Details

analyze1.7s (7.9%)

Algorithm

2×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4977	44
1	4977	44
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
42.6%	40.3%	17.1%	12
44.5%	35.7%	19.8%	13
44.5%	35.7%	19.8%	13
45.5%	34.4%	20.1%	14
45.5%	34.4%	20.1%	14

Compiler

Compiled 32 to 24 computations (25% saved)

sample1.4s (6.2%)

Algorithm

2×

intervals

Results

150.0ms	122×	body	2048	valid
94.0ms	165×	body	1024	valid
18.0ms	67×	body	512	valid
9.0ms	16×	body	1024	invalid
9.0ms	163×	body	128	nan
8.0ms	22×	body	512	invalid
7.0ms	115×	body	128	valid
6.0ms	2×	body	4096	valid
6.0ms	54×	body	128	invalid
6.0ms	41×	body	256	valid
3.0ms	12×	body	256	invalid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 6031 to 5275 computations (12.5% saved)

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5036	22

prune4.0ms (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

Error

46.0b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
2.0b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
4.6b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
9.5b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite1.6s (7.2%)

Algorithm

1×	rewrite-expression-head

Error

45.8b

Rules

584×	`times-frac_binary64_3494`
486×	`add-sqr-sqrt_binary64_3510`
367×	`*-un-lft-identity_binary64_3488`
225×	`add-cube-cbrt_binary64_3523`
174×	`associate-r_binary64_3428`
168×	`difference-of-squares_binary64_3457`
88×	`unpow-prod-down_binary64_3567`
85×	`sqr-pow_binary64_3460`
84×	`difference-of-sqr-1_binary64_3458`
29×	`div-inv_binary64_3485`
28×	`distribute-lft-out--_binary64_3440`
19×	`add-exp-log_binary64_3526`
18×	`add-cbrt-cube_binary64_3524`
13×	`associate-/l_binary64_3433` `associate-/r_binary64_3432`
7×	`pow1_binary64_3549`
6×	`div-exp_binary64_3539` `add-log-exp_binary64_3527` `cbrt-undiv_binary64_3522`
3×	`pow-unpow_binary64_3565` `cancel-sign-sub-inv_binary64_3454` `prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `unswap-sqr_binary64_3456` `associate-l_binary64_3429`
2×	`flip3--_binary64_3492` `associate-/l/_binary64_3435` `flip--_binary64_3463` `associate-/r/_binary64_3434`
1×	`frac-2neg_binary64_3499` `div-sub_binary64_3493` `clear-num_binary64_3487` `distribute-lft-out_binary64_3439` `pow-pow_binary64_3560` `pow-to-exp_binary64_3557` `pow-exp_binary64_3556` `diff-log_binary64_3580` `sub-neg_binary64_3481` `pow-prod-down_binary64_3559` `associate-r/_binary64_3430` `-commutative_binary64_3419`

Counts

4 → 451

Calls

4 calls:

58.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
19.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
11.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 14661 to 7953 computations (45.8% saved)

series1.4s (6.6%)

Error

2.6b

Counts

4 → 47

Calls

4 calls:

476.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
426.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
263.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
197.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 4129 to 3059 computations (25.9% saved)

simplify190.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

498 → 498

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4941	16033
1	4941	16033

prune994.0ms (4.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	488	10	498
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	489	10	499

Error

0.5b

Counts

499 → 10

Compiler

Compiled 15144 to 7995 computations (47.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/6 (.f64 i i))
1.9b	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
2.0b	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
7.3b	(/.f64 (*.f64 i i) n)

rewrite289.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

22×	`associate-*r/_binary64_3430`
20×	`frac-add_binary64_3496`
18×	`flip3-+_binary64_3491` `flip-+_binary64_3462`
16×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
13×	`add-log-exp_binary64_3527`
12×	`add-sqr-sqrt_binary64_3510`
11×	`pow1_binary64_3549`
9×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
6×	`sum-log_binary64_3579` `associate-l_binary64_3429`
5×	`prod-exp_binary64_3537` `cbrt-unprod_binary64_3521`
4×	`pow-prod-down_binary64_3559` `associate-r_binary64_3428`
3×	`times-frac_binary64_3494` `associate-/r*_binary64_3432`
2×	`div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `distribute-rgt-in_binary64_3438` `associate-+r+_binary64_3420` `distribute-lft-in_binary64_3437` `unswap-sqr_binary64_3456` `*-commutative_binary64_3419`
1×	`frac-2neg_binary64_3499` `clear-num_binary64_3487` `div-inv_binary64_3485` `associate-/l*_binary64_3433` `associate-+l+_binary64_3421` `+-commutative_binary64_3418`

Counts

4 → 90

Calls

4 calls:

14.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
9.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
6.0ms	(.f64 1/6 (.f64 i i))
5.0ms	(/.f64 (*.f64 i i) n)

Compiler

Compiled 5383 to 2602 computations (51.7% saved)

series975.0ms (4.4%)

Error

0.5b

Counts

4 → 36

Calls

4 calls:

589.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
190.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
112.0ms	(/.f64 (*.f64 i i) n)
36.0ms	(.f64 1/6 (.f64 i i))

Compiler

Compiled 2657 to 1882 computations (29.2% saved)

simplify88.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5436	4694

prune292.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	125	11	136

Error

0.4b

Counts

136 → 11

Compiler

Compiled 5779 to 3134 computations (45.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/3 (.f64 i (/.f64 i n)))
0.2b	(.f64 1/6 (.f64 i i))
1.9b	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
2.0b	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (.f64 i (/.f64 i n))))) (.f64 -1/2 (+.f64 i (.f64 i i))))

rewrite287.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

24×	`associate-*r/_binary64_3430`
20×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524` `frac-add_binary64_3496`
18×	`flip3-+_binary64_3491` `flip-+_binary64_3462`
16×	`pow1_binary64_3549`
13×	`add-log-exp_binary64_3527`
11×	`add-sqr-sqrt_binary64_3510`
9×	`prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `associate-l_binary64_3429`
8×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
7×	`pow-prod-down_binary64_3559`
6×	`sum-log_binary64_3579`
5×	`associate-r_binary64_3428`
3×	`*-commutative_binary64_3419`
2×	`distribute-rgt-in_binary64_3438` `associate-+r+_binary64_3420` `distribute-lft-in_binary64_3437` `unswap-sqr_binary64_3456`
1×	`associate-+l+_binary64_3421` `+-commutative_binary64_3418` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522`

Counts

4 → 90

Calls

4 calls:

14.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (.f64 i (/.f64 i n))))) (.f64 -1/2 (+.f64 i (.f64 i i))))
7.0ms	(.f64 1/3 (.f64 i (/.f64 i n)))
7.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
6.0ms	(.f64 1/6 (.f64 i i))

Compiler

Compiled 5408 to 2633 computations (51.3% saved)

series1.0s (4.7%)

Error

0.4b

Counts

4 → 36

Calls

4 calls:

602.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (.f64 i (/.f64 i n))))) (.f64 -1/2 (+.f64 i (.f64 i i))))
198.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
137.0ms	(.f64 1/3 (.f64 i (/.f64 i n)))
44.0ms	(.f64 1/6 (.f64 i i))

Compiler

Compiled 2657 to 1904 computations (28.3% saved)

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5026	4764

prune287.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	126	11	137

Error

0.4b

Counts

137 → 11

Compiler

Compiled 5755 to 3154 computations (45.2% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.5b	(.f64 n (.f64 i i))
7.7b	(+.f64 (.f64 (.f64 n (.f64 i i)) 50/3) (+.f64 (.f64 (/.f64 (pow.f64 i 3) n) 275/6) (.f64 n (+.f64 100 (.f64 25/6 (pow.f64 i 3))))))
8.5b	(+.f64 (.f64 25 (+.f64 (pow.f64 i 3) (/.f64 (pow.f64 i 3) (.f64 n n)))) (.f64 50 (+.f64 i (.f64 i i))))
12.5b	(/.f64 (pow.f64 i 3) (*.f64 n n))

rewrite428.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

22×	`add-exp-log_binary64_3526`
14×	`add-cbrt-cube_binary64_3524`
12×	`add-sqr-sqrt_binary64_3510` `times-frac_binary64_3494` `associate-/l*_binary64_3433`
11×	`add-log-exp_binary64_3527` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
9×	`pow1_binary64_3549`
8×	`associate-*r/_binary64_3430`
6×	`prod-exp_binary64_3537` `div-exp_binary64_3539` `unpow-prod-down_binary64_3567` `cube-prod_binary64_3516` `flip3-+_binary64_3491` `flip-+_binary64_3462`
4×	`cbrt-unprod_binary64_3521` `sum-log_binary64_3579` `frac-add_binary64_3496`
3×	`associate-+r+_binary64_3420` `pow-prod-down_binary64_3559` `associate-l_binary64_3429`
2×	`pow-to-exp_binary64_3557` `pow-exp_binary64_3556` `cbrt-undiv_binary64_3522` `unpow3_binary64_3554` `cube-mult_binary64_3518` `sqr-pow_binary64_3460` `distribute-rgt-in_binary64_3438` `associate-+l+_binary64_3421` `distribute-lft-in_binary64_3437` `+-commutative_binary64_3418`
1×	`frac-2neg_binary64_3499` `clear-num_binary64_3487` `div-inv_binary64_3485` `associate-/r_binary64_3432` `unswap-sqr_binary64_3456` `associate-r_binary64_3428` `-commutative_binary64_3419`

Counts

4 → 94

Calls

4 calls:

21.0ms	(+.f64 (.f64 25 (+.f64 (pow.f64 i 3) (/.f64 (pow.f64 i 3) (.f64 n n)))) (.f64 50 (+.f64 i (.f64 i i))))
19.0ms	(+.f64 (.f64 (.f64 n (.f64 i i)) 50/3) (+.f64 (.f64 (/.f64 (pow.f64 i 3) n) 275/6) (.f64 n (+.f64 100 (.f64 25/6 (pow.f64 i 3))))))
7.0ms	(/.f64 (pow.f64 i 3) (*.f64 n n))
6.0ms	(.f64 n (.f64 i i))

Compiler

Compiled 6959 to 3919 computations (43.7% saved)

series1.1s (4.8%)

Error

0.4b

Counts

4 → 33

Calls

4 calls:

493.0ms	(+.f64 (.f64 25 (+.f64 (pow.f64 i 3) (/.f64 (pow.f64 i 3) (.f64 n n)))) (.f64 50 (+.f64 i (.f64 i i))))
205.0ms	(+.f64 (.f64 (.f64 n (.f64 i i)) 50/3) (+.f64 (.f64 (/.f64 (pow.f64 i 3) n) 275/6) (.f64 n (+.f64 100 (.f64 25/6 (pow.f64 i 3))))))
166.0ms	(/.f64 (pow.f64 i 3) (*.f64 n n))
108.0ms	(.f64 n (.f64 i i))

Compiler

Compiled 5234 to 3591 computations (31.4% saved)

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5078	2792

prune430.0ms (2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	125	13	138

Error

0.4b

Counts

138 → 13

Compiler

Compiled 8336 to 4750 computations (43% saved)

regimes1.6s (7.1%)

Accuracy

Total 11.8b remaining (95.8%)

Threshold costs 0b (0%)

Compiler

Compiled 14383 to 9998 computations (30.5% saved)

bsearch198.0ms (0.9%)

Steps

Iters	Range		Point
11	2.1403337328539446e-10	2.5697688537369464e+20	0.006229383881859722
9	-0.009038278333221874	-1.4784146240838328e-09	-0.00014452224618902238

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	107
1	83	107

end0.0ms (0%)

sample7.4s (33.7%)

Algorithm

1×

intervals

Results

2.1s	1768×	body	2048	valid
1.4s	2604×	body	1024	valid
280.0ms	1183×	body	512	valid
117.0ms	192×	body	1024	invalid
116.0ms	1870×	body	128	valid
95.0ms	2320×	body	128	nan
90.0ms	243×	body	512	invalid
76.0ms	546×	body	256	valid
68.0ms	826×	body	128	invalid
63.0ms	29×	body	4096	valid
27.0ms	133×	body	256	invalid
14.0ms	15×	body	2048	invalid

Compiler

Compiled 3634 to 2522 computations (30.6% saved)

Details

analyze1.7s (7.9%)

sample1.4s (6.2%)

simplify77.0ms (0.4%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite1.6s (7.2%)

series1.4s (6.6%)

simplify190.0ms (0.9%)

prune994.0ms (4.5%)

localize18.0ms (0.1%)

rewrite289.0ms (1.3%)

series975.0ms (4.4%)

simplify88.0ms (0.4%)

prune292.0ms (1.3%)

localize23.0ms (0.1%)

rewrite287.0ms (1.3%)

series1.0s (4.7%)

simplify84.0ms (0.4%)

prune287.0ms (1.3%)

localize33.0ms (0.2%)

rewrite428.0ms (2%)

series1.1s (4.8%)

simplify60.0ms (0.3%)

prune430.0ms (2%)

regimes1.6s (7.1%)

bsearch198.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.4s (33.7%)

Profiling