Details

analyze110.0ms (1.4%)

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 (0.3%)

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)

simplify206.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4981	40
1	4981	40

prune5.0ms (0.1%)

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)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 v (.f64 -6 v))
0.2b	(/.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)))))
0.3b	(*.f64 PI.f64 t)
0.5b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))

rewrite54.0ms (0.7%)

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`
13×	`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`
1×	`frac-2neg_binary64_1773` `div-sub_binary64_1767` `clear-num_binary64_1761` `associate-/r*_binary64_1708` `div-inv_binary64_1759` `unswap-sqr_binary64_1730`

Counts

4 → 108

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))))
6.0ms	(.f64 v (.f64 -6 v))
4.0ms	(*.f64 PI.f64 t)

series631.0ms (8.3%)

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)))))
251.0ms	(.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))
27.0ms	(*.f64 PI.f64 t)

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4959	3576
1	4959	3576

prune226.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	115	7	122

Merged error: 0.0b

Counts

122 → 7

Compiler

Compiled 4467 to 2792 computations (37.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 v (.f64 v -6))
0.3b	(*.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)))))

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1768`
50×	`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-l_binary64_1705`
4×	`pow-prod-down_binary64_1830` `div-inv_binary64_1759` `add-log-exp_binary64_1798` `associate-r_binary64_1704`
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` `associate-r/_binary64_1706` `flip--_binary64_1737` `-commutative_binary64_1695`
1×	`unswap-sqr_binary64_1730`

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)))))
5.0ms	(.f64 v (.f64 v -6))
4.0ms	(*.f64 PI.f64 t)

series518.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

306.0ms	(/.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))))
135.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
44.0ms	(.f64 v (.f64 v -6))
32.0ms	(*.f64 PI.f64 t)

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4931	6101
1	4931	6101

prune343.0ms (4.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	169	5	174

Merged error: 0b

Counts

174 → 5

Compiler

Compiled 6420 to 4103 computations (36.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite73.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-exp-log_binary64_1797`
52×	`add-sqr-sqrt_binary64_1783`
49×	`add-cbrt-cube_binary64_1795`
46×	`times-frac_binary64_1768`
40×	`*-un-lft-identity_binary64_1762`
38×	`add-cube-cbrt_binary64_1794`
32×	`prod-exp_binary64_1808`
27×	`associate-l_binary64_1705`
25×	`div-exp_binary64_1810`
23×	`sqrt-prod_binary64_1777`
18×	`cbrt-unprod_binary64_1792`
14×	`cbrt-undiv_binary64_1793`
12×	`associate-r_binary64_1704`
10×	`pow1_binary64_1820`
8×	`associate-/r/_binary64_1710`
7×	`associate-/r*_binary64_1708`
6×	`unswap-sqr_binary64_1730` `associate-/l*_binary64_1709`
5×	`associate-*r/_binary64_1706` `1-exp_binary64_1803` `rec-exp_binary64_1809`
4×	`div-inv_binary64_1759` `add-log-exp_binary64_1798` `sqrt-div_binary64_1778`
3×	`flip3--_binary64_1766` `pow-flip_binary64_1833` `flip--_binary64_1737`
2×	`frac-2neg_binary64_1773` `pow-prod-down_binary64_1830` `associate-/l/_binary64_1711` `flip3-+_binary64_1765` `clear-num_binary64_1761` `flip-+_binary64_1736` `*-commutative_binary64_1695`
1×	`frac-times_binary64_1772` `div-sub_binary64_1767` `inv-pow_binary64_1844` `associate-*l/_binary64_1707` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`

Counts

4 → 167

Calls

4 calls:

24.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
11.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
4.0ms	(*.f64 PI.f64 t)

series542.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

300.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
141.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
76.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
25.0ms	(*.f64 PI.f64 t)

simplify105.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4932	5762
1	4932	5762

prune342.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	179	5	184

Merged error: 0b

Counts

184 → 5

Compiler

Compiled 6574 to 4229 computations (35.7% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

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))))))
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)))))

rewrite63.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`sqrt-prod_binary64_1777`
76×	`times-frac_binary64_1768`
70×	`add-sqr-sqrt_binary64_1783`
60×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
12×	`associate-/r*_binary64_1708`
10×	`sqrt-div_binary64_1778`
8×	`associate-/r/_binary64_1710` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
6×	`rem-sqrt-square_binary64_1775` `associate-/l*_binary64_1709` `pow1_binary64_1820`
4×	`associate-/l/_binary64_1711` `flip3-+_binary64_1765` `flip-+_binary64_1736` `div-inv_binary64_1759` `add-log-exp_binary64_1798`
2×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `div-sub_binary64_1767` `clear-num_binary64_1761` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `flip--_binary64_1737` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`

Counts

4 → 162

Calls

4 calls:

9.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
9.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
9.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

series702.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
220.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
130.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
129.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5166	7128

prune659.0ms (8.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	174	5	179

Merged error: 0b

Counts

179 → 5

Compiler

Compiled 10348 to 7061 computations (31.8% saved)

regimes671.0ms (8.8%)

Compiler: Compiled 10571 to 7931 computations (25% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	28	40

end0.0ms (0%)

sample2.0s (25.6%)

Algorithm

1×

intervals

Results

513.0ms	8000×	body	128	valid
1.0ms	17×	body	128	nan

Compiler

Compiled 1856 to 1391 computations (25.1% saved)

Details

analyze110.0ms (1.4%)

sample24.0ms (0.3%)

simplify206.0ms (2.7%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

rewrite54.0ms (0.7%)

series631.0ms (8.3%)

simplify85.0ms (1.1%)

prune226.0ms (3%)

localize19.0ms (0.2%)

rewrite57.0ms (0.7%)

series518.0ms (6.8%)

simplify103.0ms (1.3%)

prune343.0ms (4.5%)

localize16.0ms (0.2%)

rewrite73.0ms (1%)

series542.0ms (7.1%)

simplify105.0ms (1.4%)

prune342.0ms (4.5%)

localize21.0ms (0.3%)

rewrite63.0ms (0.8%)

series702.0ms (9.2%)

simplify88.0ms (1.2%)

prune659.0ms (8.6%)

regimes671.0ms (8.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (25.6%)

Profiling