Details

analyze99.0ms (1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample34.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms	71×	body	1024	valid
6.0ms	140×	body	128	valid
3.0ms	27×	body	512	valid
1.0ms	18×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

19.3b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 1 (sqrt.f64 x))
4.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite345.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

18.6b

Rules

127×	`add-sqr-sqrt_binary64_1805`
118×	`times-frac_binary64_1789`
117×	`*-un-lft-identity_binary64_1783`
76×	`sqrt-prod_binary64_1799`
56×	`add-cube-cbrt_binary64_1818`
27×	`cancel-sign-sub-inv_binary64_1749`
25×	`difference-of-squares_binary64_1752`
13×	`distribute-lft-out--_binary64_1735` `associate-/r*_binary64_1727`
12×	`add-exp-log_binary64_1821`
11×	`distribute-lft-out_binary64_1734`
9×	`pow1_binary64_1844`
8×	`add-cbrt-cube_binary64_1819`
7×	`div-inv_binary64_1780`
6×	`add-log-exp_binary64_1822` `sqrt-div_binary64_1800` `pow-flip_binary64_1857` `associate-/l*_binary64_1728`
4×	`associate-/r/_binary64_1729` `div-exp_binary64_1834`
3×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
2×	`inv-pow_binary64_1868` `1-exp_binary64_1827` `rec-exp_binary64_1833` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`diff-log_binary64_1875` `frac-sub_binary64_1792` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `rem-sqrt-square_binary64_1796`

Counts

4 → 189

Calls

4 calls:

41.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 3837 to 2945 computations (23.2% saved)

series90.0ms (1%)

Error

19.0b

Counts

4 → 18

Calls

4 calls:

25.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
20.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
17.0ms	(sqrt.f64 (+.f64 x 1))
13.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 561 to 462 computations (17.6% saved)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4860	3341
1	4860	3341

prune252.0ms (2.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	192	15	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	193	15	208

Error

18.6b

Counts

208 → 15

Compiler

Compiled 3730 to 2789 computations (25.2% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
4.0b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite186.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

18.4b

Rules

46×	`add-sqr-sqrt_binary64_1805`
42×	`sqrt-prod_binary64_1799`
38×	`*-un-lft-identity_binary64_1783`
13×	`add-cube-cbrt_binary64_1818`
12×	`difference-of-squares_binary64_1752`
11×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
10×	`times-frac_binary64_1789` `associate-/l*_binary64_1728`
9×	`pow1_binary64_1844` `distribute-lft-out--_binary64_1735`
7×	`associate-r_binary64_1723`
6×	`add-log-exp_binary64_1822` `cancel-sign-sub-inv_binary64_1749` `sqrt-div_binary64_1800` `associate-l_binary64_1724`
5×	`distribute-lft-out_binary64_1734`
4×	`unswap-sqr_binary64_1751` `associate-*r/_binary64_1725`
3×	`pow1/2_binary64_1863` `pow-prod-down_binary64_1854` `sqrt-pow1_binary64_1801` `flip3-+_binary64_1786` `flip-+_binary64_1757`
2×	`flip3--_binary64_1787` `flip--_binary64_1758` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729`
1×	`diff-log_binary64_1875` `sub-neg_binary64_1776` `sqrt-unprod_binary64_1803` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `div-sub_binary64_1788` `clear-num_binary64_1782` `div-inv_binary64_1780` `associate-/r_binary64_1727` `rem-sqrt-square_binary64_1796`

Counts

4 → 113

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 2641 to 1665 computations (37% saved)

series156.0ms (1.7%)

Error

18.5b

Counts

4 → 18

Calls

4 calls:

58.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
33.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
26.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
18.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 782 to 587 computations (24.9% saved)

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5277	2138

prune146.0ms (1.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	13	1	14
Picked	1	0	1
Done	0	0	0
Total	144	2	146

Error

0.2b

Counts

146 → 2

Compiler

Compiled 2569 to 1638 computations (36.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

rewrite337.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

118×	`*-un-lft-identity_binary64_1783`
78×	`times-frac_binary64_1789`
55×	`sqrt-prod_binary64_1799`
47×	`add-sqr-sqrt_binary64_1805`
45×	`distribute-lft-out_binary64_1734`
39×	`add-cube-cbrt_binary64_1818`
32×	`add-exp-log_binary64_1821`
27×	`associate-/l*_binary64_1728`
20×	`add-cbrt-cube_binary64_1819`
14×	`div-exp_binary64_1834`
9×	`pow1_binary64_1844`
8×	`associate-/r/_binary64_1729`
7×	`cbrt-undiv_binary64_1817` `associate-/r_binary64_1727` `associate-r*_binary64_1723`
6×	`add-log-exp_binary64_1822` `flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-l_binary64_1724`
5×	`prod-exp_binary64_1832`
4×	`div-inv_binary64_1780` `sqrt-div_binary64_1800` `associate-*r/_binary64_1725` `unswap-sqr_binary64_1751`
3×	`1-exp_binary64_1827` `rec-exp_binary64_1833` `cbrt-unprod_binary64_1816` `pow-prod-down_binary64_1854`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
1×	`associate-/l/_binary64_1730` `sqrt-unprod_binary64_1803` `*-commutative_binary64_1714` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `sum-log_binary64_1874` `+-commutative_binary64_1713`

Counts

4 → 166

Calls

4 calls:

20.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 4418 to 3053 computations (30.9% saved)

series125.0ms (1.3%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

51.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
27.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
19.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 561 to 452 computations (19.4% saved)

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4965	3678
1	4965	3678

prune254.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	173	8	181
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	174	9	183

Error

0.0b

Counts

183 → 9

Compiler

Compiled 4156 to 2869 computations (31% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x)))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
0.2b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite599.0ms (6.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

234×	`times-frac_binary64_1789`
159×	`*-un-lft-identity_binary64_1783`
156×	`add-sqr-sqrt_binary64_1805`
119×	`add-cube-cbrt_binary64_1818`
87×	`sqrt-prod_binary64_1799`
29×	`distribute-rgt-out_binary64_1736`
21×	`associate-/l*_binary64_1728`
20×	`distribute-lft-out_binary64_1734` `associate-/r/_binary64_1729`
19×	`add-exp-log_binary64_1821`
13×	`add-cbrt-cube_binary64_1819`
12×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
11×	`associate-/r*_binary64_1727`
10×	`div-inv_binary64_1780`
9×	`pow1_binary64_1844`
8×	`div-exp_binary64_1834`
7×	`associate-l_binary64_1724`
6×	`add-log-exp_binary64_1822` `associate-r_binary64_1723`
4×	`unswap-sqr_binary64_1751` `sqrt-div_binary64_1800` `cbrt-undiv_binary64_1817`
3×	`pow-prod-down_binary64_1854`
2×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `associate-*l/_binary64_1726` `1-exp_binary64_1827` `rec-exp_binary64_1833` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `sqrt-unprod_binary64_1803` `*-commutative_binary64_1714` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `associate-/l/_binary64_1730` `sum-log_binary64_1874` `+-commutative_binary64_1713`

Counts

4 → 252

Calls

4 calls:

16.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x)))
9.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Compiler

Compiled 7993 to 5774 computations (27.8% saved)

series148.0ms (1.6%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

42.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x)))
34.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
27.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Compiler

Compiled 813 to 681 computations (16.2% saved)

simplify144.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4936	9190
1	4936	9190

prune474.0ms (5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	269	4	273
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	273	9	282

Error

Counts

282 → 9

Compiler

Compiled 7292 to 5205 computations (28.6% saved)

regimes752.0ms (7.9%)

Accuracy

Total 0.3b remaining (98.6%)

Threshold costs 0.3b (98.6%)

Compiler

Compiled 9535 to 7659 computations (19.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	25
1	16	25

end0.0ms (0%)

sample5.0s (53%)

Algorithm

1×

intervals

Results

345.0ms	2242×	body	1024	valid
168.0ms	4235×	body	128	valid
111.0ms	1019×	body	512	valid
43.0ms	504×	body	256	valid

Compiler

Compiled 4726 to 3793 computations (19.7% saved)

Details

analyze99.0ms (1%)

sample34.0ms (0.4%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite345.0ms (3.6%)

series90.0ms (1%)

simplify90.0ms (1%)

prune252.0ms (2.7%)

localize7.0ms (0.1%)

rewrite186.0ms (2%)

series156.0ms (1.7%)

simplify65.0ms (0.7%)

prune146.0ms (1.5%)

localize9.0ms (0.1%)

rewrite337.0ms (3.6%)

series125.0ms (1.3%)

simplify99.0ms (1%)

prune254.0ms (2.7%)

localize10.0ms (0.1%)

rewrite599.0ms (6.3%)

series148.0ms (1.6%)

simplify144.0ms (1.5%)

prune474.0ms (5%)

regimes752.0ms (7.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.0s (53%)

Profiling