Details

analyze112.0ms (1.1%)

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)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify214.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4985	40
1	4985	40

prune10.0ms (0.1%)

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 106 to 81 computations (23.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 v (.f64 -6 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))))

rewrite58.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
20×	`pow1_binary64_1860`
16×	`prod-exp_binary64_1848` `associate-*r/_binary64_1741` `cbrt-unprod_binary64_1832`
13×	`add-sqr-sqrt_binary64_1821`
12×	`sqrt-div_binary64_1816` `associate-l_binary64_1740`
11×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
10×	`pow-prod-down_binary64_1870`
8×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `associate-/r/_binary64_1745` `frac-times_binary64_1809`
7×	`flip--_binary64_1774` `flip3--_binary64_1803`
6×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
5×	`associate-r_binary64_1739`
4×	`sub-neg_binary64_1792` `div-exp_binary64_1850` `add-log-exp_binary64_1838` `cbrt-undiv_binary64_1833` `cancel-sign-sub-inv_binary64_1765` `associate-*l/_binary64_1742`
3×	`associate-/l_binary64_1744` `sqrt-prod_binary64_1815` `times-frac_binary64_1805` `-commutative_binary64_1730`
2×	`associate-/l/_binary64_1746`
1×	`div-sub_binary64_1804` `clear-num_binary64_1798` `unswap-sqr_binary64_1767` `frac-2neg_binary64_1810` `associate-/r*_binary64_1743` `div-inv_binary64_1796`

Counts

4 → 112

Calls

4 calls:

18.0ms	(/.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)))))
15.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
6.0ms	(.f64 v (.f64 -6 v))
4.0ms	(*.f64 PI.f64 t)

series645.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

319.0ms	(/.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)))))
266.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
34.0ms	(.f64 v (.f64 -6 v))
26.0ms	(*.f64 PI.f64 t)

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5293	3762

prune600.0ms (6.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	6	125

Merged error: 0.0b

Counts

125 → 6

Compiler

Compiled 13350 to 9388 computations (29.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 v (.f64 v -6))
0.2b	(*.f64 PI.f64 t)
0.4b	(/.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)))))

rewrite62.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1805`
50×	`add-sqr-sqrt_binary64_1821`
48×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
34×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
30×	`sqrt-prod_binary64_1815`
27×	`associate-/l*_binary64_1744`
11×	`pow1_binary64_1860`
10×	`div-exp_binary64_1850` `prod-exp_binary64_1848` `cbrt-undiv_binary64_1833` `cbrt-unprod_binary64_1832`
8×	`associate-/r/_binary64_1745`
7×	`associate-/r*_binary64_1743`
6×	`sqrt-div_binary64_1816` `associate-l_binary64_1740`
4×	`add-log-exp_binary64_1838` `div-inv_binary64_1796` `pow-prod-down_binary64_1870` `associate-r_binary64_1739`
3×	`div-sub_binary64_1804` `associate-/l/_binary64_1746` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `associate-r/_binary64_1741` `flip--_binary64_1774` `flip3--_binary64_1803` `-commutative_binary64_1730`
1×	`unswap-sqr_binary64_1767`

Counts

4 → 155

Calls

4 calls:

18.0ms	(/.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))))
9.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
6.0ms	(.f64 v (.f64 v -6))
4.0ms	(*.f64 PI.f64 t)

series500.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

307.0ms	(/.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))))
130.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
36.0ms	(.f64 v (.f64 v -6))
26.0ms	(*.f64 PI.f64 t)

simplify115.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4936	6103
1	4936	6103

prune511.0ms (5.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	166	7	173

Merged error: 0b

Counts

173 → 7

Compiler

Compiled 10916 to 7464 computations (31.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 v (.f64 v -6))
0.2b	(*.f64 PI.f64 t)
0.4b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (*.f64 PI.f64 t))
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite60.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1805`
50×	`add-sqr-sqrt_binary64_1821`
48×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
30×	`sqrt-prod_binary64_1815`
27×	`associate-/l*_binary64_1744`
25×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
11×	`pow1_binary64_1860`
7×	`div-exp_binary64_1850` `associate-/r*_binary64_1743` `cbrt-undiv_binary64_1833`
6×	`sqrt-div_binary64_1816` `prod-exp_binary64_1848` `associate-l_binary64_1740` `associate-/r/_binary64_1745` `cbrt-unprod_binary64_1832`
4×	`add-log-exp_binary64_1838` `div-inv_binary64_1796` `pow-prod-down_binary64_1870` `associate-r_binary64_1739`
3×	`div-sub_binary64_1804` `associate-/l/_binary64_1746` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `*-commutative_binary64_1730`
1×	`unswap-sqr_binary64_1767` `flip--_binary64_1774` `flip3--_binary64_1803`

Counts

4 → 149

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (*.f64 PI.f64 t))
10.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
6.0ms	(.f64 v (.f64 v -6))
4.0ms	(*.f64 PI.f64 t)

series450.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

265.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (*.f64 PI.f64 t))
124.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
35.0ms	(.f64 v (.f64 v -6))
25.0ms	(*.f64 PI.f64 t)

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4930	5159
1	4930	5159

prune415.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	163	5	168

Merged error: 0b

Counts

168 → 5

Compiler

Compiled 8049 to 5409 computations (32.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 v (.f64 v -6))
0.1b	(/.f64 (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) PI.f64) t)
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
1.0b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) PI.f64)

rewrite175.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

894×	`times-frac_binary64_1805`
430×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
156×	`sqrt-prod_binary64_1815`
103×	`associate-/l*_binary64_1744`
34×	`sqrt-div_binary64_1816` `associate-/r/_binary64_1745`
25×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
23×	`div-inv_binary64_1796`
17×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
12×	`associate-/r*_binary64_1743`
10×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
9×	`pow1_binary64_1860`
6×	`div-sub_binary64_1804`
4×	`add-log-exp_binary64_1838` `associate-/l/_binary64_1746`
3×	`clear-num_binary64_1798` `prod-exp_binary64_1848` `frac-2neg_binary64_1810` `associate-l_binary64_1740` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870`
1×	`flip--_binary64_1774` `flip3--_binary64_1803` `-commutative_binary64_1730` `associate-r*_binary64_1739`

Counts

4 → 502

Calls

4 calls:

31.0ms	(/.f64 (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) PI.f64) t)
15.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) PI.f64)
9.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
6.0ms	(.f64 v (.f64 v -6))

series564.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(/.f64 (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) PI.f64) t)
151.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) PI.f64)
131.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
32.0ms	(.f64 v (.f64 v -6))

simplify256.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

514 → 514

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5261	27504

prune1.8s (18.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	512	2	514
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	514	5	519

Merged error: 0b

Counts

519 → 5

Compiler

Compiled 24449 to 15434 computations (36.9% saved)

regimes817.0ms (8.3%)

Compiler: Compiled 12667 to 9540 computations (24.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	40
1	60	40

end0.0ms (0%)

sample2.2s (22.7%)

Algorithm

1×

intervals

Results

511.0ms	8000×	body	128	valid
1.0ms	11×	body	128	nan

Compiler

Compiled 2223 to 1674 computations (24.7% saved)

Details

analyze112.0ms (1.1%)

sample27.0ms (0.3%)

simplify214.0ms (2.2%)

prune10.0ms (0.1%)

localize16.0ms (0.2%)

rewrite58.0ms (0.6%)

series645.0ms (6.5%)

simplify69.0ms (0.7%)

prune600.0ms (6.1%)

localize16.0ms (0.2%)

rewrite62.0ms (0.6%)

series500.0ms (5.1%)

simplify115.0ms (1.2%)

prune511.0ms (5.2%)

localize17.0ms (0.2%)

rewrite60.0ms (0.6%)

series450.0ms (4.6%)

simplify94.0ms (1%)

prune415.0ms (4.2%)

localize21.0ms (0.2%)

rewrite175.0ms (1.8%)

series564.0ms (5.7%)

simplify256.0ms (2.6%)

prune1.8s (18.2%)

regimes817.0ms (8.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (22.7%)

Profiling