Details

analyze180.0ms (0.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5646	316
0	3	3
1	3	3

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

Symmetry

(sort alpha beta)

Compiler

Compiled 63 to 34 computations (46% saved)

sample49.0ms (0.2%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify43.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

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

50.8b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize16.0ms (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))))
33.5b	(/.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))
43.4b	(/.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))))

rewrite1.1s (5.4%)

Algorithm

1×	rewrite-expression-head

Error

34.7b

Rules

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

Counts

4 → 228

Calls

4 calls:

45.0ms	(/.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))))
13.0ms	(.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))))

Compiler

Compiled 19221 to 7168 computations (62.7% saved)

series10.8s (52.4%)

Error

8.9b

Counts

4 → 93

Calls

4 calls:

8.5s	(/.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))
868.0ms	(/.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))))
456.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
231.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 30483 to 20681 computations (32.2% saved)

simplify259.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5025	32618

prune1.4s (6.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	313	8	321
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	314	8	322

Error

7.2b

Counts

322 → 8

Compiler

Compiled 29428 to 13311 computations (54.8% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 7.2b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune16.0ms (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

7.2b

Counts

8 → 8

Compiler

Compiled 413 to 234 computations (43.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (/.f64 (.f64 beta beta) (*.f64 i i))))
0.5b	(/.f64 1/64 (*.f64 i i))
2.7b	(/.f64 (.f64 alpha alpha) (.f64 i i))
14.5b	(/.f64 (.f64 beta beta) (.f64 i i))

rewrite131.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

35×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
10×	`prod-exp_binary64_1491` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
8×	`add-cube-cbrt_binary64_1477`
6×	`pow1_binary64_1503`
5×	`times-frac_binary64_1448` `div-inv_binary64_1439` `associate-/l_binary64_1387` `associate-r*_binary64_1382`
4×	`add-log-exp_binary64_1481`
3×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/r_binary64_1386` `associate-r/_binary64_1384` `associate-l_binary64_1383`
1×	`pow-prod-down_binary64_1513` `unswap-sqr_binary64_1410` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `frac-add_binary64_1450` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-rgt-out_binary64_1395` `distribute-lft-out_binary64_1393` `*-commutative_binary64_1373`

Counts

4 → 88

Calls

4 calls:

12.0ms	(.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (/.f64 (.f64 beta beta) (*.f64 i i))))
6.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
6.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
4.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 2929 to 953 computations (67.5% saved)

series474.0ms (2.3%)

Error

7.2b

Counts

4 → 27

Calls

4 calls:

252.0ms	(.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (/.f64 (.f64 beta beta) (*.f64 i i))))
87.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
83.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
25.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1842 to 1359 computations (26.2% saved)

simplify72.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4956	1511
1	4956	1511

prune132.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	115	8	123

Error

7.2b

Counts

123 → 8

Compiler

Compiled 3543 to 1379 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))
0.5b	(/.f64 1/64 (*.f64 i i))
4.8b	(.f64 (/.f64 1/32 i) (+.f64 (.f64 beta (/.f64 beta i)) (*.f64 alpha (/.f64 alpha i))))

rewrite181.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

45×	`add-sqr-sqrt_binary64_1464`
33×	`times-frac_binary64_1448`
30×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
29×	`associate-r_binary64_1382`
24×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
19×	`associate-l_binary64_1383`
10×	`pow1_binary64_1503`
9×	`associate-*r/_binary64_1384`
7×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
6×	`unswap-sqr_binary64_1410`
5×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
4×	`add-log-exp_binary64_1481` `div-inv_binary64_1439`
3×	`pow-prod-down_binary64_1513` `frac-times_binary64_1452` `-commutative_binary64_1373` `associate-/l_binary64_1387`
2×	`frac-add_binary64_1450` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-l/_binary64_1385` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/r_binary64_1386`

Counts

4 → 125

Calls

4 calls:

11.0ms	(.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))
5.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 3907 to 1541 computations (60.6% saved)

series436.0ms (2.1%)

Error

7.2b

Counts

4 → 27

Calls

4 calls:

248.0ms	(.f64 (/.f64 1/32 i) (+.f64 (.f64 beta (/.f64 beta i)) (*.f64 alpha (/.f64 alpha i))))
72.0ms	(*.f64 beta (/.f64 beta i))
66.0ms	(*.f64 alpha (/.f64 alpha i))
24.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1764 to 1338 computations (24.1% saved)

simplify87.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5012	2213

prune151.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	152	8	160

Error

7.2b

Counts

160 → 8

Compiler

Compiled 4214 to 1661 computations (60.6% saved)

regimes1.2s (5.9%)

Accuracy

Total 2.7b remaining (24%)

Threshold costs 0b (0%)

Compiler

Compiled 21352 to 12045 computations (43.6% saved)

bsearch37.0ms (0.2%)

Steps

Iters	Range		Point
7	6.541783925417694e+124	3.32248309419248e+126	3.262397731415471e+126

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	89
1	46	89

Remove

(sort alpha beta)

Compiler

Compiled 120 to 74 computations (38.3% saved)

end0.0ms (0%)

sample3.7s (18.1%)

Algorithm

1×

intervals

Results

651.0ms	8000×	body	128	valid
179.0ms	8000×	pre	128	true

Compiler

Compiled 5393 to 3046 computations (43.5% saved)

Details

analyze180.0ms (0.9%)

sample49.0ms (0.2%)

simplify43.0ms (0.2%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite1.1s (5.4%)

series10.8s (52.4%)

simplify259.0ms (1.3%)

prune1.4s (6.9%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune16.0ms (0.1%)

localize13.0ms (0.1%)

rewrite131.0ms (0.6%)

series474.0ms (2.3%)

simplify72.0ms (0.3%)

prune132.0ms (0.6%)

localize14.0ms (0.1%)

rewrite181.0ms (0.9%)

series436.0ms (2.1%)

simplify87.0ms (0.4%)

prune151.0ms (0.7%)

regimes1.2s (5.9%)

bsearch37.0ms (0.2%)

simplify14.0ms (0.1%)

end0.0ms (0%)

sample3.7s (18.1%)

Profiling