×	`associate-/r_binary64_3463` `associate-/l_binary64_3464`
7×	`pow1_binary64_3580`
6×	`add-log-exp_binary64_3558` `div-exp_binary64_3570` `cbrt-undiv_binary64_3553`
3×	`pow-unpow_binary64_3596` `prod-exp_binary64_3568` `cancel-sign-sub-inv_binary64_3485` `associate-l_binary64_3460` `cbrt-unprod_binary64_3552` `unswap-sqr_binary64_3487`
2×	`associate-/l/_binary64_3466` `flip--_binary64_3494` `associate-/r/_binary64_3465` `flip3--_binary64_3523`
1×	`pow-exp_binary64_3587` `pow-prod-down_binary64_3590` `pow-to-exp_binary64_3588` `diff-log_binary64_3611` `div-sub_binary64_3524` `clear-num_binary64_3518` `sub-neg_binary64_3512` `associate-r/_binary64_3461` `-commutative_binary64_3450` `distribute-lft-out_binary64_3470` `pow-pow_binary64_3591` `frac-2neg_binary64_3530`

Counts

4 → 451

Calls

4 calls:

65.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
21.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
12.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
8.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series1.9s (12.5%)

Counts

4 → 12

Calls

4 calls:

633.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
568.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
352.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
303.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify150.0ms (1%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5117	14771

prune1.4s (9.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	453	10	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	454	10	464

Merged error: 16.6b

Counts

464 → 10

Compiler

Compiled 27170 to 16126 computations (40.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.3b	(*.f64 1/6 i)
15.2b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite68.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_3525`
97×	`add-sqr-sqrt_binary64_3541`
85×	`*-un-lft-identity_binary64_3519` `add-cube-cbrt_binary64_3554`
50×	`associate-r_binary64_3459`
25×	`add-cbrt-cube_binary64_3555` `add-exp-log_binary64_3557`
13×	`associate-/r*_binary64_3463` `pow1_binary64_3580`
9×	`div-inv_binary64_3516`
7×	`prod-exp_binary64_3568` `associate-l_binary64_3460` `cbrt-unprod_binary64_3552`
6×	`div-exp_binary64_3570` `cbrt-undiv_binary64_3553`
5×	`pow-prod-down_binary64_3590` `unswap-sqr_binary64_3487`
4×	`add-log-exp_binary64_3558`
3×	`associate-r/_binary64_3461` `associate-/l_binary64_3464` `*-commutative_binary64_3450`
2×	`flip-+_binary64_3493` `flip3-+_binary64_3522` `associate-/l/_binary64_3466` `associate-/r/_binary64_3465`
1×	`clear-num_binary64_3518` `distribute-lft-in_binary64_3468` `distribute-rgt-in_binary64_3469` `frac-2neg_binary64_3530`

Counts

4 → 179

Calls

4 calls:

23.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
9.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
8.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series300.0ms (2%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
92.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
90.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
24.0ms	(*.f64 1/6 i)

simplify109.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4928	5462
1	4928	5462

prune1.8s (11.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	179	12	191
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	180	21	201

Merged error: 6.6b

Counts

201 → 21

Compiler

Compiled 36153 to 23844 computations (34% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 100 (.f64 i (+.f64 50 (.f64 50/3 i))))
0.0b	(.f64 i (+.f64 50 (.f64 50/3 i)))
0.4b	(*.f64 50/3 i)
1.9b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_3541`
10×	`add-cbrt-cube_binary64_3555` `add-exp-log_binary64_3557` `*-un-lft-identity_binary64_3519` `add-cube-cbrt_binary64_3554` `pow1_binary64_3580`
9×	`associate-r_binary64_3459` `associate-l_binary64_3460`
6×	`add-log-exp_binary64_3558`
4×	`associate-*r/_binary64_3461`
3×	`flip-+_binary64_3493` `pow-prod-down_binary64_3590` `flip3-+_binary64_3522` `prod-exp_binary64_3568` `distribute-lft-in_binary64_3468` `cbrt-unprod_binary64_3552` `unswap-sqr_binary64_3487` `distribute-rgt-in_binary64_3469` `*-commutative_binary64_3450`
2×	`associate-+r+_binary64_3451`
1×	`+-commutative_binary64_3449` `sum-log_binary64_3610`

Counts

4 → 75

Calls

4 calls:

6.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
6.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
4.0ms	(*.f64 50/3 i)
4.0ms	(+.f64 100 (.f64 i (+.f64 50 (.f64 50/3 i))))

series208.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
79.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
21.0ms	(+.f64 100 (.f64 i (+.f64 50 (.f64 50/3 i))))
20.0ms	(*.f64 50/3 i)

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4864	1188
1	4864	1188

prune213.0ms (1.4%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	3	17	20
Picked	0	1	1
Done	0	0	0
Total	88	20	108

Merged error: 6.6b

Counts

108 → 20

Compiler

Compiled 3890 to 2832 computations (27.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 i 50/3)
1.9b	(.f64 n (exp.f64 (log.f64 (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))))))
2.2b	(exp.f64 (log.f64 (+.f64 100 (.f64 i (+.f64 50 (.f64 i 50/3))))))
10.2b	(log.f64 (+.f64 100 (.f64 i (+.f64 50 (.f64 i 50/3)))))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_3541`
12×	`*-un-lft-identity_binary64_3519` `add-cube-cbrt_binary64_3554`
10×	`log-prod_binary64_3605` `pow1_binary64_3580`
9×	`associate-r_binary64_3459`
8×	`add-cbrt-cube_binary64_3555` `add-exp-log_binary64_3557`
7×	`exp-sum_binary64_3565`
6×	`log-div_binary64_3606` `associate-l_binary64_3460`
4×	`add-log-exp_binary64_3558` `exp-diff_binary64_3567` `exp-prod_binary64_3571`
3×	`flip-+_binary64_3493` `flip3-+_binary64_3522` `unswap-sqr_binary64_3487`
2×	`log-pow_binary64_3608` `pow-prod-down_binary64_3590` `prod-exp_binary64_3568` `associate-r/_binary64_3461` `cbrt-unprod_binary64_3552` `-commutative_binary64_3450`
1×	`rem-log-exp_binary64_3560` `rem-exp-log_binary64_3559`

Counts

4 → 73

Calls

4 calls:

9.0ms	(.f64 n (exp.f64 (log.f64 (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))))))
4.0ms	(exp.f64 (log.f64 (+.f64 100 (.f64 i (+.f64 50 (.f64 i 50/3))))))
4.0ms	(*.f64 i 50/3)
3.0ms	(log.f64 (+.f64 100 (.f64 i (+.f64 50 (.f64 i 50/3)))))

series278.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(.f64 n (exp.f64 (log.f64 (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))))))
60.0ms	(exp.f64 (log.f64 (+.f64 100 (.f64 i (+.f64 50 (.f64 i 50/3))))))
32.0ms	(log.f64 (+.f64 100 (.f64 i (+.f64 50 (.f64 i 50/3)))))
21.0ms	(*.f64 i 50/3)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4870	1434
1	4870	1434

prune348.0ms (2.3%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	5	13	18
Picked	1	0	1
Done	0	1	1
Total	85	20	105

Merged error: 6.5b

Counts

105 → 20

Compiler

Compiled 6228 to 4741 computations (23.9% saved)

regimes214.0ms (1.4%)

Compiler: Compiled 1442 to 1122 computations (22.2% saved)

bsearch209.0ms (1.4%)

Steps

Iters	Range		Point
11	4.714557093300575e+206	7.432471180027278e+236	3.704250745838463e+223
7	0.0038021679823958612	0.30242565689387857	0.16917926315367307
10	-354785043709138.56	-20877.454553747233	-21149.344081563468

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	76
1	49	76

end0.0ms (0%)

sample6.0s (40.5%)

Algorithm

1×

intervals

Results

2.7s	1702×	body	2048	valid
1.6s	2662×	body	1024	valid
337.0ms	1167×	body	512	valid
139.0ms	1888×	body	128	valid
94.0ms	150×	body	1024	invalid
90.0ms	553×	body	256	valid
77.0ms	28×	body	4096	valid
73.0ms	203×	body	512	invalid
50.0ms	518×	body	128	invalid
36.0ms	163×	body	256	invalid
25.0ms	18×	body	2048	invalid
15.0ms	331×	body	128	nan

Compiler

Compiled 564 to 429 computations (23.9% saved)

Details

analyze813.0ms (5.5%)

sample193.0ms (1.3%)

simplify221.0ms (1.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite186.0ms (1.3%)

series1.9s (12.5%)

simplify150.0ms (1%)

prune1.4s (9.6%)

localize11.0ms (0.1%)

rewrite68.0ms (0.5%)

series300.0ms (2%)

simplify109.0ms (0.7%)

prune1.8s (11.9%)

localize8.0ms (0.1%)

rewrite25.0ms (0.2%)

series208.0ms (1.4%)

simplify83.0ms (0.6%)

prune213.0ms (1.4%)

localize13.0ms (0.1%)

rewrite27.0ms (0.2%)

series278.0ms (1.9%)

simplify72.0ms (0.5%)

prune348.0ms (2.3%)

regimes214.0ms (1.4%)

bsearch209.0ms (1.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.0s (40.5%)

Profiling