Details

analyze918.0ms (5.8%)

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

Symmetry

Compiler

Compiled 16 to 12 computations (25% saved)

sample160.0ms (1%)

Algorithm

1×

intervals

Results

81.0ms	64×	body	2048	valid
41.0ms	79×	body	1024	valid
10.0ms	40×	body	512	valid
4.0ms	6×	body	1024	invalid
3.0ms	56×	body	128	valid
2.0ms	17×	body	256	valid
2.0ms	5×	body	512	invalid
1.0ms	15×	body	128	invalid
1.0ms	5×	body	256	invalid
1.0ms	13×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

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

48.2b

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)))
1.9b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.3b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
13.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite1.1s (7.2%)

Algorithm

1×	rewrite-expression-head

Error

47.9b

Rules

584×	`times-frac_binary64_3153`
486×	`add-sqr-sqrt_binary64_3169`
367×	`*-un-lft-identity_binary64_3147`
225×	`add-cube-cbrt_binary64_3182`
174×	`associate-r_binary64_3087`
168×	`difference-of-squares_binary64_3116`
88×	`unpow-prod-down_binary64_3226`
85×	`sqr-pow_binary64_3119`
84×	`difference-of-sqr-1_binary64_3117`
29×	`div-inv_binary64_3144`
28×	`distribute-lft-out--_binary64_3099`
19×	`add-exp-log_binary64_3185`
18×	`add-cbrt-cube_binary64_3183`
13×	`associate-/l_binary64_3092` `associate-/r_binary64_3091`
7×	`pow1_binary64_3208`
6×	`div-exp_binary64_3198` `add-log-exp_binary64_3186` `cbrt-undiv_binary64_3181`
3×	`pow-unpow_binary64_3224` `cancel-sign-sub-inv_binary64_3113` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `unswap-sqr_binary64_3115` `associate-l_binary64_3088`
2×	`flip3--_binary64_3151` `associate-/l/_binary64_3094` `flip--_binary64_3122` `associate-/r/_binary64_3093`
1×	`frac-2neg_binary64_3158` `div-sub_binary64_3152` `clear-num_binary64_3146` `distribute-lft-out_binary64_3098` `pow-pow_binary64_3219` `pow-to-exp_binary64_3216` `pow-exp_binary64_3215` `diff-log_binary64_3239` `sub-neg_binary64_3140` `pow-prod-down_binary64_3218` `associate-r/_binary64_3089` `-commutative_binary64_3078`

Counts

4 → 451

Calls

4 calls:

61.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
25.0ms	(/.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)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 14661 to 7953 computations (45.8% saved)

series783.0ms (5%)

Error

2.0b

Counts

4 → 36

Calls

4 calls:

270.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
248.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
139.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
81.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 2876 to 2125 computations (26.1% saved)

simplify162.0ms (1%)

Algorithm

1×	egg-herbie

Counts

487 → 487

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4972	15359
1	4972	15359

prune954.0ms (6.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	478	9	487
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	479	9	488

Error

0.2b

Counts

488 → 9

Compiler

Compiled 14619 to 7685 computations (47.4% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (+.f64 n (.f64 1/2 (.f64 n i))) (*.f64 1/2 i))
0.0b	(+.f64 n (.f64 1/2 (.f64 n i)))
0.0b	(.f64 100 (-.f64 (+.f64 n (.f64 1/2 (.f64 n i))) (.f64 1/2 i)))

rewrite72.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

10×	`add-log-exp_binary64_3186`
7×	`add-sqr-sqrt_binary64_3169`
5×	`pow1_binary64_3208` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
3×	`sub-neg_binary64_3140` `distribute-rgt-in_binary64_3097` `cancel-sign-sub-inv_binary64_3113` `associate--l+_binary64_3084` `distribute-lft-in_binary64_3096` `associate-l_binary64_3088` `associate-r_binary64_3087`
2×	`flip3--_binary64_3151` `associate-*r/_binary64_3089` `flip--_binary64_3122` `sum-log_binary64_3238` `diff-log_binary64_3239`
1×	`pow-prod-down_binary64_3218` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `unswap-sqr_binary64_3115` `*-commutative_binary64_3078` `flip3-+_binary64_3150` `flip-+_binary64_3121` `+-commutative_binary64_3077`

Counts

3 → 51

Calls

3 calls:

8.0ms	(.f64 100 (-.f64 (+.f64 n (.f64 1/2 (.f64 n i))) (.f64 1/2 i)))
6.0ms	(-.f64 (+.f64 n (.f64 1/2 (.f64 n i))) (*.f64 1/2 i))
3.0ms	(+.f64 n (.f64 1/2 (.f64 n i)))

Compiler

Compiled 1183 to 759 computations (35.8% saved)

series350.0ms (2.2%)

Error

0.2b

Counts

3 → 33

Calls

3 calls:

142.0ms	(.f64 100 (-.f64 (+.f64 n (.f64 1/2 (.f64 n i))) (.f64 1/2 i)))
114.0ms	(-.f64 (+.f64 n (.f64 1/2 (.f64 n i))) (*.f64 1/2 i))
73.0ms	(+.f64 n (.f64 1/2 (.f64 n i)))

Compiler

Compiled 936 to 761 computations (18.7% saved)

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5241	1265

prune85.0ms (0.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	82	11	93

Error

0.2b

Counts

93 → 11

Compiler

Compiled 1542 to 1119 computations (27.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1))) (cbrt.f64 (.f64 n (+.f64 (*.f64 i 1/2) 1))))
6.0b	(cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1)))
6.0b	(cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1)))
6.0b	(cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1)))

rewrite170.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

20×	`associate-*r/_binary64_3089`
18×	`cbrt-div_binary64_3179`
11×	`pow1_binary64_3208`
10×	`add-sqr-sqrt_binary64_3169`
9×	`pow1/3_binary64_3229` `flip3-+_binary64_3150` `flip-+_binary64_3121`
8×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
7×	`cbrt-prod_binary64_3178`
6×	`add-exp-log_binary64_3185`
4×	`add-log-exp_binary64_3186` `add-cbrt-cube_binary64_3183` `frac-times_binary64_3157` `swap-sqr_binary64_3114` `associate-l_binary64_3088` `associate-r_binary64_3087`
2×	`pow-prod-down_binary64_3218` `pow-prod-up_binary64_3217` `pow-sqr_binary64_3120` `associate-*l/_binary64_3090`
1×	`pow2_binary64_3228` `pow-plus_binary64_3210` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `unswap-sqr_binary64_3115` `*-commutative_binary64_3078`

Counts

4 → 72

Calls

4 calls:

8.0ms	(.f64 (cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1))) (cbrt.f64 (.f64 n (+.f64 (*.f64 i 1/2) 1))))
5.0ms	(cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1)))
5.0ms	(cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1)))
5.0ms	(cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1)))

Compiler

Compiled 3047 to 2428 computations (20.3% saved)

series911.0ms (5.8%)

Error

0.2b

Counts

4 → 37

Calls

4 calls:

240.0ms	(.f64 (cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1))) (cbrt.f64 (.f64 n (+.f64 (*.f64 i 1/2) 1))))
206.0ms	(cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1)))
198.0ms	(cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1)))
197.0ms	(cbrt.f64 (.f64 n (+.f64 (.f64 i 1/2) 1)))

Compiler

Compiled 4244 to 3589 computations (15.4% saved)

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4916	1953
1	4916	1953

prune211.0ms (1.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	109	11	120

Error

0.2b

Counts

120 → 11

Compiler

Compiled 4054 to 3167 computations (21.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
0.1b	(.f64 n (+.f64 100 (.f64 i 50)))
0.1b	(.f64 (+.f64 n (.f64 i (-.f64 (.f64 n 1/2) 1/2))) (+.f64 (.f64 n (+.f64 100 (.f64 i 50))) (.f64 i 50)))
32.0b	(/.f64 (.f64 (+.f64 n (.f64 i (-.f64 (.f64 n 1/2) 1/2))) (+.f64 (.f64 n (+.f64 100 (.f64 i 50))) (.f64 i 50))) (+.f64 (+.f64 n (.f64 1/2 (.f64 n i))) (*.f64 1/2 i)))

rewrite281.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

15×	`flip3-+_binary64_3150` `flip-+_binary64_3121`
14×	`add-sqr-sqrt_binary64_3169`
13×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
10×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
8×	`pow1_binary64_3208` `frac-times_binary64_3157` `associate-/l/_binary64_3094`
6×	`add-log-exp_binary64_3186` `associate-r/_binary64_3089` `associate-l_binary64_3088` `associate-r*_binary64_3087`
4×	`associate-*l/_binary64_3090`
3×	`prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `times-frac_binary64_3153` `associate-/r*_binary64_3091` `distribute-rgt-in_binary64_3097` `distribute-lft-in_binary64_3096`
2×	`div-exp_binary64_3198` `cbrt-undiv_binary64_3181` `associate-/r/_binary64_3093` `pow-prod-down_binary64_3218` `unswap-sqr_binary64_3115` `*-commutative_binary64_3078` `associate-+l+_binary64_3080`
1×	`frac-2neg_binary64_3158` `clear-num_binary64_3146` `div-inv_binary64_3144` `associate-/l*_binary64_3092` `sum-log_binary64_3238` `+-commutative_binary64_3077`

Counts

4 → 94

Calls

4 calls:

19.0ms	(/.f64 (.f64 (+.f64 n (.f64 i (-.f64 (.f64 n 1/2) 1/2))) (+.f64 (.f64 n (+.f64 100 (.f64 i 50))) (.f64 i 50))) (+.f64 (+.f64 n (.f64 1/2 (.f64 n i))) (*.f64 1/2 i)))
11.0ms	(.f64 (+.f64 n (.f64 i (-.f64 (.f64 n 1/2) 1/2))) (+.f64 (.f64 n (+.f64 100 (.f64 i 50))) (.f64 i 50)))
6.0ms	(+.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
6.0ms	(.f64 n (+.f64 100 (.f64 i 50)))

Compiler

Compiled 4904 to 3389 computations (30.9% saved)

series886.0ms (5.6%)

Error

0.2b

Counts

4 → 46

Calls

4 calls:

383.0ms	(/.f64 (.f64 (+.f64 n (.f64 i (-.f64 (.f64 n 1/2) 1/2))) (+.f64 (.f64 n (+.f64 100 (.f64 i 50))) (.f64 i 50))) (+.f64 (+.f64 n (.f64 1/2 (.f64 n i))) (*.f64 1/2 i)))
224.0ms	(.f64 (+.f64 n (.f64 i (-.f64 (.f64 n 1/2) 1/2))) (+.f64 (.f64 n (+.f64 100 (.f64 i 50))) (.f64 i 50)))
136.0ms	(+.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
80.0ms	(.f64 n (+.f64 100 (.f64 i 50)))

Compiler

Compiled 4038 to 3077 computations (23.8% saved)

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5365	4587

prune462.0ms (2.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	140	11	151

Error

0.2b

Counts

151 → 11

Compiler

Compiled 5756 to 3961 computations (31.2% saved)

regimes934.0ms (5.9%)

Accuracy

Total 11.2b remaining (95.3%)

Threshold costs 0b (0%)

Compiler

Compiled 9996 to 7127 computations (28.7% saved)

bsearch235.0ms (1.5%)

Steps

Iters	Range		Point
8	1.1732978747722337e+286	5.686495304695921e+289	2.852084085226162e+286
8	4.3875124683841505e+244	3.693180496930438e+248	1.853747270743323e+248
9	9.981503025574787e-38	4.1119062329121405e-32	3.3504134620314933e-32
10	-4047.4980348570502	-1.4056777015139969e-14	-2.1678153021847697e-06

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	330	251
1	330	251

Removed

()

end0.0ms (0%)

sample6.7s (42.3%)

Algorithm

1×

intervals

Results

2.2s	1785×	body	2048	valid
1.4s	2583×	body	1024	valid
284.0ms	1195×	body	512	valid
118.0ms	1842×	body	128	valid
105.0ms	175×	body	1024	invalid
89.0ms	42×	body	4096	valid
83.0ms	232×	body	512	invalid
79.0ms	553×	body	256	valid
49.0ms	494×	body	128	invalid
31.0ms	144×	body	256	invalid
18.0ms	17×	body	2048	invalid
13.0ms	305×	body	128	nan

Compiler

Compiled 2634 to 1854 computations (29.6% saved)

Details

analyze918.0ms (5.8%)

sample160.0ms (1%)

simplify79.0ms (0.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite1.1s (7.2%)

series783.0ms (5%)

simplify162.0ms (1%)

prune954.0ms (6.1%)

localize8.0ms (0%)

rewrite72.0ms (0.5%)

series350.0ms (2.2%)

simplify70.0ms (0.4%)

prune85.0ms (0.5%)

localize12.0ms (0.1%)

rewrite170.0ms (1.1%)

series911.0ms (5.8%)

simplify79.0ms (0.5%)

prune211.0ms (1.3%)

localize18.0ms (0.1%)

rewrite281.0ms (1.8%)

series886.0ms (5.6%)

simplify73.0ms (0.5%)

prune462.0ms (2.9%)

regimes934.0ms (5.9%)

bsearch235.0ms (1.5%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample6.7s (42.3%)

Profiling