Details

analyze46.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Compiler

Compiled 63 to 34 computations (46% saved)

sample41.0ms (0.2%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify136.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5395	79

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

55.8b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
37.6b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
47.6b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite842.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

37.9b

Rules

86×	`times-frac_binary64_1107`
66×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-/r/_binary64_1047`
61×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
46×	`add-sqr-sqrt_binary64_1123`
44×	`*-un-lft-identity_binary64_1101` `frac-times_binary64_1111`
34×	`associate-*r/_binary64_1043`
30×	`add-cube-cbrt_binary64_1136`
28×	`difference-of-squares_binary64_1070`
22×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `associate-*l/_binary64_1044`
19×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
16×	`pow1_binary64_1162`
14×	`associate-/l*_binary64_1046` `difference-of-sqr-1_binary64_1071`
9×	`div-inv_binary64_1098` `associate-/l/_binary64_1048`
7×	`associate-/r*_binary64_1045`
6×	`associate-r_binary64_1041`
4×	`add-log-exp_binary64_1140` `pow-prod-down_binary64_1172` `associate-l_binary64_1042`
3×	`swap-sqr_binary64_1068`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `*-commutative_binary64_1032`
1×	`flip3--_binary64_1105` `flip--_binary64_1076` `pow2_binary64_1182` `pow-prod-up_binary64_1171` `pow-plus_binary64_1164` `pow-sqr_binary64_1074` `unswap-sqr_binary64_1069`

Counts

4 → 228

Calls

4 calls:

40.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
26.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
16.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
13.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 19221 to 7168 computations (62.7% saved)

series8.6s (51.3%)

Error

10.3b

Counts

4 → 88

Calls

4 calls:

6.8s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
761.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
487.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
254.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 22543 to 14974 computations (33.6% saved)

simplify205.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5541	24309

prune1.1s (6.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	308	8	316
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	309	8	317

Error

7.6b

Counts

317 → 8

Compiler

Compiled 23808 to 10444 computations (56.1% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 7.6b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune12.0ms (0.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Error

7.6b

Counts

8 → 8

Compiler

Compiled 296 to 184 computations (37.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (/.f64 (.f64 beta beta) (*.f64 i i))))
0.7b	(/.f64 1/64 (*.f64 i i))
9.3b	(/.f64 (.f64 beta beta) (.f64 i i))
10.6b	(/.f64 (.f64 alpha alpha) (.f64 i i))

rewrite141.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

7.5b

Rules

35×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
8×	`add-cube-cbrt_binary64_1136`
6×	`pow1_binary64_1162`
5×	`times-frac_binary64_1107` `div-inv_binary64_1098` `associate-/l_binary64_1046` `associate-r*_binary64_1041`
4×	`add-log-exp_binary64_1140`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r_binary64_1045` `associate-r/_binary64_1043` `associate-l_binary64_1042`
1×	`pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `frac-add_binary64_1109` `flip3-+_binary64_1104` `flip-+_binary64_1075` `distribute-rgt-out_binary64_1054` `distribute-lft-out_binary64_1052` `*-commutative_binary64_1032`

Counts

4 → 88

Calls

4 calls:

13.0ms	(.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (/.f64 (.f64 beta beta) (*.f64 i i))))
6.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
6.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
4.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 2929 to 953 computations (67.5% saved)

series485.0ms (2.9%)

Error

7.6b

Counts

4 → 27

Calls

4 calls:

257.0ms	(.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (/.f64 (.f64 beta beta) (*.f64 i i))))
90.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
83.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
28.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1842 to 1359 computations (26.2% saved)

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4956	1511
1	4956	1511

prune131.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	114	9	123

Error

7.5b

Counts

123 → 9

Compiler

Compiled 3450 to 1343 computations (61.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 alpha (/.f64 alpha i))
0.1b	(*.f64 beta (/.f64 beta i))
0.7b	(/.f64 1/64 (*.f64 i i))
5.7b	(.f64 (/.f64 1/32 i) (+.f64 (.f64 beta (/.f64 beta i)) (*.f64 alpha (/.f64 alpha i))))

rewrite183.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.5b

Rules

45×	`add-sqr-sqrt_binary64_1123`
33×	`times-frac_binary64_1107`
30×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
29×	`associate-r_binary64_1041`
24×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
19×	`associate-l_binary64_1042`
10×	`pow1_binary64_1162`
9×	`associate-*r/_binary64_1043`
7×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
6×	`unswap-sqr_binary64_1069`
5×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098`
3×	`pow-prod-down_binary64_1172` `frac-times_binary64_1111` `-commutative_binary64_1032` `associate-/l_binary64_1046`
2×	`frac-add_binary64_1109` `flip3-+_binary64_1104` `flip-+_binary64_1075`
1×	`distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `associate-l/_binary64_1044` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r_binary64_1045`

Counts

4 → 125

Calls

4 calls:

12.0ms	(.f64 (/.f64 1/32 i) (+.f64 (.f64 beta (/.f64 beta i)) (*.f64 alpha (/.f64 alpha i))))
7.0ms	(*.f64 alpha (/.f64 alpha i))
7.0ms	(*.f64 beta (/.f64 beta i))
4.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 3907 to 1541 computations (60.6% saved)

series449.0ms (2.7%)

Error

7.5b

Counts

4 → 27

Calls

4 calls:

254.0ms	(.f64 (/.f64 1/32 i) (+.f64 (.f64 beta (/.f64 beta i)) (*.f64 alpha (/.f64 alpha i))))
72.0ms	(*.f64 beta (/.f64 beta i))
69.0ms	(*.f64 alpha (/.f64 alpha i))
27.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1764 to 1338 computations (24.1% saved)

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5012	2213

prune159.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	152	9	161

Error

7.5b

Counts

161 → 9

Compiler

Compiled 4214 to 1661 computations (60.6% saved)

regimes894.0ms (5.3%)

Accuracy

Total 2.8b remaining (25.5%)

Threshold costs 0b (0%)

Compiler

Compiled 13760 to 7913 computations (42.5% saved)

bsearch34.0ms (0.2%)

Steps

Iters	Range		Point
7	3.6625389487281318e+143	4.560156136360782e+145	3.965046976416819e+144

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	89
1	44	89

end0.0ms (0%)

sample3.1s (18.3%)

Algorithm

1×

intervals

Results

788.0ms	8000×	body	128	valid
174.0ms	8000×	pre	128	true

Compiler

Compiled 3495 to 2009 computations (42.5% saved)

Details

analyze46.0ms (0.3%)

sample41.0ms (0.2%)

simplify136.0ms (0.8%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite842.0ms (5%)

series8.6s (51.3%)

simplify205.0ms (1.2%)

prune1.1s (6.7%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0.1%)

prune12.0ms (0.1%)

localize13.0ms (0.1%)

rewrite141.0ms (0.8%)

series485.0ms (2.9%)

simplify76.0ms (0.4%)

prune131.0ms (0.8%)

localize14.0ms (0.1%)

rewrite183.0ms (1.1%)

series449.0ms (2.7%)

simplify89.0ms (0.5%)

prune159.0ms (0.9%)

regimes894.0ms (5.3%)

bsearch34.0ms (0.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (18.3%)

Profiling