Details

analyze172.0ms (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)

sample46.0ms (0.2%)

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)

simplify44.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5395	79

prune7.0ms (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

54.5b

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))))
36.8b	(/.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))
46.5b	(/.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))))

rewrite858.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

37.9b

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:

43.0ms	(/.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))))
17.0ms	(.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)

series10.7s (55.5%)

Error

9.5b

Counts

4 → 88

Calls

4 calls:

8.8s	(/.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))
698.0ms	(/.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))))
458.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
237.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 24801 to 16647 computations (32.9% saved)

simplify218.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5768	25218

prune1.1s (5.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	310	6	316
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	311	6	317

Error

7.6b

Counts

317 → 6

Compiler

Compiled 24223 to 10662 computations (56% 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%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune7.0ms (0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	0	0
Total	6	6

Error

7.6b

Counts

6 → 6

Compiler

Compiled 147 to 96 computations (34.7% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.7b	(/.f64 1/64 (*.f64 i i))
2.2b	(/.f64 (.f64 alpha alpha) (.f64 i i))
18.8b	(/.f64 (.f64 beta beta) (.f64 i i))

rewrite92.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

7.3b

Rules

32×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
10×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
9×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
5×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `times-frac_binary64_1448` `-un-lft-identity_binary64_1442` `associate-/l_binary64_1387`
3×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `associate-/r*_binary64_1386`

Counts

3 → 63

Calls

3 calls:

7.0ms	(/.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 1972 to 684 computations (65.3% saved)

series223.0ms (1.2%)

Error

7.6b

Counts

3 → 15

Calls

3 calls:

97.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
83.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
29.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1125 to 756 computations (32.8% saved)

simplify55.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5084	712

prune82.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	78	6	84

Error

7.3b

Counts

84 → 6

Compiler

Compiled 2218 to 878 computations (60.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 beta i) 6)
0.7b	(/.f64 1/64 (*.f64 i i))
2.2b	(/.f64 (.f64 alpha alpha) (.f64 i i))
18.3b	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))

rewrite159.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

7.3b

Rules

26×	`unpow-prod-down_binary64_1521`
24×	`add-exp-log_binary64_1480`
22×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `times-frac_binary64_1448` `*-un-lft-identity_binary64_1442`
21×	`add-cbrt-cube_binary64_1478`
17×	`cbrt-prod_binary64_1473`
7×	`div-exp_binary64_1493`
6×	`cbrt-undiv_binary64_1476`
5×	`pow1_binary64_1503` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
4×	`add-log-exp_binary64_1481` `div-inv_binary64_1439` `associate-/l*_binary64_1387`
3×	`pow-unpow_binary64_1519`
2×	`sqr-pow_binary64_1414` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/r*_binary64_1386` `pow-exp_binary64_1510`
1×	`pow1/3_binary64_1524` `pow-pow_binary64_1514` `pow-to-exp_binary64_1511`

Counts

4 → 95

Calls

4 calls:

6.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
6.0ms	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))
5.0ms	(pow.f64 (/.f64 beta i) 6)
4.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 2961 to 1449 computations (51.1% saved)

series347.0ms (1.8%)

Error

7.3b

Counts

4 → 21

Calls

4 calls:

113.0ms	(pow.f64 (/.f64 beta i) 6)
93.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
92.0ms	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))
28.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1566 to 1144 computations (26.9% saved)

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5069	1309

prune143.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	116	6	122

Error

7.3b

Counts

122 → 6

Compiler

Compiled 3182 to 1603 computations (49.6% saved)

regimes1.1s (5.9%)

Accuracy

Total 3.1b remaining (26.9%)

Threshold costs 0b (0%)

Compiler

Compiled 20004 to 11657 computations (41.7% saved)

bsearch26.0ms (0.1%)

Steps

Iters	Range		Point
5	8.113889814503846e+121	2.0659321366427148e+122	2.0327187607865832e+122

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

Removed

((sort alpha beta))

Compiler

Compiled 120 to 74 computations (38.3% saved)

end0.0ms (0%)

sample3.7s (19.2%)

Algorithm

1×

intervals

Results

610.0ms	8000×	body	128	valid
181.0ms	8000×	pre	128	true

Compiler

Compiled 5056 to 2949 computations (41.7% saved)

Details

analyze172.0ms (0.9%)

sample46.0ms (0.2%)

simplify44.0ms (0.2%)

prune7.0ms (0%)

localize16.0ms (0.1%)

rewrite858.0ms (4.5%)

series10.7s (55.5%)

simplify218.0ms (1.1%)

prune1.1s (5.9%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0%)

prune7.0ms (0%)

localize13.0ms (0.1%)

rewrite92.0ms (0.5%)

series223.0ms (1.2%)

simplify55.0ms (0.3%)

prune82.0ms (0.4%)

localize15.0ms (0.1%)

rewrite159.0ms (0.8%)

series347.0ms (1.8%)

simplify68.0ms (0.4%)

prune143.0ms (0.7%)

regimes1.1s (5.9%)

bsearch26.0ms (0.1%)

simplify14.0ms (0.1%)

end0.0ms (0%)

sample3.7s (19.2%)

Profiling