Details

analyze924.0ms (6.6%)

Algorithm

1×	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%	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)

sample156.0ms (1.1%)

Algorithm

1×

intervals

Results

77.0ms	60×	body	2048	valid
40.0ms	77×	body	1024	valid
11.0ms	47×	body	512	valid
4.0ms	6×	body	1024	invalid
4.0ms	51×	body	128	valid
3.0ms	9×	body	512	invalid
3.0ms	21×	body	256	valid
2.0ms	18×	body	128	invalid
1.0ms	4×	body	256	invalid
0.0ms	7×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (90.0ms)

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

Error

46.4b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize8.0ms (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)))
1.8b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.8b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
12.1b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite169.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_2471`
486×	`add-sqr-sqrt_binary64_2487`
367×	`*-un-lft-identity_binary64_2465`
225×	`add-cube-cbrt_binary64_2500`
174×	`associate-r_binary64_2405`
168×	`difference-of-squares_binary64_2434`
88×	`unpow-prod-down_binary64_2544`
85×	`sqr-pow_binary64_2437`
84×	`difference-of-sqr-1_binary64_2435`
29×	`div-inv_binary64_2462`
28×	`distribute-lft-out--_binary64_2417`
19×	`add-exp-log_binary64_2503`
18×	`add-cbrt-cube_binary64_2501`
13×	`associate-/r_binary64_2409` `associate-/l_binary64_2410`
7×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
3×	`unswap-sqr_binary64_2433` `cancel-sign-sub-inv_binary64_2431` `prod-exp_binary64_2514` `pow-unpow_binary64_2542` `associate-l_binary64_2406` `cbrt-unprod_binary64_2498`
2×	`flip--_binary64_2440` `associate-/l/_binary64_2412` `associate-/r/_binary64_2411` `flip3--_binary64_2469`
1×	`-commutative_binary64_2396` `associate-r/_binary64_2407` `clear-num_binary64_2464` `div-sub_binary64_2470` `pow-exp_binary64_2533` `sub-neg_binary64_2458` `pow-to-exp_binary64_2534` `diff-log_binary64_2557` `pow-pow_binary64_2537` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416`

Counts

4 → 451

Calls

4 calls:

60.0ms	(*.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))
11.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series986.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

335.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
310.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
188.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
153.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify196.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4954	14743
1	4954	14743

prune863.0ms (6.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	455	8	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	456	8	464

Error

20.9b

Counts

464 → 8

Compiler

Compiled 14021 to 7360 computations (47.5% 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)))
0.4b	(*.f64 1/6 i)
18.9b	(/.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_2471`
97×	`add-sqr-sqrt_binary64_2487`
85×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
50×	`associate-r_binary64_2405`
25×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
13×	`associate-/r*_binary64_2409` `pow1_binary64_2526`
9×	`div-inv_binary64_2462`
7×	`prod-exp_binary64_2514` `associate-l_binary64_2406` `cbrt-unprod_binary64_2498`
6×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
5×	`unswap-sqr_binary64_2433` `pow-prod-down_binary64_2536`
4×	`add-log-exp_binary64_2504`
3×	`-commutative_binary64_2396` `associate-r/_binary64_2407` `associate-/l*_binary64_2410`
2×	`flip3-+_binary64_2468` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `associate-/r/_binary64_2411`
1×	`distribute-lft-in_binary64_2414` `clear-num_binary64_2464` `distribute-rgt-in_binary64_2415` `frac-2neg_binary64_2476`

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)))
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)

series159.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
52.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
42.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
11.0ms	(*.f64 1/6 i)

simplify110.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4971	5462
1	4971	5462

prune312.0ms (2.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	181	18	199

Error

8.5b

Counts

199 → 18

Compiler

Compiled 5974 to 3291 computations (44.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 50 (*.f64 50/3 i))
0.1b	(.f64 i (+.f64 50 (.f64 50/3 i)))
0.5b	(*.f64 50/3 i)
1.7b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_2487`
10×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
9×	`associate-r_binary64_2405` `associate-l_binary64_2406`
6×	`add-log-exp_binary64_2504`
4×	`associate-*r/_binary64_2407`
3×	`flip3-+_binary64_2468` `*-commutative_binary64_2396` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
2×	`distribute-lft-in_binary64_2414` `distribute-rgt-in_binary64_2415`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
6.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
4.0ms	(*.f64 50/3 i)
3.0ms	(+.f64 50 (*.f64 50/3 i))

series117.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
39.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
23.0ms	(+.f64 50 (*.f64 50/3 i))
12.0ms	(*.f64 50/3 i)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4938	1060
1	4938	1060

prune105.0ms (0.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	84	19	103

Error

8.5b

Counts

103 → 19

Compiler

Compiled 1830 to 1361 computations (25.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))))
12.4b	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
12.4b	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
12.4b	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-*r/_binary64_2407` `add-sqr-sqrt_binary64_2487`
6×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `cbrt-div_binary64_2497` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
4×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `flip-+_binary64_2439`
3×	`pow1/3_binary64_2547` `associate-r_binary64_2405` `cbrt-prod_binary64_2496` `associate-l_binary64_2406`
1×	`distribute-lft-in_binary64_2414` `*-commutative_binary64_2396` `unswap-sqr_binary64_2433` `distribute-rgt-in_binary64_2415` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`

Counts

4 → 55

Calls

4 calls:

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

series430.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
130.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
129.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
39.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))))

simplify114.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4865	1667
1	4865	1667

prune152.0ms (1.1%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	61	6	67
Fresh	2	15	17
Picked	1	0	1
Done	0	1	1
Total	64	22	86

Error

8.5b

Counts

86 → 22

Compiler

Compiled 3147 to 2387 computations (24.1% saved)

regimes1.5s (10.4%)

Accuracy

Total 6.6b remaining (43.5%)

Threshold costs 0b (0%)

Compiler

Compiled 14430 to 10091 computations (30.1% saved)

bsearch123.0ms (0.9%)

Steps

Iters	Range		Point
7	0.20449193727261442	6.812707797302908	0.44104711938434427
9	-1.5423901741043836e-20	-6.1399468800122396e-27	-1.5142820983801714e-20

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	87
1	49	87

end0.0ms (0%)

sample7.3s (52%)

Algorithm

1×

intervals

Results

2.1s	1781×	body	2048	valid
1.4s	2610×	body	1024	valid
298.0ms	1194×	body	512	valid
130.0ms	1809×	body	128	valid
92.0ms	152×	body	1024	invalid
86.0ms	237×	body	512	invalid
83.0ms	575×	body	256	valid
71.0ms	31×	body	4096	valid
50.0ms	495×	body	128	invalid
31.0ms	140×	body	256	invalid
23.0ms	23×	body	2048	invalid
13.0ms	288×	body	128	nan

Compiler

Compiled 3663 to 2553 computations (30.3% saved)

Details

analyze924.0ms (6.6%)

sample156.0ms (1.1%)

simplify96.0ms (0.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite169.0ms (1.2%)

series986.0ms (7.1%)

simplify196.0ms (1.4%)

prune863.0ms (6.2%)

localize11.0ms (0.1%)

rewrite58.0ms (0.4%)

series159.0ms (1.1%)

simplify110.0ms (0.8%)

prune312.0ms (2.2%)

localize8.0ms (0.1%)

rewrite24.0ms (0.2%)

series117.0ms (0.8%)

simplify72.0ms (0.5%)

prune105.0ms (0.8%)

localize14.0ms (0.1%)

rewrite26.0ms (0.2%)

series430.0ms (3.1%)

simplify114.0ms (0.8%)

prune152.0ms (1.1%)

regimes1.5s (10.4%)

bsearch123.0ms (0.9%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.3s (52%)

Profiling