Details

analyze106.0ms (0.7%)

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)

sample26.0ms (0.2%)

Algorithm

1×

intervals

Results

19.0ms

256×

body

128

valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify204.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4985	40
1	4985	40

prune7.0ms (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 (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.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))))

rewrite55.0ms (0.4%)

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

series641.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

316.0ms	(/.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)))))
260.0ms	(.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))
26.0ms	(*.f64 PI.f64 t)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5276	3774

prune226.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Merged error: 0.0b

Counts

126 → 6

Compiler

Compiled 4624 to 2874 computations (37.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.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)))))

rewrite57.0ms (0.4%)

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:

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)

series516.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

314.0ms	(/.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))))
139.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
36.0ms	(.f64 (.f64 v v) 5)
26.0ms	(*.f64 PI.f64 t)

simplify102.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4924	6117
1	4924	6117

prune351.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	168	6	174

Merged error: 0b

Counts

174 → 6

Compiler

Compiled 6475 to 4149 computations (35.9% saved)

localize16.0ms (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))
0.5b	(.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)))))

rewrite119.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

243×	`times-frac_binary64_1789`
160×	`add-sqr-sqrt_binary64_1805`
141×	`*-un-lft-identity_binary64_1783`
129×	`associate-r_binary64_1723`
115×	`add-cube-cbrt_binary64_1818`
75×	`add-exp-log_binary64_1821`
59×	`sqrt-prod_binary64_1799`
49×	`add-cbrt-cube_binary64_1819`
48×	`difference-of-squares_binary64_1752`
32×	`div-exp_binary64_1834`
22×	`prod-exp_binary64_1832`
18×	`cbrt-undiv_binary64_1817`
14×	`associate-/r/_binary64_1729` `cbrt-unprod_binary64_1816`
12×	`sqrt-div_binary64_1800`
10×	`associate-l_binary64_1724` `pow1_binary64_1844`
9×	`div-inv_binary64_1780`
7×	`associate-/r*_binary64_1727` `unswap-sqr_binary64_1751`
6×	`associate-/l*_binary64_1728` `flip-+_binary64_1757` `flip3-+_binary64_1786`
4×	`1-exp_binary64_1827` `rec-exp_binary64_1833` `add-log-exp_binary64_1822`
3×	`pow-flip_binary64_1857`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `flip--_binary64_1758`
1×	`div-sub_binary64_1788` `associate-r/_binary64_1725` `inv-pow_binary64_1868` `pow1/2_binary64_1863` `associate-l/_binary64_1726` `frac-times_binary64_1793` `sqrt-pow1_binary64_1801`

Counts

4 → 264

Calls

4 calls:

59.0ms	(.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)

series523.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

320.0ms	(.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))))
98.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (*.f64 PI.f64 t))
78.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
27.0ms	(*.f64 PI.f64 t)

simplify124.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4986	9831
1	4986	9831

prune746.0ms (5.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	274	2	276
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	277	5	282

Merged error: 0b

Counts

282 → 5

Compiler

Compiled 11148 to 7430 computations (33.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite490.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

2290×	`times-frac_binary64_1789`
1142×	`add-sqr-sqrt_binary64_1805`
1084×	`*-un-lft-identity_binary64_1783`
911×	`add-cube-cbrt_binary64_1818`
385×	`associate-r_binary64_1723`
336×	`difference-of-squares_binary64_1752`
330×	`sqrt-prod_binary64_1799`
129×	`associate-/l*_binary64_1728`
86×	`associate-/r/_binary64_1729`
80×	`add-exp-log_binary64_1821`
72×	`sqrt-div_binary64_1800`
52×	`add-cbrt-cube_binary64_1819`
46×	`div-inv_binary64_1780`
39×	`div-exp_binary64_1834`
36×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
23×	`cbrt-undiv_binary64_1817`
19×	`prod-exp_binary64_1832`
16×	`unswap-sqr_binary64_1751`
14×	`associate-l_binary64_1724`
11×	`cbrt-unprod_binary64_1816` `pow1_binary64_1844`
9×	`associate-/r*_binary64_1727`
8×	`flip3--_binary64_1787` `flip--_binary64_1758`
4×	`div-sub_binary64_1788` `1-exp_binary64_1827` `pow-prod-down_binary64_1854` `rec-exp_binary64_1833` `add-log-exp_binary64_1822`
3×	`associate-/l/_binary64_1730`
2×	`*-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`associate-r/_binary64_1725` `associate-l/_binary64_1726` `frac-times_binary64_1793`

Counts

4 → 1034

Calls

4 calls:

173.0ms	(.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))
43.0ms	(/.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)))))
7.0ms	(.f64 (.f64 v v) 5)

series725.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

313.0ms	(.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))
254.0ms	(/.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)
123.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
34.0ms	(.f64 (.f64 v v) 5)

simplify680.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1046 → 1046

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5484	57069

prune5.7s (40.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1045	1	1046
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	1046	5	1051

Merged error: 0b

Counts

1051 → 5

Compiler

Compiled 53969 to 35716 computations (33.8% saved)

regimes693.0ms (4.9%)

Compiler: Compiled 11023 to 8333 computations (24.4% 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%)

sample2.0s (14%)

Algorithm

1×

intervals

Results

505.0ms	8000×	body	128	valid
1.0ms	15×	body	128	nan

Compiler

Compiled 1920 to 1451 computations (24.4% saved)

Details

analyze106.0ms (0.7%)

sample26.0ms (0.2%)

simplify204.0ms (1.4%)

prune7.0ms (0%)

localize15.0ms (0.1%)

rewrite55.0ms (0.4%)

series641.0ms (4.5%)

simplify68.0ms (0.5%)

prune226.0ms (1.6%)

localize18.0ms (0.1%)

rewrite57.0ms (0.4%)

series516.0ms (3.6%)

simplify102.0ms (0.7%)

prune351.0ms (2.5%)

localize16.0ms (0.1%)

rewrite119.0ms (0.8%)

series523.0ms (3.7%)

simplify124.0ms (0.9%)

prune746.0ms (5.2%)

localize16.0ms (0.1%)

rewrite490.0ms (3.4%)

series725.0ms (5.1%)

simplify680.0ms (4.8%)

prune5.7s (40.2%)

regimes693.0ms (4.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (14%)

Profiling