Details

analyze106.0ms (0.9%)

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)

sample23.0ms (0.2%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify208.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4981	40
1	4981	40

prune5.0ms (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: 0.4b

Counts

2 → 2

Compiler

Compiled 80 to 61 computations (23.8% saved)

localize15.0ms (0.1%)

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 (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
20×	`pow1_binary64_1820`
16×	`prod-exp_binary64_1808` `associate-*r/_binary64_1706` `cbrt-unprod_binary64_1792`
14×	`add-sqr-sqrt_binary64_1783`
12×	`sqrt-div_binary64_1778` `associate-l_binary64_1705`
11×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
10×	`pow-prod-down_binary64_1830`
8×	`associate-/r/_binary64_1710` `frac-times_binary64_1772`
7×	`flip3--_binary64_1766` `flip--_binary64_1737`
6×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
5×	`associate-r_binary64_1704`
4×	`associate-*l/_binary64_1707` `cbrt-undiv_binary64_1793` `add-log-exp_binary64_1798` `div-exp_binary64_1810` `distribute-rgt-in_binary64_1714` `sub-neg_binary64_1755` `distribute-lft-in_binary64_1713`
3×	`times-frac_binary64_1768` `sqrt-prod_binary64_1777` `-commutative_binary64_1695` `associate-/l_binary64_1709`
2×	`associate-/l/_binary64_1711` `unswap-sqr_binary64_1730`
1×	`frac-2neg_binary64_1773` `div-sub_binary64_1767` `clear-num_binary64_1761` `associate-/r*_binary64_1708` `div-inv_binary64_1759`

Counts

4 → 109

Calls

4 calls:

20.0ms	(/.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))))
6.0ms	(.f64 5 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)

series652.0ms (5.3%)

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)))))
267.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
38.0ms	(.f64 5 (.f64 v v))
27.0ms	(*.f64 PI.f64 t)

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4976	3590
1	4976	3590

prune229.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	117	6	123

Merged error: 0.0b

Counts

123 → 6

Compiler

Compiled 4386 to 2739 computations (37.6% saved)

localize16.0ms (0.1%)

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)))))

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1768`
51×	`add-sqr-sqrt_binary64_1783`
48×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
34×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
30×	`sqrt-prod_binary64_1777`
27×	`associate-/l*_binary64_1709`
11×	`pow1_binary64_1820`
10×	`prod-exp_binary64_1808` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `cbrt-unprod_binary64_1792`
8×	`associate-/r/_binary64_1710`
7×	`associate-/r*_binary64_1708`
6×	`sqrt-div_binary64_1778` `associate-r_binary64_1704`
4×	`pow-prod-down_binary64_1830` `div-inv_binary64_1759` `add-log-exp_binary64_1798` `associate-l_binary64_1705`
3×	`div-sub_binary64_1767` `associate-/l/_binary64_1711` `flip3-+_binary64_1765` `flip-+_binary64_1736`
2×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `clear-num_binary64_1761` `unswap-sqr_binary64_1730` `associate-r/_binary64_1706` `flip--_binary64_1737` `-commutative_binary64_1695`

Counts

4 → 156

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 (.f64 v v) 5)
4.0ms	(*.f64 PI.f64 t)

series509.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

318.0ms	(/.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))))
127.0ms	(/.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)

simplify108.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4937	6117
1	4937	6117

prune321.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	167	7	174

Merged error: 0b

Counts

174 → 7

Compiler

Compiled 6489 to 4160 computations (35.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 t)
0.3b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (*.f64 PI.f64 t))
0.4b	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 PI.f64 t)) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (-.f64 1 (*.f64 v v))))
1.0b	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite123.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

243×	`times-frac_binary64_1768`
160×	`add-sqr-sqrt_binary64_1783`
141×	`*-un-lft-identity_binary64_1762`
129×	`associate-r_binary64_1704`
115×	`add-cube-cbrt_binary64_1794`
75×	`add-exp-log_binary64_1797`
59×	`sqrt-prod_binary64_1777`
49×	`add-cbrt-cube_binary64_1795`
48×	`difference-of-squares_binary64_1731`
32×	`div-exp_binary64_1810`
22×	`prod-exp_binary64_1808`
18×	`cbrt-undiv_binary64_1793`
14×	`associate-/r/_binary64_1710` `cbrt-unprod_binary64_1792`
12×	`sqrt-div_binary64_1778`
10×	`pow1_binary64_1820` `associate-l_binary64_1705`
9×	`div-inv_binary64_1759`
7×	`associate-/r*_binary64_1708` `unswap-sqr_binary64_1730`
6×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `associate-/l*_binary64_1709`
4×	`add-log-exp_binary64_1798` `1-exp_binary64_1803` `rec-exp_binary64_1809`
3×	`pow-flip_binary64_1833`
2×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `pow-prod-down_binary64_1830` `associate-/l/_binary64_1711` `clear-num_binary64_1761` `flip--_binary64_1737` `*-commutative_binary64_1695`
1×	`frac-times_binary64_1772` `div-sub_binary64_1767` `inv-pow_binary64_1844` `associate-l/_binary64_1707` `associate-r/_binary64_1706` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`

Counts

4 → 264

Calls

4 calls:

56.0ms	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 PI.f64 t)) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (-.f64 1 (*.f64 v v))))
7.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (*.f64 PI.f64 t))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
4.0ms	(*.f64 PI.f64 t)

series507.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

307.0ms	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 PI.f64 t)) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (-.f64 1 (*.f64 v v))))
93.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (*.f64 PI.f64 t))
82.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
25.0ms	(*.f64 PI.f64 t)

simplify118.0ms (1%)

Algorithm

1×	egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4979	9831
1	4979	9831

prune680.0ms (5.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	273	3	276
Fresh	3	1	4
Picked	1	0	1
Done	0	2	2
Total	277	6	283

Merged error: 0b

Counts

283 → 6

Compiler

Compiled 11155 to 7435 computations (33.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 5)
0.4b	(.f64 (/.f64 1 PI.f64) (/.f64 (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (-.f64 1 (.f64 v v))) t))
0.5b	(/.f64 (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (-.f64 1 (*.f64 v v))) t)
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite494.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

2290×	`times-frac_binary64_1768`
1142×	`add-sqr-sqrt_binary64_1783`
1084×	`*-un-lft-identity_binary64_1762`
911×	`add-cube-cbrt_binary64_1794`
385×	`associate-r_binary64_1704`
336×	`difference-of-squares_binary64_1731`
330×	`sqrt-prod_binary64_1777`
129×	`associate-/l*_binary64_1709`
86×	`associate-/r/_binary64_1710`
80×	`add-exp-log_binary64_1797`
72×	`sqrt-div_binary64_1778`
52×	`add-cbrt-cube_binary64_1795`
46×	`div-inv_binary64_1759`
39×	`div-exp_binary64_1810`
36×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
23×	`cbrt-undiv_binary64_1793`
19×	`prod-exp_binary64_1808`
16×	`unswap-sqr_binary64_1730`
14×	`associate-l_binary64_1705`
11×	`cbrt-unprod_binary64_1792` `pow1_binary64_1820`
9×	`associate-/r*_binary64_1708`
8×	`flip3--_binary64_1766` `flip--_binary64_1737`
4×	`div-sub_binary64_1767` `pow-prod-down_binary64_1830` `add-log-exp_binary64_1798` `1-exp_binary64_1803` `rec-exp_binary64_1809`
3×	`associate-/l/_binary64_1711`
2×	`frac-2neg_binary64_1773` `clear-num_binary64_1761` `*-commutative_binary64_1695`
1×	`frac-times_binary64_1772` `associate-l/_binary64_1707` `associate-r/_binary64_1706`

Counts

4 → 1034

Calls

4 calls:

171.0ms	(.f64 (/.f64 1 PI.f64) (/.f64 (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (-.f64 1 (.f64 v v))) t))
45.0ms	(/.f64 (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (-.f64 1 (*.f64 v v))) t)
9.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
6.0ms	(.f64 (.f64 v v) 5)

series709.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

297.0ms	(.f64 (/.f64 1 PI.f64) (/.f64 (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (-.f64 1 (.f64 v v))) t))
251.0ms	(/.f64 (/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (-.f64 1 (*.f64 v v))) t)
125.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
35.0ms	(.f64 (.f64 v v) 5)

simplify460.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1046 → 1046

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5490	57066

prune5.9s (48.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1045	1	1046
Fresh	1	2	3
Picked	1	0	1
Done	2	0	2
Total	1049	3	1052

Merged error: 0b

Counts

1052 → 3

Compiler

Compiled 53967 to 35714 computations (33.8% saved)

regimes53.0ms (0.4%)

Compiler: Compiled 314 to 256 computations (18.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	40
1	60	40

end0.0ms (0%)

sample774.0ms (6.3%)

Algorithm

1×

intervals

Results

506.0ms	8000×	body	128	valid
3.0ms	14×	body	128	nan

Compiler

Compiled 136 to 107 computations (21.3% saved)

Details

analyze106.0ms (0.9%)

sample23.0ms (0.2%)

simplify208.0ms (1.7%)

prune5.0ms (0%)

localize15.0ms (0.1%)

rewrite57.0ms (0.5%)

series652.0ms (5.3%)

simplify81.0ms (0.7%)

prune229.0ms (1.9%)

localize16.0ms (0.1%)

rewrite62.0ms (0.5%)

series509.0ms (4.1%)

simplify108.0ms (0.9%)

prune321.0ms (2.6%)

localize17.0ms (0.1%)

rewrite123.0ms (1%)

series507.0ms (4.1%)

simplify118.0ms (1%)

prune680.0ms (5.5%)

localize17.0ms (0.1%)

rewrite494.0ms (4%)

series709.0ms (5.8%)

simplify460.0ms (3.8%)

prune5.9s (48.3%)

regimes53.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample774.0ms (6.3%)

Profiling