Details

analyze1.2s (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample71.0ms (0.1%)

Algorithm

1×

intervals

Results

24.0ms	250×	body	128	valid
17.0ms	292×	pre	128	true
9.0ms	36×	body	128	nan
1.0ms	6×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify719.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (552.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune10.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.2b

Counts

2 → 2

Compiler

Compiled 49 to 40 computations (18.4% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.2b	(.f64 (.f64 3 a) c)
0.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
29.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

rewrite85.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_1783`
14×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
10×	`add-log-exp_binary64_1822`
9×	`pow1_binary64_1844`
7×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
6×	`distribute-lft-out_binary64_1734`
5×	`associate-/l*_binary64_1728` `times-frac_binary64_1789`
4×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
3×	`pow-prod-down_binary64_1854` `distribute-rgt-neg-in_binary64_1741` `associate-r_binary64_1723`
2×	`associate-/l/_binary64_1730` `flip-+_binary64_1757` `associate-+l-_binary64_1718` `cbrt-undiv_binary64_1817` `sum-log_binary64_1874` `div-exp_binary64_1834` `neg-sub0_binary64_1778` `flip3-+_binary64_1786`
1×	`flip3--_binary64_1787` `div-sub_binary64_1788` `+-commutative_binary64_1713` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `associate-/r_binary64_1727` `associate-l_binary64_1724` `diff-log_binary64_1875` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `neg-log_binary64_1876` `clear-num_binary64_1782` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 73

Calls

4 calls:

27.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
24.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
11.0ms	(.f64 (.f64 3 a) c)
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series457.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
135.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
27.0ms	(.f64 (.f64 3 a) c)

simplify141.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	6150	1664

prune1.2s (1.7%)

Pruning

38 alts after pruning (37 fresh and 1 done)

	Pruned	Kept	Total
New	49	36	85
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	49	38	87

Merged error: 0.4b

Counts

87 → 38

Compiler

Compiled 2829 to 1802 computations (36.3% saved)

localize54.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.2b	(.f64 (.f64 3 a) c)
0.3b	(/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
0.4b	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))

rewrite236.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
34×	`times-frac_binary64_1789`
28×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
19×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
17×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
14×	`associate-/l*_binary64_1728` `pow1_binary64_1844`
12×	`add-cube-cbrt_binary64_1818`
8×	`difference-of-squares_binary64_1752` `associate-/r*_binary64_1727` `distribute-lft-out--_binary64_1735`
6×	`associate-/r/_binary64_1729` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
4×	`div-inv_binary64_1780` `sqrt-prod_binary64_1799` `add-log-exp_binary64_1822` `distribute-rgt-neg-in_binary64_1741`
3×	`flip3--_binary64_1787` `flip--_binary64_1758`
2×	`associate-l_binary64_1724` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`associate-/l/_binary64_1730`

Counts

4 → 123

Calls

4 calls:

74.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
61.0ms	(/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
19.0ms	(.f64 (.f64 3 a) c)
19.0ms	(.f64 (.f64 3 a) c)

series1.5s (2.1%)

Counts

4 → 12

Calls

4 calls:

707.0ms	(/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
650.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
69.0ms	(.f64 (.f64 3 a) c)
65.0ms	(.f64 (.f64 3 a) c)

simplify372.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (234.0ms)

Iter	Nodes	Cost
0	4928	3312
1	4928	3312

prune2.8s (3.9%)

Pruning

76 alts after pruning (75 fresh and 1 done)

	Pruned	Kept	Total
New	87	48	135
Fresh	9	27	36
Picked	1	0	1
Done	0	1	1
Total	97	76	173

Merged error: 0.0b

Counts

173 → 76

Compiler

Compiled 6078 to 3815 computations (37.2% saved)

localize50.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))
0.2b	(.f64 c (.f64 3 a))
0.3b	(.f64 a (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 3 a)))))) a))
0.3b	(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))) a)

rewrite334.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

312×	`times-frac_binary64_1789`
238×	`add-sqr-sqrt_binary64_1805`
229×	`*-un-lft-identity_binary64_1783`
141×	`add-cube-cbrt_binary64_1818`
86×	`associate-r_binary64_1723`
44×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
27×	`associate-/l*_binary64_1728`
25×	`sqrt-prod_binary64_1799`
23×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
22×	`distribute-rgt-neg-in_binary64_1741`
14×	`associate-/r/_binary64_1729`
11×	`pow1_binary64_1844`
9×	`div-inv_binary64_1780`
8×	`flip3--_binary64_1787` `flip--_binary64_1758` `add-log-exp_binary64_1822`
6×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
4×	`pow-prod-down_binary64_1854`
3×	`associate-/r*_binary64_1727` `unswap-sqr_binary64_1751`
2×	`diff-log_binary64_1875` `*-commutative_binary64_1714`
1×	`associate-*r/_binary64_1725` `associate-/l/_binary64_1730` `associate--l-_binary64_1721` `frac-2neg_binary64_1794` `neg-sub0_binary64_1778` `neg-log_binary64_1876` `clear-num_binary64_1782` `sub-neg_binary64_1776`

Counts

4 → 274

Calls

4 calls:

139.0ms	(.f64 a (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 3 a)))))) a))
65.0ms	(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))) a)
38.0ms	(.f64 c (.f64 3 a))
19.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))

series1.6s (2.3%)

Counts

4 → 12

Calls

4 calls:

625.0ms	(.f64 a (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 3 a)))))) a))
545.0ms	(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))) a)
366.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))
76.0ms	(.f64 c (.f64 3 a))

simplify496.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	4992	9877
1	4992	9877

prune6.6s (9.2%)

Pruning

157 alts after pruning (155 fresh and 2 done)

	Pruned	Kept	Total
New	189	97	286
Fresh	16	58	74
Picked	0	1	1
Done	0	1	1
Total	205	157	362

Merged error: 0b

Counts

362 → 157

Compiler

Compiled 15234 to 8196 computations (46.2% saved)

localize28.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))
0.2b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))
0.2b	(.f64 c (.f64 3 a))

rewrite76.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
21×	`times-frac_binary64_1789`
19×	`add-cube-cbrt_binary64_1818`
11×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
10×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `add-log-exp_binary64_1822`
9×	`pow1_binary64_1844`
8×	`sqrt-prod_binary64_1799`
7×	`cancel-sign-sub-inv_binary64_1749` `associate-/r*_binary64_1727`
5×	`distribute-rgt-neg-in_binary64_1741`
3×	`flip3--_binary64_1787` `associate-/l_binary64_1728` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `associate-l*_binary64_1724` `diff-log_binary64_1875` `pow-prod-down_binary64_1854` `flip--_binary64_1758`
2×	`associate-/r/_binary64_1729` `sub-neg_binary64_1776`
1×	`div-inv_binary64_1780` `associate--l-_binary64_1721` `cbrt-undiv_binary64_1817` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `neg-sub0_binary64_1778` `neg-log_binary64_1876` `clear-num_binary64_1782` `associate-r*_binary64_1723`

Counts

4 → 98

Calls

4 calls:

21.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a))))))
19.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))
10.0ms	(.f64 c (.f64 3 a))
8.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))

series657.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

401.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a))))))
140.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))
88.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))
27.0ms	(.f64 c (.f64 3 a))

simplify225.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	4936	2689
1	4936	2689

prune4.0s (5.6%)

Pruning

178 alts after pruning (175 fresh and 3 done)

	Pruned	Kept	Total
New	77	33	110
Fresh	12	142	154
Picked	0	1	1
Done	0	2	2
Total	89	178	267

Merged error: 0b

Counts

267 → 178

Compiler

Compiled 2698 to 1475 computations (45.3% saved)

regimes9.9s (13.8%)

Compiler: Compiled 55858 to 38985 computations (30.2% saved)

bsearch14.8s (20.7%)

simplify17.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	113	44
1	113	44

end0.0ms (0%)

sample23.9s (33.4%)

Algorithm

1×

intervals

Results

797.0ms	7702×	body	128	valid
625.0ms	8959×	pre	128	true
91.0ms	959×	body	128	nan
69.0ms	298×	body	256	valid

Compiler

Compiled 10523 to 7306 computations (30.6% saved)

Pareto

0.2857142857142857

Details

analyze1.2s (1.7%)

sample71.0ms (0.1%)

simplify719.0ms (1%)

prune10.0ms (0%)

localize24.0ms (0%)

rewrite85.0ms (0.1%)

series457.0ms (0.6%)

simplify141.0ms (0.2%)

prune1.2s (1.7%)

localize54.0ms (0.1%)

rewrite236.0ms (0.3%)

series1.5s (2.1%)

simplify372.0ms (0.5%)

prune2.8s (3.9%)

localize50.0ms (0.1%)

rewrite334.0ms (0.5%)

series1.6s (2.3%)

simplify496.0ms (0.7%)

prune6.6s (9.2%)

localize28.0ms (0%)

rewrite76.0ms (0.1%)

series657.0ms (0.9%)

simplify225.0ms (0.3%)

prune4.0s (5.6%)

regimes9.9s (13.8%)

bsearch14.8s (20.7%)

simplify17.0ms (0%)

end0.0ms (0%)

sample23.9s (33.4%)

Profiling