Details

analyze278.0ms (5.3%)

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)

sample48.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms	125×	body	256	valid
9.0ms	284×	pre	128	true
8.0ms	53×	body	512	valid
4.0ms	78×	body	128	valid
1.0ms	28×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify398.0ms (7.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (308.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune6.0ms (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: 53.1b

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))
24.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite33.0ms (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:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series267.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
64.0ms	(-.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))

simplify89.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune100.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Merged error: 0.1b

Counts

87 → 3

Compiler

Compiled 2031 to 1200 computations (40.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite47.0ms (0.9%)

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))
11.0ms	(/.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))

series449.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
156.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
64.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune146.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	107	7	114

Merged error: 0.0b

Counts

114 → 7

Compiler

Compiled 3163 to 1948 computations (38.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite29.0ms (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))))

series322.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
58.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
36.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune107.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	3	2	5
Picked	1	0	1
Done	1	0	1
Total	86	5	91

Merged error: 0b

Counts

91 → 5

Compiler

Compiled 2264 to 1408 computations (37.8% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
0.3b	(.f64 c (.f64 (*.f64 c a) 16))
0.5b	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
27×	`pow1_binary64_1844`
16×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854`
14×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`times-frac_binary64_1789`
6×	`associate-l_binary64_1724` `add-log-exp_binary64_1822`
3×	`associate-/l_binary64_1728` `associate-/r_binary64_1727`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `-commutative_binary64_1714` `flip3-+_binary64_1786` `associate-r*_binary64_1723`
1×	`flip3--_binary64_1787` `div-sub_binary64_1788` `+-commutative_binary64_1713` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782` `flip--_binary64_1758`

Counts

4 → 88

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
10.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
7.0ms	(.f64 c (.f64 (*.f64 c a) 16))
5.0ms	(+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series163.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
29.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
29.0ms	(+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
19.0ms	(.f64 c (.f64 (*.f64 c a) 16))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5017	2422

prune157.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	100	5	105

Merged error: 0b

Counts

105 → 5

Compiler

Compiled 3894 to 2311 computations (40.7% saved)

regimes263.0ms (5%)

Compiler: Compiled 3524 to 2678 computations (24% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.0s (38.8%)

Algorithm

1×

intervals

Results

400.0ms	3788×	body	256	valid
272.0ms	8839×	pre	128	true
222.0ms	1425×	body	512	valid
157.0ms	2787×	body	128	valid
42.0ms	839×	body	128	nan

Compiler

Compiled 917 to 698 computations (23.9% saved)

Details

analyze278.0ms (5.3%)

sample48.0ms (0.9%)

simplify398.0ms (7.6%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite33.0ms (0.6%)

series267.0ms (5.1%)

simplify89.0ms (1.7%)

prune100.0ms (1.9%)

localize15.0ms (0.3%)

rewrite47.0ms (0.9%)

series449.0ms (8.6%)

simplify60.0ms (1.1%)

prune146.0ms (2.8%)

localize12.0ms (0.2%)

rewrite29.0ms (0.5%)

series322.0ms (6.1%)

simplify74.0ms (1.4%)

prune107.0ms (2%)

localize22.0ms (0.4%)

rewrite43.0ms (0.8%)

series163.0ms (3.1%)

simplify69.0ms (1.3%)

prune157.0ms (3%)

regimes263.0ms (5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.0s (38.8%)

Profiling