Details

analyze265.0ms (4.6%)

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)

sample44.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	121×	body	256	valid
9.0ms	293×	pre	128	true
8.0ms	56×	body	512	valid
4.0ms	79×	body	128	valid
2.0ms	37×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify402.0ms (7%)

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: 52.7b

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 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))
22.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite34.0ms (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)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series272.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(/.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)
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune103.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	5	87

Merged error: 0.1b

Counts

87 → 5

Compiler

Compiled 2037 to 1207 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)))))

rewrite45.0ms (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:

14.0ms	(/.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))

series453.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
155.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
37.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune150.0ms (2.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	3	0	3
Picked	1	0	1
Done	1	0	1
Total	110	6	116

Merged error: 0b

Counts

116 → 6

Compiler

Compiled 3186 to 1962 computations (38.4% saved)

localize14.0ms (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 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite28.0ms (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)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series325.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
34.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune103.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	84	6	90

Merged error: 0b

Counts

90 → 6

Compiler

Compiled 2283 to 1419 computations (37.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
17×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
16×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
15×	`*-un-lft-identity_binary64_1783`
11×	`add-sqr-sqrt_binary64_1805`
10×	`associate-r_binary64_1723`
9×	`add-cube-cbrt_binary64_1818` `times-frac_binary64_1789`
6×	`add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`associate-/r*_binary64_1727`
4×	`associate-/r/_binary64_1729`
3×	`distribute-lft-out_binary64_1734` `div-inv_binary64_1780` `associate-l_binary64_1724`
2×	`associate-r/_binary64_1725` `associate-/l_binary64_1728` `flip-+_binary64_1757` `frac-2neg_binary64_1794` `flip3-+_binary64_1786` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `*-commutative_binary64_1714` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 97

Calls

4 calls:

13.0ms	(/.f64 (.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
12.0ms	(.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series574.0ms (10%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
186.0ms	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
150.0ms	(/.f64 (.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5110	2689

prune120.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	109	6	115

Merged error: 0b

Counts

115 → 6

Compiler

Compiled 2856 to 1744 computations (38.9% saved)

regimes310.0ms (5.4%)

Compiler: Compiled 4264 to 3218 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 (36.8%)

Algorithm

1×

intervals

Results

366.0ms	3769×	body	256	valid
278.0ms	8803×	pre	128	true
217.0ms	1502×	body	512	valid
139.0ms	2729×	body	128	valid
37.0ms	803×	body	128	nan

Compiler

Compiled 1102 to 833 computations (24.4% saved)

Details

analyze265.0ms (4.6%)

sample44.0ms (0.8%)

simplify402.0ms (7%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite34.0ms (0.6%)

series272.0ms (4.7%)

simplify87.0ms (1.5%)

prune103.0ms (1.8%)

localize14.0ms (0.2%)

rewrite45.0ms (0.8%)

series453.0ms (7.9%)

simplify61.0ms (1.1%)

prune150.0ms (2.6%)

localize14.0ms (0.2%)

rewrite28.0ms (0.5%)

series325.0ms (5.7%)

simplify75.0ms (1.3%)

prune103.0ms (1.8%)

localize14.0ms (0.2%)

rewrite53.0ms (0.9%)

series574.0ms (10%)

simplify70.0ms (1.2%)

prune120.0ms (2.1%)

regimes310.0ms (5.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (36.8%)

Profiling