Details

analyze44.0ms (0.2%)

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)

sample37.0ms (0.1%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify134.0ms (0.5%)

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

57.5b

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 beta alpha) (.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))))
37.8b	(/.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))
49.3b	(/.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))))

rewrite133.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64_1789`
66×	`associate-/r/_binary64_1729`
61×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
59×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
40×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783` `frac-times_binary64_1793`
32×	`associate-*r/_binary64_1725`
28×	`difference-of-squares_binary64_1752`
26×	`add-cube-cbrt_binary64_1818`
21×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
20×	`associate-*l/_binary64_1726`
19×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
14×	`associate-/l*_binary64_1728` `difference-of-sqr-1_binary64_1753`
9×	`associate-/l/_binary64_1730` `div-inv_binary64_1780` `pow1_binary64_1844`
7×	`associate-/r*_binary64_1727`
6×	`add-log-exp_binary64_1822`
3×	`pow-prod-down_binary64_1854` `associate-r_binary64_1723`
2×	`associate-+r+_binary64_1715` `distribute-lft-in_binary64_1732` `frac-2neg_binary64_1794` `distribute-rgt-in_binary64_1733` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `associate-l_binary64_1724` `*-commutative_binary64_1714` `sum-log_binary64_1874` `flip--_binary64_1758`

Counts

4 → 206

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))
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))))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
6.0ms	(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))

series9.7s (37.8%)

Counts

4 → 77

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))
516.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
443.0ms	(/.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))))
199.0ms	(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))

Compiler

Compiled 15496 to 10869 computations (29.9% saved)

simplify195.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5692	23152

prune1.0s (4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	278	5	283
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	279	5	284

Error

9.5b

Counts

284 → 5

Compiler

Compiled 21641 to 9027 computations (58.3% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune5.0ms (0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Error

9.5b

Counts

5 → 5

Compiler

Compiled 126 to 70 computations (44.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.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))
0.1b	(.f64 (/.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)) (/.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)))
37.6b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
38.3b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite256.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

414×	`times-frac_binary64_1789`
314×	`add-sqr-sqrt_binary64_1805`
280×	`*-un-lft-identity_binary64_1783`
169×	`add-cube-cbrt_binary64_1818`
111×	`associate-r_binary64_1723`
70×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
62×	`difference-of-squares_binary64_1752`
48×	`associate-/r/_binary64_1729`
42×	`associate-l_binary64_1724`
33×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
31×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
24×	`flip-+_binary64_1757` `div-inv_binary64_1780` `flip3-+_binary64_1786`
19×	`associate-/l*_binary64_1728`
16×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
13×	`associate-/r*_binary64_1727`
9×	`distribute-lft-out_binary64_1734`
6×	`unswap-sqr_binary64_1751` `pow1_binary64_1844`
5×	`associate-/l/_binary64_1730`
4×	`add-log-exp_binary64_1822`
3×	`associate-*r/_binary64_1725` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
2×	`flip3--_binary64_1787` `flip--_binary64_1758`
1×	`associate-l/_binary64_1726` `-commutative_binary64_1714` `frac-times_binary64_1793` `pow-prod-down_binary64_1854`

Counts

4 → 395

Calls

4 calls:

122.0ms	(.f64 (/.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)) (/.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)))
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)))
11.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series6.7s (26.1%)

Counts

4 → 62

Calls

4 calls:

5.3s	(.f64 (/.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)) (/.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)))
967.0ms	(/.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))
246.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
160.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

Compiler

Compiled 13610 to 9283 computations (31.8% saved)

simplify267.0ms (1%)

Algorithm

1×	egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5229	35129

prune1.6s (6.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	453	4	457
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	454	8	462

Error

9.0b

Counts

462 → 8

Compiler

Compiled 36836 to 15538 computations (57.8% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

37.6b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
38.3b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
38.3b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
38.3b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite92.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `times-frac_binary64_1789`
15×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
12×	`associate-/r*_binary64_1727`
10×	`associate-/l*_binary64_1728`
8×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `flip3-+_binary64_1786`
5×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
4×	`div-inv_binary64_1780` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `add-log-exp_binary64_1822` `pow1_binary64_1844`
2×	`associate-*r/_binary64_1725`
1×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`

Counts

4 → 118

Calls

4 calls:

13.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
11.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
11.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
11.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series1.2s (4.6%)

Counts

4 → 68

Calls

4 calls:

321.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
319.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
314.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
218.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

Compiler

Compiled 19276 to 9752 computations (49.4% saved)

simplify79.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5034	6013

prune1.2s (4.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	186	8	194

Error

9.0b

Counts

194 → 8

Compiler

Compiled 33053 to 13387 computations (59.5% saved)

regimes618.0ms (2.4%)

Accuracy

Total 3.8b remaining (34.3%)

Threshold costs 0b (0%)

Compiler

Compiled 9140 to 4965 computations (45.7% saved)

bsearch76.0ms (0.3%)

Steps

Iters	Range		Point
5	1.1203204637154722e+144	3.070549782475045e+144	2.061938149421035e+144
6	8.967726587919945e+142	6.3532539500270875e+143	6.09812200291671e+143
6	5.543601248696082e+84	2.5475346241518746e+85	2.5206724026500415e+85

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	221
1	67	221

end0.0ms (0%)

sample2.1s (8.4%)

Algorithm

1×

intervals

Results

639.0ms	8000×	body	128	valid
181.0ms	8000×	pre	128	true

Compiler

Compiled 2428 to 1315 computations (45.8% saved)

Details

analyze44.0ms (0.2%)

sample37.0ms (0.1%)

simplify134.0ms (0.5%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite133.0ms (0.5%)

series9.7s (37.8%)

simplify195.0ms (0.8%)

prune1.0s (4%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite256.0ms (1%)

series6.7s (26.1%)

simplify267.0ms (1%)

prune1.6s (6.3%)

localize26.0ms (0.1%)

rewrite92.0ms (0.4%)

series1.2s (4.6%)

simplify79.0ms (0.3%)

prune1.2s (4.8%)

regimes618.0ms (2.4%)

bsearch76.0ms (0.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.1s (8.4%)

Profiling