Details

analyze723.0ms (3.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4733	38
1	4733	38
0	2	2
1	2	2

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)

sample62.0ms (0.3%)

Algorithm

1×

intervals

Results

14.0ms	256×	pre	128	true
12.0ms	186×	body	128	valid
8.0ms	32×	body	1024	valid
4.0ms	19×	body	512	valid
2.0ms	18×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify477.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (466.0ms)

Iter	Nodes	Cost
0	5018	19

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

17.4b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.9b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite233.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

16.5b

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-log-exp_binary64_1822` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
2×	`pow1_binary64_1844` `flip3-+_binary64_1786` `flip-+_binary64_1757` `div-sub_binary64_1788` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729`
1×	`sum-log_binary64_1874` `associate-+l-_binary64_1718` `+-commutative_binary64_1713` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `flip3--_binary64_1787` `flip--_binary64_1758`

Counts

2 → 65

Calls

2 calls:

38.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
22.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1500 to 803 computations (46.5% saved)

series851.0ms (4.2%)

Error

0.0b

Counts

2 → 44

Calls

2 calls:

425.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
279.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 3588 to 2887 computations (19.5% saved)

simplify143.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4957	3204
1	4957	3204

prune244.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	3	110

Error

0.0b

Counts

110 → 3

Compiler

Compiled 2841 to 1741 computations (38.7% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 alpha (+.f64 2 beta)))
0.1b	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta))))
5.0b	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta)))) 1)

rewrite305.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

61×	`*-un-lft-identity_binary64_1783`
32×	`add-sqr-sqrt_binary64_1805` `times-frac_binary64_1789`
23×	`add-cube-cbrt_binary64_1818`
21×	`associate-r_binary64_1723` `distribute-lft-out_binary64_1734`
16×	`add-exp-log_binary64_1821`
10×	`add-cbrt-cube_binary64_1819`
6×	`pow1_binary64_1844`
5×	`add-log-exp_binary64_1822` `associate-l_binary64_1724` `associate-/r*_binary64_1727`
4×	`div-exp_binary64_1834` `prod-exp_binary64_1832` `associate-/r/_binary64_1729`
3×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `unswap-sqr_binary64_1751` `associate-/l*_binary64_1728`
2×	`1-exp_binary64_1827` `rec-exp_binary64_1833` `cbrt-unprod_binary64_1816` `cbrt-undiv_binary64_1817` `flip3--_binary64_1787` `frac-times_binary64_1793` `flip--_binary64_1758` `associate-*l/_binary64_1726` `div-inv_binary64_1780`
1×	`sum-log_binary64_1874` `+-commutative_binary64_1713` `pow-prod-down_binary64_1854` `un-div-inv_binary64_1781` `associate-r/_binary64_1725` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `-commutative_binary64_1714` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `frac-2neg_binary64_1794` `clear-num_binary64_1782`

Counts

3 → 102

Calls

3 calls:

34.0ms	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta))))
27.0ms	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta)))) 1)
14.0ms	(/.f64 1 (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 2485 to 1729 computations (30.4% saved)

series1.1s (5.5%)

Error

0.0b

Counts

3 → 65

Calls

3 calls:

424.0ms	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta)))) 1)
265.0ms	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta))))
236.0ms	(/.f64 1 (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 5189 to 4149 computations (20% saved)

simplify159.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4968	4298
1	4968	4298

prune366.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	167	3	170

Error

0.0b

Counts

170 → 3

Compiler

Compiled 4321 to 2797 computations (35.3% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 4 (*.f64 alpha alpha))
0.2b	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
0.2b	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
3.0b	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha)))

rewrite687.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

84×	`add-sqr-sqrt_binary64_1805`
76×	`times-frac_binary64_1789`
62×	`*-un-lft-identity_binary64_1783`
58×	`add-cube-cbrt_binary64_1818`
33×	`cancel-sign-sub-inv_binary64_1749`
26×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `associate-l_binary64_1724`
19×	`associate-r_binary64_1723`
14×	`distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732`
13×	`pow1_binary64_1844` `swap-sqr_binary64_1750`
9×	`add-log-exp_binary64_1822` `div-inv_binary64_1780`
7×	`frac-sub_binary64_1792` `div-exp_binary64_1834` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `cbrt-undiv_binary64_1817`
6×	`frac-add_binary64_1791` `unswap-sqr_binary64_1751`
5×	`flip3--_binary64_1787` `frac-times_binary64_1793` `flip--_binary64_1758` `associate-*r/_binary64_1725`
4×	`associate-*l/_binary64_1726` `difference-of-squares_binary64_1752`
3×	`sub-neg_binary64_1776` `associate-/l*_binary64_1728`
2×	`diff-log_binary64_1875` `distribute-lft-out--_binary64_1735` `pow-prod-down_binary64_1854` `*-commutative_binary64_1714`
1×	`sum-log_binary64_1874` `flip3-+_binary64_1786` `flip-+_binary64_1757` `sub-div_binary64_1790` `associate--l+_binary64_1720` `pow2_binary64_1864` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `pow-sqr_binary64_1756` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-/r*_binary64_1727`

Counts

4 → 186

Calls

4 calls:

31.0ms	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
25.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha)))
20.0ms	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
10.0ms	(/.f64 4 (*.f64 alpha alpha))

Compiler

Compiled 7837 to 4169 computations (46.8% saved)

series998.0ms (4.9%)

Error

0.0b

Counts

4 → 28

Calls

4 calls:

493.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha)))
208.0ms	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
171.0ms	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
56.0ms	(/.f64 4 (*.f64 alpha alpha))

Compiler

Compiled 2461 to 1726 computations (29.9% saved)

simplify187.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4971	3946
1	4971	3946

prune632.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	213	4	217

Error

Counts

217 → 4

Compiler

Compiled 7952 to 4315 computations (45.7% saved)

localize66.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.0b	(+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))
7.9b	(/.f64 beta (*.f64 alpha alpha))
11.4b	(-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
15.4b	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))

rewrite2.6s (12.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

123×	`frac-add_binary64_1791`
79×	`associate-*r/_binary64_1725`
63×	`add-log-exp_binary64_1822`
49×	`frac-sub_binary64_1792`
37×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
33×	`sum-log_binary64_1874`
24×	`*-un-lft-identity_binary64_1783`
22×	`add-exp-log_binary64_1821`
15×	`add-sqr-sqrt_binary64_1805` `times-frac_binary64_1789`
14×	`add-cbrt-cube_binary64_1819`
13×	`add-cube-cbrt_binary64_1818` `associate-/r*_binary64_1727`
12×	`diff-log_binary64_1875`
8×	`div-exp_binary64_1834`
7×	`frac-times_binary64_1793` `associate-*l/_binary64_1726`
6×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
4×	`pow1_binary64_1844` `prod-exp_binary64_1832` `cbrt-undiv_binary64_1817` `associate-/l*_binary64_1728` `distribute-lft-out_binary64_1734`
3×	`cancel-sign-sub-inv_binary64_1749` `distribute-lft-out--_binary64_1735`
2×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `cbrt-unprod_binary64_1816` `frac-2neg_binary64_1794` `unpow3_binary64_1849` `cube-mult_binary64_1813` `sqr-pow_binary64_1755` `clear-num_binary64_1782` `div-inv_binary64_1780`
1×	`flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `difference-of-squares_binary64_1752` `associate--l+_binary64_1720` `associate--r+_binary64_1719` `associate-+r+_binary64_1715` `+-commutative_binary64_1713`

Counts

4 → 161

Calls

4 calls:

117.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
53.0ms	(+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))
14.0ms	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
9.0ms	(/.f64 beta (*.f64 alpha alpha))

Compiler

Compiled 22551 to 12871 computations (42.9% saved)

series2.1s (10.3%)

Error

Counts

4 → 38

Calls

4 calls:

1.1s	(-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
497.0ms	(+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))
223.0ms	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
141.0ms	(/.f64 beta (*.f64 alpha alpha))

Compiler

Compiled 5796 to 3993 computations (31.1% saved)

simplify324.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5271	21051

prune2.4s (11.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	199	4	203

Error

Counts

203 → 4

Compiler

Compiled 21600 to 12641 computations (41.5% saved)

regimes1.2s (5.7%)

Accuracy

Total 0.1b remaining (61.4%)

Threshold costs 0.1b (61.4%)

Compiler

Compiled 8855 to 6493 computations (26.7% saved)

bsearch6.0ms (0%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	85	86
1	85	86

end0.0ms (0%)

sample4.5s (21.9%)

Algorithm

1×

intervals

Results

386.0ms	5926×	body	128	valid
255.0ms	1034×	body	1024	valid
245.0ms	8000×	pre	128	true
112.0ms	617×	body	512	valid
40.0ms	326×	body	256	valid
35.0ms	97×	body	2048	valid

Compiler

Compiled 1763 to 1290 computations (26.8% saved)

Details

analyze723.0ms (3.6%)

sample62.0ms (0.3%)

simplify477.0ms (2.3%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite233.0ms (1.1%)

series851.0ms (4.2%)

simplify143.0ms (0.7%)

prune244.0ms (1.2%)

localize18.0ms (0.1%)

rewrite305.0ms (1.5%)

series1.1s (5.5%)

simplify159.0ms (0.8%)

prune366.0ms (1.8%)

localize31.0ms (0.2%)

rewrite687.0ms (3.4%)

series998.0ms (4.9%)

simplify187.0ms (0.9%)

prune632.0ms (3.1%)

localize66.0ms (0.3%)

rewrite2.6s (12.8%)

series2.1s (10.3%)

simplify324.0ms (1.6%)

prune2.4s (11.6%)

regimes1.2s (5.7%)

bsearch6.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample4.5s (21.9%)

Profiling