Details

analyze179.0ms (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)

sample52.0ms (0.3%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
6.0ms	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

53.3b

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 i (+.f64 (+.f64 alpha beta) i))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
36.9b	(/.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))
45.1b	(/.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))))

rewrite862.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

38.4b

Rules

86×	`times-frac_binary64_1789`
66×	`associate-/r/_binary64_1729`
61×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `flip3-+_binary64_1786` `flip-+_binary64_1757`
47×	`*-un-lft-identity_binary64_1783`
44×	`add-sqr-sqrt_binary64_1805`
40×	`frac-times_binary64_1793`
34×	`associate-*r/_binary64_1725`
28×	`add-cube-cbrt_binary64_1818` `difference-of-squares_binary64_1752`
22×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
20×	`associate-*l/_binary64_1726`
19×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
14×	`associate-/l*_binary64_1728` `difference-of-sqr-1_binary64_1753`
11×	`pow1_binary64_1844`
9×	`div-inv_binary64_1780` `associate-/l/_binary64_1730`
8×	`associate-r_binary64_1723`
7×	`associate-/r*_binary64_1727`
4×	`add-log-exp_binary64_1822` `pow-prod-down_binary64_1854` `associate-l_binary64_1724`
3×	`distribute-lft-out_binary64_1734`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `*-commutative_binary64_1714`
1×	`flip3--_binary64_1787` `flip--_binary64_1758` `unswap-sqr_binary64_1751`

Counts

4 → 217

Calls

4 calls:

44.0ms	(/.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))
25.0ms	(/.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 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
10.0ms	(*.f64 i (+.f64 (+.f64 alpha beta) i))

Compiler

Compiled 18268 to 6772 computations (62.9% saved)

series10.8s (51.7%)

Error

9.6b

Counts

4 → 91

Calls

4 calls:

8.6s	(/.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))
869.0ms	(/.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))))
446.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
132.0ms	(*.f64 i (+.f64 (+.f64 alpha beta) i))

Compiler

Compiled 30337 to 20809 computations (31.4% saved)

simplify268.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4979	32886
1	4979	32886

prune1.6s (7.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	302	6	308
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	302	7	309

Error

9.4b

Counts

309 → 7

Compiler

Compiled 29057 to 13341 computations (54.1% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

9.4b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 9.4b
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

prune14.0ms (0.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	1	1
Total	7	7

Error

9.4b

Counts

7 → 7

Compiler

Compiled 276 to 168 computations (39.1% saved)

localize15.0ms (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))))
0.4b	(/.f64 1/64 (*.f64 i i))
3.6b	(/.f64 (.f64 alpha alpha) (.f64 i i))
16.8b	(/.f64 (.f64 beta beta) (.f64 i i))

rewrite138.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

Rules

35×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
10×	`prod-exp_binary64_1832` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `cbrt-unprod_binary64_1816` `add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
8×	`add-cube-cbrt_binary64_1818`
6×	`pow1_binary64_1844`
5×	`times-frac_binary64_1789` `div-inv_binary64_1780` `associate-/l_binary64_1728` `associate-r*_binary64_1723`
4×	`add-log-exp_binary64_1822`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-/r_binary64_1727` `associate-r/_binary64_1725` `associate-l_binary64_1724`
1×	`pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `frac-add_binary64_1791` `flip3-+_binary64_1786` `flip-+_binary64_1757` `distribute-rgt-out_binary64_1736` `distribute-lft-out_binary64_1734` `*-commutative_binary64_1714`

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 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)

series354.0ms (1.7%)

Error

9.4b

Counts

4 → 24

Calls

4 calls:

133.0ms	(.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (/.f64 (.f64 beta beta) (*.f64 i i))))
86.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
84.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
24.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1680 to 1227 computations (27% saved)

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4967	1445
1	4967	1445

prune128.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	112	7	119

Error

9.3b

Counts

119 → 7

Compiler

Compiled 3338 to 1290 computations (61.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (*.f64 i i)) (cbrt.f64 (pow.f64 (/.f64 beta i) 6))))
0.4b	(/.f64 1/64 (*.f64 i i))
3.6b	(/.f64 (.f64 alpha alpha) (.f64 i i))
15.8b	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))

rewrite166.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

Rules

23×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
18×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
17×	`cbrt-prod_binary64_1814`
16×	`add-cube-cbrt_binary64_1818`
13×	`unpow-prod-down_binary64_1862` `times-frac_binary64_1789`
6×	`pow1_binary64_1844` `prod-exp_binary64_1832` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `cbrt-unprod_binary64_1816`
4×	`add-log-exp_binary64_1822` `associate-/l_binary64_1728` `associate-r*_binary64_1723`
3×	`div-inv_binary64_1780` `associate-l_binary64_1724`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-/r_binary64_1727` `associate-r/_binary64_1725`
1×	`pow1/3_binary64_1865` `sqr-pow_binary64_1755` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `flip3-+_binary64_1786` `flip-+_binary64_1757` `distribute-lft-out_binary64_1734` `*-commutative_binary64_1714`

Counts

4 → 90

Calls

4 calls:

19.0ms	(.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (*.f64 i i)) (cbrt.f64 (pow.f64 (/.f64 beta i) 6))))
6.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
5.0ms	(/.f64 1/64 (*.f64 i i))
4.0ms	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))

Compiler

Compiled 2950 to 1432 computations (51.5% saved)

series379.0ms (1.8%)

Error

9.3b

Counts

4 → 24

Calls

4 calls:

138.0ms	(.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (*.f64 i i)) (cbrt.f64 (pow.f64 (/.f64 beta i) 6))))
94.0ms	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))
93.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
29.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1653 to 1291 computations (21.9% saved)

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4944	1650
1	4944	1650

prune138.0ms (0.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	113	8	121

Error

9.3b

Counts

121 → 8

Compiler

Compiled 3157 to 1571 computations (50.2% saved)

regimes1.3s (6.1%)

Accuracy

Total 2.7b remaining (24.9%)

Threshold costs 0b (0%)

Compiler

Compiled 24023 to 13498 computations (43.8% saved)

bsearch32.0ms (0.2%)

Steps

Iters	Range		Point
6	1.971947347539624e+143	1.693783121249433e+144	2.393721103576982e+143

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	89
1	44	89

Removed

((sort alpha beta))

Compiler

Compiled 120 to 66 computations (45% saved)

end0.0ms (0%)

sample4.3s (20.5%)

Algorithm

1×

intervals

Results

685.0ms	8000×	body	128	valid
189.0ms	8000×	pre	128	true

Compiler

Compiled 6006 to 3381 computations (43.7% saved)

Details

analyze179.0ms (0.9%)

sample52.0ms (0.3%)

simplify43.0ms (0.2%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite862.0ms (4.1%)

series10.8s (51.7%)

simplify268.0ms (1.3%)

prune1.6s (7.5%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune14.0ms (0.1%)

localize15.0ms (0.1%)

rewrite138.0ms (0.7%)

series354.0ms (1.7%)

simplify68.0ms (0.3%)

prune128.0ms (0.6%)

localize15.0ms (0.1%)

rewrite166.0ms (0.8%)

series379.0ms (1.8%)

simplify77.0ms (0.4%)

prune138.0ms (0.7%)

regimes1.3s (6.1%)

bsearch32.0ms (0.2%)

simplify12.0ms (0.1%)

end0.0ms (0%)

sample4.3s (20.5%)

Profiling