Details

analyze108.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 29 to 22 computations (24.1% saved)

sample24.0ms (0%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify140.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4990	40
1	4990	40

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.4b

Counts

2 → 1

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
0.5b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))

rewrite57.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
20×	`pow1_binary64_1844`
16×	`associate-*r/_binary64_1725` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
14×	`add-sqr-sqrt_binary64_1805`
12×	`associate-l_binary64_1724` `sqrt-div_binary64_1800`
11×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`pow-prod-down_binary64_1854`
8×	`associate-/r/_binary64_1729` `distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733` `frac-times_binary64_1793`
7×	`flip3--_binary64_1787` `flip--_binary64_1758`
6×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
5×	`associate-r_binary64_1723`
4×	`cancel-sign-sub-inv_binary64_1749` `associate-*l/_binary64_1726` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `sub-neg_binary64_1776` `add-log-exp_binary64_1822`
3×	`associate-/l_binary64_1728` `sqrt-prod_binary64_1799` `times-frac_binary64_1789` `-commutative_binary64_1714`
2×	`associate-/l/_binary64_1730` `unswap-sqr_binary64_1751`
1×	`div-sub_binary64_1788` `div-inv_binary64_1780` `associate-/r*_binary64_1727` `frac-2neg_binary64_1794` `clear-num_binary64_1782`

Counts

4 → 113

Calls

4 calls:

17.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
14.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
7.0ms	(*.f64 PI.f64 t)
6.0ms	(.f64 5 (.f64 v v))

series571.0ms (0.5%)

Counts

4 → 24

Calls

4 calls:

321.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
198.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
28.0ms	(.f64 5 (.f64 v v))
23.0ms	(*.f64 PI.f64 t)

Compiler

Compiled 1324 to 1094 computations (17.4% saved)

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5053	4323

prune235.0ms (0.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	6	138

Merged error: 0.0b

Counts

138 → 6

Compiler

Compiled 4873 to 3017 computations (38.1% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 5)
0.2b	(*.f64 PI.f64 t)
0.5b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite53.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1789`
51×	`add-sqr-sqrt_binary64_1805`
48×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
34×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
30×	`sqrt-prod_binary64_1799`
27×	`associate-/l*_binary64_1728`
11×	`pow1_binary64_1844`
10×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
8×	`associate-/r/_binary64_1729`
7×	`associate-/r*_binary64_1727`
6×	`sqrt-div_binary64_1800` `associate-r_binary64_1723`
4×	`div-inv_binary64_1780` `associate-l_binary64_1724` `pow-prod-down_binary64_1854` `add-log-exp_binary64_1822`
3×	`div-sub_binary64_1788` `associate-/l/_binary64_1730` `flip-+_binary64_1757` `flip3-+_binary64_1786`
2×	`flip3--_binary64_1787` `associate-r/_binary64_1725` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `unswap-sqr_binary64_1751` `flip--_binary64_1758`

Counts

4 → 156

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
8.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
6.0ms	(.f64 (.f64 v v) 5)
4.0ms	(*.f64 PI.f64 t)

series486.0ms (0.4%)

Counts

4 → 21

Calls

4 calls:

344.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
78.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
36.0ms	(.f64 (.f64 v v) 5)
28.0ms	(*.f64 PI.f64 t)

Compiler

Compiled 1081 to 904 computations (16.4% saved)

simplify103.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4968	6468
1	4968	6468

prune345.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	177	6	183

Merged error: 0b

Counts

183 → 6

Compiler

Compiled 6694 to 4273 computations (36.2% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 t)
0.3b	(/.f64 (.f64 PI.f64 t) (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))) (-.f64 1 (.f64 v v))))
0.5b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))) (/.f64 (.f64 PI.f64 t) (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))) (-.f64 1 (*.f64 v v)))))
1.0b	(/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (*.f64 v -6)))))))

rewrite1.5s (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

11481×	`times-frac_binary64_1789`
3296×	`add-sqr-sqrt_binary64_1805`
3294×	`*-un-lft-identity_binary64_1783`
2700×	`add-cube-cbrt_binary64_1818`
2316×	`cbrt-div_binary64_1815` `sqrt-div_binary64_1800`
1658×	`associate-/r/_binary64_1729`
1620×	`cbrt-prod_binary64_1814`
1188×	`difference-of-squares_binary64_1752`
1158×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
810×	`sqrt-prod_binary64_1799`
712×	`frac-times_binary64_1793`
356×	`associate-r/_binary64_1725` `associate-l/_binary64_1726`
348×	`associate-/r*_binary64_1727`
304×	`div-inv_binary64_1780`
276×	`add-exp-log_binary64_1821`
177×	`div-exp_binary64_1834`
116×	`add-cbrt-cube_binary64_1819`
85×	`cbrt-undiv_binary64_1817`
49×	`prod-exp_binary64_1832`
21×	`cbrt-unprod_binary64_1816`
19×	`associate-/l*_binary64_1728`
18×	`flip3--_binary64_1787` `flip--_binary64_1758`
16×	`1-exp_binary64_1827` `rec-exp_binary64_1833`
14×	`pow1_binary64_1844`
9×	`pow-flip_binary64_1857`
6×	`pow1/3_binary64_1865`
4×	`add-log-exp_binary64_1822`
3×	`associate-l_binary64_1724` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
2×	`pow-prod-up_binary64_1853` `pow-sqr_binary64_1756`
1×	`associate-/l/_binary64_1730` `inv-pow_binary64_1868` `pow-plus_binary64_1846` `*-commutative_binary64_1714` `unswap-sqr_binary64_1751` `pow2_binary64_1864`

Counts

4 → 3340

Calls

4 calls:

132.0ms	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))) (/.f64 (.f64 PI.f64 t) (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))) (-.f64 1 (*.f64 v v)))))
50.0ms	(/.f64 (.f64 PI.f64 t) (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))) (-.f64 1 (.f64 v v))))
13.0ms	(/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (*.f64 v -6)))))))
4.0ms	(*.f64 PI.f64 t)

series882.0ms (0.7%)

Counts

4 → 27

Calls

4 calls:

417.0ms	(/.f64 (.f64 PI.f64 t) (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))) (-.f64 1 (.f64 v v))))
361.0ms	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))) (/.f64 (.f64 PI.f64 t) (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))) (-.f64 1 (*.f64 v v)))))
74.0ms	(/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (cbrt.f64 (sqrt.f64 (+.f64 2 (.f64 v (*.f64 v -6)))))))
29.0ms	(*.f64 PI.f64 t)

Compiler

Compiled 1858 to 1552 computations (16.5% saved)

simplify3.2s (2.6%)

Algorithm

1×	egg-herbie

Counts

3367 → 3367

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	6765	437552

prune1.8min (90.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	3367	0	3367
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	3367	6	3373

Merged error: 0b

Counts

3373 → 6

Compiler

Compiled 300855 to 222937 computations (25.9% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
1.0b	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
1.0b	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))

rewrite62.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`sqrt-prod_binary64_1799`
76×	`times-frac_binary64_1789`
70×	`add-sqr-sqrt_binary64_1805`
60×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
12×	`associate-/r*_binary64_1727`
10×	`sqrt-div_binary64_1800`
8×	`add-cbrt-cube_binary64_1819` `associate-/r/_binary64_1729` `add-exp-log_binary64_1821`
6×	`associate-/l*_binary64_1728` `rem-sqrt-square_binary64_1796` `pow1_binary64_1844`
4×	`associate-/l/_binary64_1730` `flip-+_binary64_1757` `div-inv_binary64_1780` `flip3-+_binary64_1786` `add-log-exp_binary64_1822`
2×	`flip3--_binary64_1787` `div-sub_binary64_1788` `pow1/2_binary64_1863` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `flip--_binary64_1758`

Counts

4 → 162

Calls

4 calls:

8.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
8.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
8.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
8.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))

series355.0ms (0.3%)

Counts

4 → 24

Calls

4 calls:

106.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
101.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
75.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
73.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

Compiler

Compiled 1682 to 1396 computations (17% saved)

simplify140.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4896	6840
1	4896	6840

prune666.0ms (0.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	186	6	192

Merged error: 0b

Counts

192 → 6

Compiler

Compiled 10504 to 7092 computations (32.5% saved)

regimes482.0ms (0.4%)

Compiler: Compiled 7881 to 5906 computations (25.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	40
1	62	40

end0.0ms (0%)

sample1.7s (1.4%)

Algorithm

1×

intervals

Results

506.0ms	8000×	body	128	valid
1.0ms	11×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 1606 to 1203 computations (25.1% saved)

Details

analyze108.0ms (0.1%)

sample24.0ms (0%)

simplify140.0ms (0.1%)

prune4.0ms (0%)

localize15.0ms (0%)

rewrite57.0ms (0%)

series571.0ms (0.5%)

simplify80.0ms (0.1%)

prune235.0ms (0.2%)

localize17.0ms (0%)

rewrite53.0ms (0%)

series486.0ms (0.4%)

simplify103.0ms (0.1%)

prune345.0ms (0.3%)

localize20.0ms (0%)

rewrite1.5s (1.2%)

series882.0ms (0.7%)

simplify3.2s (2.6%)

prune1.8min (90.7%)

localize18.0ms (0%)

rewrite62.0ms (0.1%)

series355.0ms (0.3%)

simplify140.0ms (0.1%)

prune666.0ms (0.5%)

regimes482.0ms (0.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.7s (1.4%)

Profiling