Details

analyze777.0ms (5.9%)

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%	35.7%	19.8%	13
45.5%	34.4%	20.1%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample149.0ms (1.1%)

Algorithm

1×

intervals

Results

63.0ms	48×	body	2048	valid
53.0ms	98×	body	1024	valid
11.0ms	41×	body	512	valid
4.0ms	58×	body	128	valid
2.0ms	3×	body	1024	invalid
2.0ms	11×	body	256	valid
1.0ms	6×	body	256	invalid
1.0ms	11×	body	128	invalid
1.0ms	1×	body	2048	invalid
1.0ms	2×	body	512	invalid
1.0ms	11×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify165.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5036	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: 47.2b

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)))
1.3b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.8b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
9.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite167.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_2812`
486×	`add-sqr-sqrt_binary64_2828`
367×	`*-un-lft-identity_binary64_2806`
225×	`add-cube-cbrt_binary64_2841`
174×	`associate-r_binary64_2746`
168×	`difference-of-squares_binary64_2775`
88×	`unpow-prod-down_binary64_2885`
85×	`sqr-pow_binary64_2778`
84×	`difference-of-sqr-1_binary64_2776`
29×	`div-inv_binary64_2803`
28×	`distribute-lft-out--_binary64_2758`
19×	`add-exp-log_binary64_2844`
18×	`add-cbrt-cube_binary64_2842`
13×	`associate-/r_binary64_2750` `associate-/l_binary64_2751`
7×	`pow1_binary64_2867`
6×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `add-log-exp_binary64_2845`
3×	`associate-l_binary64_2747` `cancel-sign-sub-inv_binary64_2772` `prod-exp_binary64_2855` `pow-unpow_binary64_2883` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774`
2×	`associate-/l/_binary64_2753` `flip3--_binary64_2810` `flip--_binary64_2781` `associate-/r/_binary64_2752`
1×	`pow-exp_binary64_2874` `distribute-lft-out_binary64_2757` `-commutative_binary64_2737` `div-sub_binary64_2811` `pow-pow_binary64_2878` `diff-log_binary64_2898` `sub-neg_binary64_2799` `pow-to-exp_binary64_2875` `clear-num_binary64_2805` `associate-r/_binary64_2748` `pow-prod-down_binary64_2877` `frac-2neg_binary64_2817`

Counts

4 → 451

Calls

4 calls:

59.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
20.0ms	(/.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)

series945.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

317.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
292.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
178.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
157.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify183.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4954	14743
1	4954	14743

prune798.0ms (6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	456	7	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	457	7	464

Merged error: 17.6b

Counts

464 → 7

Compiler

Compiled 13998 to 7345 computations (47.5% saved)

localize10.0ms (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)
15.4b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_2812`
97×	`add-sqr-sqrt_binary64_2828`
85×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
50×	`associate-r_binary64_2746`
25×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
13×	`associate-/r*_binary64_2750` `pow1_binary64_2867`
9×	`div-inv_binary64_2803`
7×	`associate-l_binary64_2747` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
6×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
5×	`pow-prod-down_binary64_2877` `unswap-sqr_binary64_2774`
4×	`add-log-exp_binary64_2845`
3×	`-commutative_binary64_2737` `associate-r/_binary64_2748` `associate-/l*_binary64_2751`
2×	`associate-/l/_binary64_2753` `flip-+_binary64_2780` `flip3-+_binary64_2809` `associate-/r/_binary64_2752`
1×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

Counts

4 → 179

Calls

4 calls:

18.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
10.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
7.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series148.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
45.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
45.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
10.0ms	(*.f64 1/6 i)

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4971	5462
1	4971	5462

prune293.0ms (2.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	181	17	198

Merged error: 8.1b

Counts

198 → 17

Compiler

Compiled 5909 to 3249 computations (45% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(.f64 i (+.f64 50 (.f64 50/3 i)))
0.5b	(*.f64 50/3 i)
3.1b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_2828`
9×	`associate-l_binary64_2747` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `associate-r*_binary64_2746` `pow1_binary64_2867`
4×	`associate-*r/_binary64_2748`
3×	`*-commutative_binary64_2737` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `add-log-exp_binary64_2845` `pow-prod-down_binary64_2877` `unswap-sqr_binary64_2774`
2×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `flip-+_binary64_2780` `flip3-+_binary64_2809`

Counts

3 → 62

Calls

3 calls:

7.0ms	(.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)

series87.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

40.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
36.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
10.0ms	(*.f64 50/3 i)

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5005	915

prune84.0ms (0.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	71	17	88

Merged error: 8.1b

Counts

88 → 17

Compiler

Compiled 1582 to 1160 computations (26.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))
0.3b	(*.f64 i 1/6)
2.1b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)
3.2b	(/.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i) (/.f64 1 n))

rewrite74.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

430×	`times-frac_binary64_2812`
214×	`add-sqr-sqrt_binary64_2828`
211×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
35×	`add-exp-log_binary64_2844`
30×	`div-inv_binary64_2803`
25×	`add-cbrt-cube_binary64_2842`
17×	`div-exp_binary64_2857`
16×	`associate-/r_binary64_2750` `associate-/l_binary64_2751`
11×	`pow1_binary64_2867`
9×	`cbrt-undiv_binary64_2840`
6×	`associate-r_binary64_2746`
4×	`associate-l_binary64_2747` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `add-log-exp_binary64_2845` `pow-prod-down_binary64_2877`
3×	`associate-/l/_binary64_2753`
2×	`1-exp_binary64_2850` `rec-exp_binary64_2856` `-commutative_binary64_2737` `flip-+_binary64_2780` `flip3-+_binary64_2809` `clear-num_binary64_2805` `associate-r/_binary64_2748` `unswap-sqr_binary64_2774` `frac-2neg_binary64_2817`
1×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `associate-/r/_binary64_2752`

Counts

4 → 289

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i) (/.f64 1 n))
7.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))
5.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)
4.0ms	(*.f64 i 1/6)

series124.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))
44.0ms	(/.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i) (/.f64 1 n))
21.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)
10.0ms	(*.f64 i 1/6)

simplify149.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4945	12081
1	4945	12081

prune558.0ms (4.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	297	4	301
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	300	18	318

Merged error: 8.1b

Counts

318 → 18

Compiler

Compiled 9950 to 5989 computations (39.8% saved)

regimes1.2s (9.2%)

Compiler: Compiled 13541 to 9255 computations (31.7% saved)

bsearch100.0ms (0.8%)

Steps

Iters	Range		Point
5	3.841522714324763e-07	1.0751989982496457e-06	1.0526062084788294e-06
8	-1.2471203750733142e+20	-20162399870516788.0	-20604699981894388.0

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	51	72
1	51	72

end0.0ms (0%)

sample6.9s (52.4%)

Algorithm

1×

intervals

Results

2.1s	1713×	body	2048	valid
1.4s	2667×	body	1024	valid
298.0ms	1204×	body	512	valid
116.0ms	1784×	body	128	valid
99.0ms	164×	body	1024	invalid
85.0ms	601×	body	256	valid
83.0ms	228×	body	512	invalid
64.0ms	31×	body	4096	valid
45.0ms	462×	body	128	invalid
32.0ms	146×	body	256	invalid
19.0ms	20×	body	2048	invalid
15.0ms	315×	body	128	nan

Compiler

Compiled 3427 to 2335 computations (31.9% saved)

Details

analyze777.0ms (5.9%)

sample149.0ms (1.1%)

simplify165.0ms (1.2%)

prune3.0ms (0%)

localize12.0ms (0.1%)

rewrite167.0ms (1.3%)

series945.0ms (7.1%)

simplify183.0ms (1.4%)

prune798.0ms (6%)

localize10.0ms (0.1%)

rewrite58.0ms (0.4%)

series148.0ms (1.1%)

simplify93.0ms (0.7%)

prune293.0ms (2.2%)

localize7.0ms (0.1%)

rewrite20.0ms (0.2%)

series87.0ms (0.7%)

simplify74.0ms (0.6%)

prune84.0ms (0.6%)

localize12.0ms (0.1%)

rewrite74.0ms (0.6%)

series124.0ms (0.9%)

simplify149.0ms (1.1%)

prune558.0ms (4.2%)

regimes1.2s (9.2%)

bsearch100.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.9s (52.4%)

Profiling