Details

analyze1.5s (6.8%)

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)

sample310.0ms (1.4%)

Algorithm

1×

intervals

Results

153.0ms	55×	body	2048	valid
83.0ms	83×	body	1024	valid
23.0ms	40×	body	512	valid
7.0ms	61×	body	128	valid
5.0ms	4×	body	1024	invalid
4.0ms	1×	body	4096	valid
4.0ms	16×	body	256	valid
3.0ms	5×	body	512	invalid
2.0ms	9×	body	128	invalid
1.0ms	2×	body	256	invalid
1.0ms	7×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify319.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4966	22
1	4966	22

prune5.0ms (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: 44.6b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize17.0ms (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)))
0.4b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
6.6b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
9.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite350.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_2442`
485×	`add-sqr-sqrt_binary64_2457`
366×	`*-un-lft-identity_binary64_2436`
224×	`add-cube-cbrt_binary64_2468`
174×	`associate-r_binary64_2378`
168×	`difference-of-squares_binary64_2405`
88×	`unpow-prod-down_binary64_2512`
85×	`sqr-pow_binary64_2408`
84×	`difference-of-sqr-1_binary64_2406`
29×	`div-inv_binary64_2433`
28×	`distribute-lft-out--_binary64_2390`
19×	`add-exp-log_binary64_2471`
18×	`add-cbrt-cube_binary64_2469`
13×	`associate-/l_binary64_2383` `associate-/r_binary64_2382`
7×	`pow1_binary64_2494`
6×	`cbrt-undiv_binary64_2467` `add-log-exp_binary64_2472` `div-exp_binary64_2484`
3×	`prod-exp_binary64_2482` `pow-unpow_binary64_2510` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404` `associate-l_binary64_2379`
2×	`associate-/r/_binary64_2384` `flip3--_binary64_2440` `associate-/l/_binary64_2385` `flip--_binary64_2411`
1×	`distribute-lft-out_binary64_2389` `-commutative_binary64_2369` `diff-log_binary64_2525` `pow-prod-down_binary64_2504` `associate-r/_binary64_2380` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-exp_binary64_2501` `pow-pow_binary64_2505` `div-sub_binary64_2441` `frac-2neg_binary64_2447` `sub-neg_binary64_2429`

Counts

4 → 448

Calls

4 calls:

125.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
42.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
22.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
16.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series3.4s (15.5%)

Counts

4 → 12

Calls

4 calls:

1.1s	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.0s	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
650.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
548.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify297.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5097	14768

prune1.4s (6.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	455	5	460
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	456	5	461

Merged error: 17.2b

Counts

461 → 5

Compiler

Compiled 13947 to 7324 computations (47.5% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.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)
16.6b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite124.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_2442`
97×	`add-sqr-sqrt_binary64_2457`
85×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
50×	`associate-r_binary64_2378`
25×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
13×	`associate-/r*_binary64_2382` `pow1_binary64_2494`
9×	`div-inv_binary64_2433`
7×	`prod-exp_binary64_2482` `cbrt-unprod_binary64_2466` `associate-l_binary64_2379`
6×	`cbrt-undiv_binary64_2467` `div-exp_binary64_2484`
5×	`pow-prod-down_binary64_2504` `unswap-sqr_binary64_2404`
4×	`add-log-exp_binary64_2472`
3×	`-commutative_binary64_2369` `associate-/l_binary64_2383` `associate-*r/_binary64_2380`
2×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/r/_binary64_2384` `associate-/l/_binary64_2385`
1×	`distribute-rgt-in_binary64_2388` `clear-num_binary64_2435` `frac-2neg_binary64_2447` `distribute-lft-in_binary64_2387`

Counts

4 → 179

Calls

4 calls:

36.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
17.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
15.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
12.0ms	(*.f64 1/6 i)

series547.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
165.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
156.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
46.0ms	(*.f64 1/6 i)

simplify145.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5624	5462

prune521.0ms (2.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	181	15	196

Merged error: 7.6b

Counts

196 → 15

Compiler

Compiled 5863 to 3218 computations (45.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
0.1b	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
0.3b	(*.f64 i 1/6)
1.9b	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2457`
15×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494`
12×	`associate-l_binary64_2379`
11×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
10×	`associate-r_binary64_2378`
8×	`associate-*r/_binary64_2380`
6×	`prod-exp_binary64_2482` `distribute-rgt-in_binary64_2388` `pow-prod-down_binary64_2504` `cbrt-unprod_binary64_2466` `distribute-lft-in_binary64_2387`
4×	`*-commutative_binary64_2369` `add-log-exp_binary64_2472`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `unswap-sqr_binary64_2404`

Counts

4 → 86

Calls

4 calls:

14.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
12.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
11.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
7.0ms	(*.f64 i 1/6)

series512.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
159.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
143.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
42.0ms	(*.f64 i 1/6)

simplify95.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4943	1381
1	4943	1381

prune209.0ms (1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	99	14	113

Merged error: 7.6b

Counts

113 → 14

Compiler

Compiled 2149 to 1537 computations (28.5% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 1/6)
1.0b	(cbrt.f64 1/6)
1.0b	(cbrt.f64 1/6)
1.9b	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 i (*.f64 (cbrt.f64 1/6) (cbrt.f64 1/6))) (cbrt.f64 1/6)))))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64_2471` `cbrt-prod_binary64_2464` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494`
8×	`add-sqr-sqrt_binary64_2457` `add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
4×	`distribute-rgt-in_binary64_2388` `add-log-exp_binary64_2472` `associate-*r/_binary64_2380` `distribute-lft-in_binary64_2387`
3×	`pow1/3_binary64_2515` `prod-exp_binary64_2482` `pow-prod-down_binary64_2504` `cbrt-unprod_binary64_2466` `associate-l_binary64_2379`
1×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `-commutative_binary64_2369` `associate-r*_binary64_2378`

Counts

4 → 57

Calls

4 calls:

15.0ms	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 i (*.f64 (cbrt.f64 1/6) (cbrt.f64 1/6))) (cbrt.f64 1/6)))))
3.0ms	(cbrt.f64 1/6)
3.0ms	(cbrt.f64 1/6)
3.0ms	(cbrt.f64 1/6)

series298.0ms (1.4%)

Counts

4 → 6

Calls

4 calls:

297.0ms	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 i (*.f64 (cbrt.f64 1/6) (cbrt.f64 1/6))) (cbrt.f64 1/6)))))
0.0ms	(cbrt.f64 1/6)
0.0ms	(cbrt.f64 1/6)
0.0ms	(cbrt.f64 1/6)

simplify136.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4947	637
1	4947	637

prune140.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	63	14	77

Merged error: 7.6b

Counts

77 → 14

Compiler

Compiled 1361 to 1083 computations (20.4% saved)

regimes283.0ms (1.3%)

Compiler: Compiled 754 to 540 computations (28.4% saved)

bsearch218.0ms (1%)

Steps

Iters	Range		Point
5	9.982255063804125	31.383630798498903	13.623857027906789
9	-160423.5480050719	-0.17586239670600753	-0.183119611805929

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	73
1	45	73

end0.0ms (0%)

sample10.7s (49.6%)

Algorithm

1×

intervals

Results

5.0s	1779×	body	2048	valid
2.9s	2626×	body	1024	valid
610.0ms	1155×	body	512	valid
239.0ms	1848×	body	128	valid
213.0ms	194×	body	1024	invalid
198.0ms	40×	body	4096	valid
161.0ms	552×	body	256	valid
143.0ms	214×	body	512	invalid
77.0ms	433×	body	128	invalid
59.0ms	148×	body	256	invalid
53.0ms	21×	body	2048	invalid
30.0ms	357×	body	128	nan

Compiler

Compiled 478 to 342 computations (28.5% saved)

Details

analyze1.5s (6.8%)

sample310.0ms (1.4%)

simplify319.0ms (1.5%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite350.0ms (1.6%)

series3.4s (15.5%)

simplify297.0ms (1.4%)

prune1.4s (6.4%)

localize22.0ms (0.1%)

rewrite124.0ms (0.6%)

series547.0ms (2.5%)

simplify145.0ms (0.7%)

prune521.0ms (2.4%)

localize18.0ms (0.1%)

rewrite58.0ms (0.3%)

series512.0ms (2.4%)

simplify95.0ms (0.4%)

prune209.0ms (1%)

localize29.0ms (0.1%)

rewrite33.0ms (0.2%)

series298.0ms (1.4%)

simplify136.0ms (0.6%)

prune140.0ms (0.6%)

regimes283.0ms (1.3%)

bsearch218.0ms (1%)

simplify5.0ms (0%)

end0.0ms (0%)

sample10.7s (49.6%)

Profiling