Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample24.0ms (0.3%)

Algorithm

1×

intervals

Results

6.0ms	184×	body	128	valid
4.0ms	256×	pre	128	true
3.0ms	28×	body	1024	valid
2.0ms	22×	body	512	valid
1.0ms	18×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify343.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (244.0ms)

Iter	Nodes	Cost
0	5018	19

prune3.0ms (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

18.0b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
3.3b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_1783`
26×	`add-sqr-sqrt_binary64_1805`
25×	`times-frac_binary64_1789`
19×	`distribute-lft-out_binary64_1734`
14×	`add-cube-cbrt_binary64_1818`
6×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
5×	`associate-/l_binary64_1728` `associate-/r_binary64_1727`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-log-exp_binary64_1822`
2×	`div-sub_binary64_1788` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow1_binary64_1844`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `div-inv_binary64_1780` `associate-+l-_binary64_1718` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782` `flip--_binary64_1758`

Counts

2 → 65

Calls

2 calls:

24.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series373.0ms (4.5%)

Counts

2 → 44

Calls

2 calls:

227.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
145.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1856 to 1558 computations (16.1% saved)

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5004	3414

prune165.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	6	110

Error

0.0b

Counts

110 → 6

Compiler

Compiled 3080 to 1795 computations (41.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) (-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
0.1b	(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3)
1.3b	(-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
3.2b	(+.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3))

rewrite138.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

157×	`*-un-lft-identity_binary64_1783`
99×	`add-sqr-sqrt_binary64_1805`
82×	`times-frac_binary64_1789`
46×	`distribute-lft-out_binary64_1734`
42×	`add-cube-cbrt_binary64_1818`
31×	`unpow-prod-down_binary64_1862` `associate-l_binary64_1724` `cube-prod_binary64_1811`
23×	`difference-of-squares_binary64_1752`
17×	`distribute-lft-out--_binary64_1735`
12×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
10×	`associate-r_binary64_1723`
9×	`cancel-sign-sub-inv_binary64_1749`
8×	`add-log-exp_binary64_1822`
7×	`pow1_binary64_1844`
6×	`associate-/r/_binary64_1729`
4×	`distribute-lft-in_binary64_1732` `difference-of-sqr-1_binary64_1753` `flip-+_binary64_1757` `distribute-rgt-in_binary64_1733` `flip3-+_binary64_1786`
3×	`flip3--_binary64_1787` `pow-unpow_binary64_1860` `div-inv_binary64_1780` `flip--_binary64_1758` `sub-neg_binary64_1776`
2×	`associate-*r/_binary64_1725` `rem-cube-cbrt_binary64_1806` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `frac-times_binary64_1793` `unswap-sqr_binary64_1751` `pow-exp_binary64_1851`
1×	`div-sub_binary64_1788` `+-commutative_binary64_1713` `sqr-pow_binary64_1755` `cube-mult_binary64_1813` `unpow3_binary64_1849` `associate--l-_binary64_1721` `associate-l/_binary64_1726` `diff-log_binary64_1875` `-commutative_binary64_1714` `sum-log_binary64_1874` `pow-pow_binary64_1855` `pow-prod-down_binary64_1854` `cube-div_binary64_1812` `pow-to-exp_binary64_1852`

Counts

4 → 185

Calls

4 calls:

38.0ms	(*.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) (-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
28.0ms	(+.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3))
21.0ms	(-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
17.0ms	(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3)

series1.2s (14.3%)

Counts

4 → 73

Calls

4 calls:

405.0ms	(+.f64 1 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3))
356.0ms	(*.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) (-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
239.0ms	(-.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
192.0ms	(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 3)

Compiler

Compiled 5842 to 4498 computations (23% saved)

simplify96.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4977	8759
1	4977	8759

prune632.0ms (7.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	258	6	264

Error

Counts

264 → 6

Compiler

Compiled 13366 to 7400 computations (44.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
0.2b	(exp.f64 (log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
3.3b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
3.6b	(log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))

rewrite81.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_1783`
31×	`add-sqr-sqrt_binary64_1805`
25×	`times-frac_binary64_1789`
21×	`distribute-lft-out_binary64_1734`
19×	`add-cube-cbrt_binary64_1818`
8×	`log-prod_binary64_1869`
7×	`add-exp-log_binary64_1821`
6×	`add-cbrt-cube_binary64_1819` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`associate-/l_binary64_1728` `associate-/r_binary64_1727`
4×	`exp-sum_binary64_1829` `flip-+_binary64_1757` `flip3-+_binary64_1786` `exp-prod_binary64_1835` `log-div_binary64_1870`
2×	`div-sub_binary64_1788` `exp-diff_binary64_1831` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `log-pow_binary64_1872`
1×	`flip3--_binary64_1787` `rem-exp-log_binary64_1823` `+-commutative_binary64_1713` `div-inv_binary64_1780` `associate-+l-_binary64_1718` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782` `flip--_binary64_1758` `rem-log-exp_binary64_1824`

Counts

4 → 98

Calls

4 calls:

23.0ms	(exp.f64 (log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
19.0ms	(log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))

series1.3s (15%)

Counts

4 → 77

Calls

4 calls:

533.0ms	(log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
358.0ms	(exp.f64 (log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
214.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
147.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 4698 to 3897 computations (17% saved)

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4948	6566
1	4948	6566

prune278.0ms (3.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	175	6	181

Error

Counts

181 → 6

Compiler

Compiled 5752 to 3612 computations (37.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
0.2b	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
0.5b	(/.f64 -4 (*.f64 alpha alpha))
2.8b	(+.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (+.f64 (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) -2) (/.f64 -4 (.f64 alpha alpha))))

rewrite95.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-add_binary64_1791`
78×	`add-sqr-sqrt_binary64_1805`
72×	`times-frac_binary64_1789`
60×	`*-un-lft-identity_binary64_1783`
56×	`add-cube-cbrt_binary64_1818`
35×	`associate-*l/_binary64_1726`
26×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724`
20×	`associate-*r/_binary64_1725` `frac-times_binary64_1793`
19×	`associate-r_binary64_1723`
16×	`add-log-exp_binary64_1822`
14×	`distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733`
13×	`swap-sqr_binary64_1750` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow1_binary64_1844`
12×	`flip3--_binary64_1787` `flip--_binary64_1758`
8×	`div-inv_binary64_1780` `sum-log_binary64_1874`
7×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
6×	`unswap-sqr_binary64_1751`
3×	`associate-/l*_binary64_1728`
2×	`difference-of-squares_binary64_1752` `*-commutative_binary64_1714` `pow-prod-down_binary64_1854` `sub-neg_binary64_1776`
1×	`associate-+r+_binary64_1715` `+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `associate-/r*_binary64_1727` `distribute-lft-out--_binary64_1735` `associate-+l+_binary64_1716` `pow-sqr_binary64_1756` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow2_binary64_1864`

Counts

4 → 207

Calls

4 calls:

24.0ms	(+.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (+.f64 (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) -2) (/.f64 -4 (.f64 alpha alpha))))
15.0ms	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
12.0ms	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
5.0ms	(/.f64 -4 (*.f64 alpha alpha))

series664.0ms (8%)

Counts

4 → 31

Calls

4 calls:

421.0ms	(+.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (+.f64 (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) -2) (/.f64 -4 (.f64 alpha alpha))))
121.0ms	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
94.0ms	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
27.0ms	(/.f64 -4 (*.f64 alpha alpha))

Compiler

Compiled 1600 to 1265 computations (20.9% saved)

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5031	8548

prune491.0ms (5.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	238	6	244

Error

Counts

244 → 6

Compiler

Compiled 10511 to 5770 computations (45.1% saved)

regimes490.0ms (5.9%)

Accuracy

Total 0.1b remaining (66.9%)

Threshold costs 0.1b (66.9%)

Compiler

Compiled 6179 to 4504 computations (27.1% saved)

bsearch3.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	80
1	65	80

end0.0ms (0%)

sample1.6s (19.7%)

Algorithm

1×

intervals

Results

196.0ms	5970×	body	128	valid
139.0ms	8000×	pre	128	true
134.0ms	1058×	body	1024	valid
55.0ms	576×	body	512	valid
19.0ms	299×	body	256	valid
15.0ms	97×	body	2048	valid

Compiler

Compiled 1273 to 923 computations (27.5% saved)

Details

analyze3.0ms (0%)

sample24.0ms (0.3%)

simplify343.0ms (4.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite41.0ms (0.5%)

series373.0ms (4.5%)

simplify78.0ms (0.9%)

prune165.0ms (2%)

localize14.0ms (0.2%)

rewrite138.0ms (1.7%)

series1.2s (14.3%)

simplify96.0ms (1.2%)

prune632.0ms (7.6%)

localize11.0ms (0.1%)

rewrite81.0ms (1%)

series1.3s (15%)

simplify98.0ms (1.2%)

prune278.0ms (3.3%)

localize19.0ms (0.2%)

rewrite95.0ms (1.1%)

series664.0ms (8%)

simplify98.0ms (1.2%)

prune491.0ms (5.9%)

regimes490.0ms (5.9%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (19.7%)

Profiling