Details

analyze262.0ms (5.2%)

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 (0.9%)

Algorithm

1×

intervals

Results

11.0ms	115×	body	256	valid
11.0ms	280×	pre	128	true
7.0ms	49×	body	512	valid
5.0ms	92×	body	128	valid
1.0ms	24×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify393.0ms (7.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (303.0ms)

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

Error

52.8b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (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 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))
27.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite38.0ms (0.7%)

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:

15.0ms	(/.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)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series266.0ms (5.2%)

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))
65.0ms	(-.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)))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune99.0ms (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

Error

0.1b

Counts

87 → 3

Compiler

Compiled 2017 to 1191 computations (41% saved)

localize14.0ms (0.3%)

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))
0.2b	(/.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))

rewrite50.0ms (1%)

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:

18.0ms	(/.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))

series460.0ms (9%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
163.0ms	(/.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))))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune140.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	108	6	114

Error

Counts

114 → 6

Compiler

Compiled 3132 to 1925 computations (38.5% saved)

localize11.0ms (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 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(-.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))))))

rewrite28.0ms (0.6%)

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)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series328.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
32.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune97.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	84	6	90

Error

Counts

90 → 6

Compiler

Compiled 2227 to 1382 computations (37.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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)))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
0.3b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_1789`
96×	`*-un-lft-identity_binary64_1783`
62×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
19×	`associate-/r*_binary64_1727`
17×	`add-exp-log_binary64_1821` `distribute-lft-out_binary64_1734`
11×	`add-cbrt-cube_binary64_1819`
8×	`div-exp_binary64_1834` `add-log-exp_binary64_1822`
7×	`associate-/l*_binary64_1728`
6×	`div-inv_binary64_1780`
5×	`pow1_binary64_1844`
4×	`cbrt-undiv_binary64_1817`
2×	`associate-/l/_binary64_1730` `1-exp_binary64_1827` `flip-+_binary64_1757` `frac-2neg_binary64_1794` `flip3-+_binary64_1786` `clear-num_binary64_1782` `rec-exp_binary64_1833`
1×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `+-commutative_binary64_1713` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `sum-log_binary64_1874` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 145

Calls

4 calls:

11.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))
9.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series282.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))
74.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
58.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
31.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify104.0ms (2%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5148	4909

prune207.0ms (4.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	158	5	163

Error

Counts

163 → 5

Compiler

Compiled 4701 to 2935 computations (37.6% saved)

regimes201.0ms (4%)

Accuracy

Total 0.1b remaining (94.1%)

Threshold costs 0.1b (94.1%)

Compiler

Compiled 2444 to 1946 computations (20.4% 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%)

sample1.8s (34.6%)

Algorithm

1×

intervals

Results

364.0ms	3839×	body	256	valid
265.0ms	8812×	pre	128	true
212.0ms	1502×	body	512	valid
131.0ms	2659×	body	128	valid
41.0ms	812×	body	128	nan

Compiler

Compiled 647 to 515 computations (20.4% saved)

Details

analyze262.0ms (5.2%)

sample43.0ms (0.9%)

simplify393.0ms (7.7%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite38.0ms (0.7%)

series266.0ms (5.2%)

simplify86.0ms (1.7%)

prune99.0ms (1.9%)

localize14.0ms (0.3%)

rewrite50.0ms (1%)

series460.0ms (9%)

simplify63.0ms (1.2%)

prune140.0ms (2.8%)

localize11.0ms (0.2%)

rewrite28.0ms (0.6%)

series328.0ms (6.5%)

simplify75.0ms (1.5%)

prune97.0ms (1.9%)

localize12.0ms (0.2%)

rewrite48.0ms (0.9%)

series282.0ms (5.5%)

simplify104.0ms (2%)

prune207.0ms (4.1%)

regimes201.0ms (4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (34.6%)

Profiling