Details

analyze273.0ms (1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4894	172
1	4894	172
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample40.0ms (0.1%)

Algorithm

1×

intervals

Results

12.0ms	208×	body	128	valid
5.0ms	256×	pre	128	true
4.0ms	19×	body	1024	valid
3.0ms	20×	body	512	valid
1.0ms	8×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify76.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5371	43

prune3.0ms (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

24.9b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

1.2b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

21.1b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite326.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

11.5b

Rules

54×	`times-frac_binary64_1448`
47×	`*-un-lft-identity_binary64_1442`
25×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
17×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
14×	`associate-/r/_binary64_1388`
11×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out_binary64_1393`
10×	`associate-/l*_binary64_1387`
9×	`associate-/l/_binary64_1389`
7×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `associate-/r*_binary64_1386`
5×	`add-log-exp_binary64_1481`
4×	`frac-times_binary64_1452`
3×	`pow1_binary64_1503` `flip3--_binary64_1446` `flip--_binary64_1417`
2×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-l/_binary64_1385` `associate-r/_binary64_1384`
1×	`sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

3 → 111

Calls

3 calls:

38.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

22.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

15.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 5370 to 2710 computations (49.5% saved)

series1.8s (6.5%)

Error

0.0b

Counts

3 → 58

Calls

3 calls:

887.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

596.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

166.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 8459 to 6506 computations (23.1% saved)

simplify90.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5141	8422

prune345.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	3	170

Error

Counts

170 → 3

Compiler

Compiled 7551 to 4012 computations (46.9% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
0.8b	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
3.3b	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)

rewrite887.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

321×	`times-frac_binary64_1448`
290×	`*-un-lft-identity_binary64_1442`
211×	`add-sqr-sqrt_binary64_1464`
140×	`add-cube-cbrt_binary64_1477`
90×	`associate-r_binary64_1382`
44×	`distribute-lft-out_binary64_1393`
31×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
26×	`associate-/l*_binary64_1387`
24×	`associate-/r/_binary64_1388`
20×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
15×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
12×	`div-inv_binary64_1439`
7×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `associate-/r*_binary64_1386`
6×	`add-log-exp_binary64_1481` `pow1_binary64_1503`
4×	`associate-l_binary64_1383`
3×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `div-sub_binary64_1447` `associate-/l/_binary64_1389`
2×	`frac-times_binary64_1452` `associate-*l/_binary64_1385` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`sum-log_binary64_1533` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `associate-r/_binary64_1384` `-commutative_binary64_1373` `flip3--_binary64_1446` `flip--_binary64_1417`

Counts

4 → 295

Calls

4 calls:

46.0ms	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
34.0ms	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)
23.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
18.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 14908 to 7929 computations (46.8% saved)

series2.5s (9.2%)

Error

Counts

4 → 78

Calls

4 calls:

905.0ms	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)
640.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
607.0ms	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
168.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 12174 to 9224 computations (24.2% saved)

simplify163.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

373 → 373

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5003	17876

prune1.0s (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	373	0	373
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	373	3	376

Error

Counts

376 → 3

Compiler

Compiled 17832 to 9523 computations (46.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
0.1b	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.1b	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
1.2b	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

rewrite306.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

48×	`*-un-lft-identity_binary64_1442`
45×	`add-sqr-sqrt_binary64_1464`
35×	`times-frac_binary64_1448`
26×	`add-cube-cbrt_binary64_1477`
21×	`associate-r_binary64_1382`
20×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
8×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
7×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `associate-/l/_binary64_1389` `associate-/r*_binary64_1386`
6×	`add-log-exp_binary64_1481` `pow1_binary64_1503` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `associate-/r/_binary64_1388` `associate-/l*_binary64_1387`
4×	`distribute-lft-out_binary64_1393` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `frac-times_binary64_1452` `associate-l/_binary64_1385` `associate-l*_binary64_1383`
3×	`div-inv_binary64_1439`
2×	`unswap-sqr_binary64_1410` `associate-*r/_binary64_1384` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`sum-log_binary64_1533` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `div-sub_binary64_1447` `flip3--_binary64_1446` `flip--_binary64_1417`

Counts

4 → 129

Calls

4 calls:

27.0ms	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
24.0ms	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
22.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 5642 to 2885 computations (48.9% saved)

series2.0s (7.4%)

Error

Counts

4 → 75

Calls

4 calls:

925.0ms	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
601.0ms	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
180.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
169.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 10132 to 7704 computations (24% saved)

simplify104.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4978	7675
1	4978	7675

prune377.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	204	3	207

Error

Counts

207 → 3

Compiler

Compiled 8276 to 4600 computations (44.4% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b	(+.f64 (.f64 (/.f64 beta alpha) (/.f64 i alpha)) (.f64 (/.f64 i alpha) (/.f64 i alpha)))
7.5b	(/.f64 i (*.f64 alpha alpha))
8.8b	(-.f64 (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (/.f64 2 alpha))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (+.f64 (.f64 12 (+.f64 (.f64 (/.f64 beta alpha) (/.f64 i alpha)) (.f64 (/.f64 i alpha) (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))
10.7b	(/.f64 beta (*.f64 alpha alpha))

rewrite5.5s (20.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1498×	`frac-add_binary64_1450`
1475×	`associate-*r/_binary64_1384`
305×	`frac-sub_binary64_1451`
218×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
211×	`frac-times_binary64_1452` `associate-*l/_binary64_1385`
81×	`add-log-exp_binary64_1481`
46×	`sum-log_binary64_1533`
15×	`diff-log_binary64_1534`
14×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
11×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
9×	`add-cube-cbrt_binary64_1477`
6×	`times-frac_binary64_1448` `associate-/l*_binary64_1387`
4×	`pow1_binary64_1503` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `associate-/r*_binary64_1386`
1×	`flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `associate--l+_binary64_1379` `associate--r+_binary64_1378` `distribute-rgt-out_binary64_1395` `+-commutative_binary64_1372`

Counts

4 → 400

Calls

4 calls:

92.0ms	(-.f64 (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (/.f64 2 alpha))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (+.f64 (.f64 12 (+.f64 (.f64 (/.f64 beta alpha) (/.f64 i alpha)) (.f64 (/.f64 i alpha) (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))
9.0ms	(+.f64 (.f64 (/.f64 beta alpha) (/.f64 i alpha)) (.f64 (/.f64 i alpha) (/.f64 i alpha)))
5.0ms	(/.f64 beta (*.f64 alpha alpha))
5.0ms	(/.f64 i (*.f64 alpha alpha))

Compiler

Compiled 99320 to 33967 computations (65.8% saved)

series1.4s (5.3%)

Error

Counts

4 → 43

Calls

4 calls:

1.0s	(-.f64 (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (/.f64 2 alpha))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (+.f64 (.f64 12 (+.f64 (.f64 (/.f64 beta alpha) (/.f64 i alpha)) (.f64 (/.f64 i alpha) (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))
133.0ms	(+.f64 (.f64 (/.f64 beta alpha) (/.f64 i alpha)) (.f64 (/.f64 i alpha) (/.f64 i alpha)))
88.0ms	(/.f64 i (*.f64 alpha alpha))
86.0ms	(/.f64 beta (*.f64 alpha alpha))

Compiler

Compiled 6666 to 4328 computations (35.1% saved)

simplify878.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

443 → 443

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5822	125873

prune4.9s (18.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	443	0	443
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	443	3	446

Error

Counts

446 → 3

Compiler

Compiled 90505 to 32005 computations (64.6% saved)

regimes1.2s (4.3%)

Accuracy

Total 1.4b remaining (95.1%)

Threshold costs 0b (0%)

Compiler

Compiled 20520 to 13990 computations (31.8% saved)

bsearch6.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	104
1	51	104

end0.0ms (0%)

sample2.9s (10.7%)

Algorithm

1×

intervals

Results

380.0ms	6508×	body	128	valid
180.0ms	8000×	pre	128	true
148.0ms	664×	body	1024	valid
86.0ms	490×	body	512	valid
35.0ms	285×	body	256	valid
15.0ms	53×	body	2048	valid

Compiler

Compiled 2924 to 1995 computations (31.8% saved)

Details

analyze273.0ms (1%)

sample40.0ms (0.1%)

simplify76.0ms (0.3%)

prune3.0ms (0%)

localize13.0ms (0%)

rewrite326.0ms (1.2%)

series1.8s (6.5%)

simplify90.0ms (0.3%)

prune345.0ms (1.3%)

localize13.0ms (0%)

rewrite887.0ms (3.3%)

series2.5s (9.2%)

simplify163.0ms (0.6%)

prune1.0s (3.7%)

localize15.0ms (0.1%)

rewrite306.0ms (1.1%)

series2.0s (7.4%)

simplify104.0ms (0.4%)

prune377.0ms (1.4%)

localize34.0ms (0.1%)

rewrite5.5s (20.2%)

series1.4s (5.3%)

simplify878.0ms (3.2%)

prune4.9s (18.1%)

regimes1.2s (4.3%)

bsearch6.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (10.7%)

Profiling