Details

analyze270.0ms (4.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample43.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	120×	body	256	valid
9.0ms	284×	pre	128	true
5.0ms	38×	body	512	valid
5.0ms	98×	body	128	valid
1.0ms	28×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify405.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (307.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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: 50.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
24.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1805`
14×	`*-un-lft-identity_binary64_1783`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
8×	`add-cube-cbrt_binary64_1818` `add-log-exp_binary64_1822`
6×	`difference-of-squares_binary64_1752` `associate-/l*_binary64_1728` `sqrt-prod_binary64_1799` `times-frac_binary64_1789`
5×	`pow1_binary64_1844`
4×	`flip3--_binary64_1787` `cancel-sign-sub-inv_binary64_1749` `flip--_binary64_1758`
3×	`distribute-lft-out--_binary64_1735`
2×	`associate-/l/_binary64_1730` `diff-log_binary64_1875` `sqrt-div_binary64_1800` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `sub-neg_binary64_1776`
1×	`div-sub_binary64_1788` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `pow1/2_binary64_1863` `associate-/r*_binary64_1727` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series271.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
71.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune101.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Merged error: 0.1b

Counts

87 → 4

Compiler

Compiled 2063 to 1224 computations (40.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
22×	`times-frac_binary64_1789`
20×	`*-un-lft-identity_binary64_1783`
17×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
13×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
11×	`associate-/l*_binary64_1728`
10×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
8×	`add-log-exp_binary64_1822`
6×	`associate-/r/_binary64_1729`
5×	`distribute-lft-out_binary64_1734` `associate-/r*_binary64_1727`
4×	`flip-+_binary64_1757` `div-inv_binary64_1780` `flip3-+_binary64_1786` `pow1_binary64_1844`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `+-commutative_binary64_1713` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `sum-log_binary64_1874` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series460.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
158.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
63.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune152.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Merged error: 0b

Counts

115 → 5

Compiler

Compiled 3154 to 1937 computations (38.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1783`
15×	`add-sqr-sqrt_binary64_1805`
14×	`add-cube-cbrt_binary64_1818`
12×	`times-frac_binary64_1789`
8×	`add-log-exp_binary64_1822`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
5×	`distribute-lft-out_binary64_1734` `pow1_binary64_1844`
4×	`associate-/r*_binary64_1727`
3×	`associate-/l*_binary64_1728` `sqrt-prod_binary64_1799`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `sqrt-div_binary64_1800` `flip3-+_binary64_1786` `flip--_binary64_1758`
1×	`+-commutative_binary64_1713` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `pow1/2_binary64_1863` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series335.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
70.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune101.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	84	5	89

Merged error: 0b

Counts

89 → 5

Compiler

Compiled 2251 to 1394 computations (38.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4))) (*.f64 a 2))
0.3b	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4)))

rewrite70.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`times-frac_binary64_1789`
77×	`*-un-lft-identity_binary64_1783`
53×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
50×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
36×	`associate-/l*_binary64_1728`
25×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
15×	`div-inv_binary64_1780`
12×	`distribute-lft-out_binary64_1734`
10×	`associate-/r*_binary64_1727`
8×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
6×	`add-log-exp_binary64_1822`
4×	`pow1_binary64_1844`
3×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `flip-+_binary64_1757` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `flip3-+_binary64_1786` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 175

Calls

4 calls:

21.0ms	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4))) (*.f64 a 2))
12.0ms	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4)))
11.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series534.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

231.0ms	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4)))
177.0ms	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4))) (*.f64 a 2))
88.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4))
38.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4965	6374
1	4965	6374

prune268.0ms (4.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	187	5	192

Merged error: 0b

Counts

192 → 5

Compiler

Compiled 5836 to 3430 computations (41.2% saved)

regimes508.0ms (8.3%)

Compiler: Compiled 4224 to 3190 computations (24.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.1s (34.5%)

Algorithm

1×

intervals

Results

398.0ms	3884×	body	256	valid
275.0ms	8800×	pre	128	true
213.0ms	1446×	body	512	valid
136.0ms	2670×	body	128	valid
38.0ms	800×	body	128	nan

Compiler

Compiled 1092 to 826 computations (24.4% saved)

Details

analyze270.0ms (4.4%)

sample43.0ms (0.7%)

simplify405.0ms (6.6%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite36.0ms (0.6%)

series271.0ms (4.4%)

simplify87.0ms (1.4%)

prune101.0ms (1.7%)

localize14.0ms (0.2%)

rewrite51.0ms (0.8%)

series460.0ms (7.5%)

simplify62.0ms (1%)

prune152.0ms (2.5%)

localize13.0ms (0.2%)

rewrite30.0ms (0.5%)

series335.0ms (5.5%)

simplify73.0ms (1.2%)

prune101.0ms (1.6%)

localize14.0ms (0.2%)

rewrite70.0ms (1.1%)

series534.0ms (8.7%)

simplify100.0ms (1.6%)

prune268.0ms (4.4%)

regimes508.0ms (8.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (34.5%)

Profiling