Details

analyze44.0ms (0.4%)

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)

sample35.0ms (0.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify135.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

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

52.5b

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))))
36.1b	(/.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))
44.8b	(/.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))))

rewrite150.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64_1448`
66×	`associate-/r/_binary64_1388` `flip3-+_binary64_1445` `flip-+_binary64_1416`
61×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
46×	`add-sqr-sqrt_binary64_1464`
44×	`frac-times_binary64_1452` `*-un-lft-identity_binary64_1442`
34×	`associate-*r/_binary64_1384`
30×	`add-cube-cbrt_binary64_1477`
28×	`difference-of-squares_binary64_1411`
22×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `associate-*l/_binary64_1385`
19×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
16×	`pow1_binary64_1503`
14×	`associate-/l*_binary64_1387` `difference-of-sqr-1_binary64_1412`
9×	`associate-/l/_binary64_1389` `div-inv_binary64_1439`
7×	`associate-/r*_binary64_1386`
6×	`associate-r_binary64_1382`
4×	`associate-l_binary64_1383` `pow-prod-down_binary64_1513` `add-log-exp_binary64_1481`
3×	`swap-sqr_binary64_1409`
2×	`clear-num_binary64_1441` `*-commutative_binary64_1373` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
1×	`pow2_binary64_1523` `pow-plus_binary64_1505` `flip3--_binary64_1446` `pow-sqr_binary64_1415` `flip--_binary64_1417` `pow-prod-up_binary64_1512` `unswap-sqr_binary64_1410`

Counts

4 → 228

Calls

4 calls:

47.0ms	(/.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))
27.0ms	(/.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))))
14.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))

series1.9s (17.1%)

Counts

4 → 12

Calls

4 calls:

1.6s	(/.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))
210.0ms	(/.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))))
95.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
47.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify152.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5261	18181

prune702.0ms (6.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	233	7	240
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	233	8	241

Error

34.2b

Counts

241 → 8

Compiler

Compiled 17724 to 6652 computations (62.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.5b	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
36.2b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.4b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite130.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_1448`
174×	`*-un-lft-identity_binary64_1442`
170×	`add-sqr-sqrt_binary64_1464`
106×	`add-cube-cbrt_binary64_1477`
34×	`associate-/r/_binary64_1388`
32×	`difference-of-squares_binary64_1411`
28×	`associate-/l*_binary64_1387`
25×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
18×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
17×	`associate-/r*_binary64_1386` `div-inv_binary64_1439`
16×	`difference-of-sqr-1_binary64_1412` `distribute-lft-out--_binary64_1394`
11×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
10×	`distribute-lft-out_binary64_1393`
6×	`associate-/l/_binary64_1389`
4×	`clear-num_binary64_1441` `add-log-exp_binary64_1481` `frac-2neg_binary64_1453` `pow1_binary64_1503`
2×	`associate-*r/_binary64_1384` `cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
1×	`flip3--_binary64_1446` `flip--_binary64_1417`

Counts

4 → 268

Calls

4 calls:

22.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
22.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
13.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
13.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series461.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
116.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
98.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
64.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify178.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4952	16880
1	4952	16880

prune815.0ms (7.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	275	5	280
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	279	9	288

Error

34.2b

Counts

288 → 9

Compiler

Compiled 21323 to 8688 computations (59.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.5b	(/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))))
36.2b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.4b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite134.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_1448`
174×	`*-un-lft-identity_binary64_1442`
170×	`add-sqr-sqrt_binary64_1464`
106×	`add-cube-cbrt_binary64_1477`
33×	`associate-/r/_binary64_1388`
32×	`difference-of-squares_binary64_1411`
25×	`associate-/r*_binary64_1386` `add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
20×	`associate-/l*_binary64_1387`
18×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
17×	`div-inv_binary64_1439`
16×	`difference-of-sqr-1_binary64_1412` `distribute-lft-out--_binary64_1394`
11×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
10×	`distribute-lft-out_binary64_1393`
7×	`associate-/l/_binary64_1389`
4×	`clear-num_binary64_1441` `add-log-exp_binary64_1481` `frac-2neg_binary64_1453` `pow1_binary64_1503`
2×	`associate-*r/_binary64_1384` `cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
1×	`flip3--_binary64_1446` `flip--_binary64_1417` `div-sub_binary64_1447`

Counts

4 → 269

Calls

4 calls:

23.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
22.0ms	(/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))))
14.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
14.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

series523.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))))
113.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
104.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
64.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify162.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5192	17021

prune897.0ms (8.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	280	1	281
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	281	9	290

Error

34.0b

Counts

290 → 9

Compiler

Compiled 21872 to 9177 computations (58% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.5b	(/.f64 (.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
36.2b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.5b	(.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2))))

rewrite111.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`times-frac_binary64_1448`
63×	`*-un-lft-identity_binary64_1442`
51×	`add-sqr-sqrt_binary64_1464`
42×	`add-exp-log_binary64_1480`
36×	`add-cube-cbrt_binary64_1477`
32×	`add-cbrt-cube_binary64_1478`
18×	`associate-/r/_binary64_1388`
16×	`div-exp_binary64_1493`
15×	`associate-r_binary64_1382`
14×	`associate-/r*_binary64_1386`
13×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
12×	`cbrt-undiv_binary64_1476`
11×	`associate-/l*_binary64_1387`
10×	`distribute-lft-out_binary64_1393` `prod-exp_binary64_1491`
9×	`associate-/l/_binary64_1389` `div-inv_binary64_1439`
6×	`cbrt-unprod_binary64_1475` `pow1_binary64_1503`
4×	`associate-r/_binary64_1384` `add-log-exp_binary64_1481` `frac-times_binary64_1452` `difference-of-squares_binary64_1411` `associate-l/_binary64_1385`
3×	`clear-num_binary64_1441` `associate-l_binary64_1383` `frac-2neg_binary64_1453` `unswap-sqr_binary64_1410`
2×	`1-exp_binary64_1486` `difference-of-sqr-1_binary64_1412` `rec-exp_binary64_1492` `un-div-inv_binary64_1440` `distribute-lft-out--_binary64_1394`
1×	`flip3--_binary64_1446` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `flip--_binary64_1417`

Counts

4 → 176

Calls

4 calls:

26.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
23.0ms	(/.f64 (.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
16.0ms	(.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2))))
14.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

series472.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(/.f64 (.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
114.0ms	(.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2))))
106.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
62.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify114.0ms (1%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5046	7816

prune447.0ms (4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	188	9	197

Error

34.0b

Counts

197 → 9

Compiler

Compiled 12677 to 5350 computations (57.8% saved)

regimes839.0ms (7.5%)

Accuracy

Total 2.5b remaining (6.9%)

Threshold costs 0b (0%)

Compiler

Compiled 15508 to 7765 computations (49.9% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 53 to 27 computations (49.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	164
1	44	164

end0.0ms (0%)

sample2.7s (23.8%)

Algorithm

1×

intervals

Results

608.0ms	8000×	body	128	valid
192.0ms	8000×	pre	128	true

Compiler

Compiled 3982 to 1989 computations (50.1% saved)

Details

analyze44.0ms (0.4%)

sample35.0ms (0.3%)

simplify135.0ms (1.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite150.0ms (1.3%)

series1.9s (17.1%)

simplify152.0ms (1.4%)

prune702.0ms (6.3%)

localize17.0ms (0.2%)

rewrite130.0ms (1.2%)

series461.0ms (4.1%)

simplify178.0ms (1.6%)

prune815.0ms (7.3%)

localize18.0ms (0.2%)

rewrite134.0ms (1.2%)

series523.0ms (4.7%)

simplify162.0ms (1.5%)

prune897.0ms (8.1%)

localize19.0ms (0.2%)

rewrite111.0ms (1%)

series472.0ms (4.2%)

simplify114.0ms (1%)

prune447.0ms (4%)

regimes839.0ms (7.5%)

bsearch8.0ms (0.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.7s (23.8%)

Profiling