Details

analyze110.0ms (1.3%)

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)

sample30.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	78×	body	1024	valid
5.0ms	131×	body	128	valid
4.0ms	36×	body	512	valid
1.0ms	11×	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

20.1b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
1.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite326.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

19.6b

Rules

124×	`add-sqr-sqrt_binary64_1805`
118×	`times-frac_binary64_1789`
113×	`*-un-lft-identity_binary64_1783`
72×	`sqrt-prod_binary64_1799`
54×	`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`
11×	`add-exp-log_binary64_1821`
10×	`distribute-lft-out_binary64_1734`
7×	`pow1_binary64_1844` `add-cbrt-cube_binary64_1819` `div-inv_binary64_1780`
6×	`pow-flip_binary64_1857` `associate-/l*_binary64_1728`
5×	`add-log-exp_binary64_1822`
4×	`sqrt-div_binary64_1800` `associate-/r/_binary64_1729` `div-exp_binary64_1834`
2×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `inv-pow_binary64_1868` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `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`

Counts

3 → 173

Calls

3 calls:

42.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 3566 to 2737 computations (23.2% saved)

series68.0ms (0.8%)

Error

20.0b

Counts

3 → 12

Calls

3 calls:

26.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
20.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
13.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 369 to 304 computations (17.6% saved)

simplify107.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4846	3144
1	4846	3144

prune219.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	175	10	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	176	10	186

Error

19.6b

Counts

186 → 10

Compiler

Compiled 3270 to 2436 computations (25.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
1.5b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite166.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

19.6b

Rules

43×	`add-sqr-sqrt_binary64_1805`
38×	`sqrt-prod_binary64_1799`
34×	`*-un-lft-identity_binary64_1783`
12×	`difference-of-squares_binary64_1752`
11×	`add-cube-cbrt_binary64_1818`
10×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `times-frac_binary64_1789` `associate-/l*_binary64_1728`
9×	`distribute-lft-out--_binary64_1735`
7×	`pow1_binary64_1844` `associate-r_binary64_1723`
6×	`cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724`
5×	`add-log-exp_binary64_1822`
4×	`distribute-lft-out_binary64_1734` `unswap-sqr_binary64_1751` `sqrt-div_binary64_1800` `associate-*r/_binary64_1725`
3×	`pow-prod-down_binary64_1854`
2×	`flip3--_binary64_1787` `flip--_binary64_1758` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `flip3-+_binary64_1786` `flip-+_binary64_1757` `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`

Counts

3 → 97

Calls

3 calls:

19.0ms	(/.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))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 2306 to 1441 computations (37.5% saved)

series127.0ms (1.5%)

Error

19.5b

Counts

3 → 12

Calls

3 calls:

54.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
32.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
29.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 534 to 416 computations (22.1% saved)

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5675	1943

prune115.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	116	3	119

Error

0.3b

Counts

119 → 3

Compiler

Compiled 2175 to 1390 computations (36.1% saved)

localize11.0ms (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 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite333.0ms (3.9%)

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×	`associate-r_binary64_1723` `cbrt-undiv_binary64_1817` `associate-/r*_binary64_1727`
6×	`add-log-exp_binary64_1822` `flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-l_binary64_1724`
5×	`prod-exp_binary64_1832`
4×	`unswap-sqr_binary64_1751` `sqrt-div_binary64_1800` `associate-*r/_binary64_1725` `div-inv_binary64_1780`
3×	`pow-prod-down_binary64_1854` `cbrt-unprod_binary64_1816` `1-exp_binary64_1827` `rec-exp_binary64_1833`
2×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`sqrt-unprod_binary64_1803` `*-commutative_binary64_1714` `associate-/l/_binary64_1730` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `sum-log_binary64_1874` `+-commutative_binary64_1713`

Counts

4 → 166

Calls

4 calls:

22.0ms	(/.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)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 4418 to 3053 computations (30.9% saved)

series120.0ms (1.4%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

47.0ms	(/.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)))
18.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
17.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 561 to 452 computations (19.4% saved)

simplify98.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4965	3678
1	4965	3678

prune237.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	174	7	181
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	176	8	184

Error

Counts

184 → 8

Compiler

Compiled 4132 to 2846 computations (31.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.1b	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite426.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

109×	`add-sqr-sqrt_binary64_1805`
82×	`times-frac_binary64_1789`
66×	`*-un-lft-identity_binary64_1783`
54×	`add-exp-log_binary64_1821`
53×	`add-cube-cbrt_binary64_1818`
38×	`sqrt-prod_binary64_1799`
29×	`associate-r_binary64_1723`
28×	`associate-l_binary64_1724`
22×	`add-cbrt-cube_binary64_1819`
20×	`div-exp_binary64_1834`
19×	`unswap-sqr_binary64_1751`
17×	`prod-exp_binary64_1832`
15×	`pow1_binary64_1844`
12×	`associate-/r/_binary64_1729`
11×	`flip3-+_binary64_1786` `associate-*r/_binary64_1725` `flip-+_binary64_1757`
10×	`sqrt-div_binary64_1800` `1-exp_binary64_1827` `rec-exp_binary64_1833` `associate-/r*_binary64_1727`
8×	`frac-add_binary64_1791`
7×	`distribute-rgt-out_binary64_1736`
6×	`pow-prod-down_binary64_1854` `pow-flip_binary64_1857` `cbrt-undiv_binary64_1817` `associate-/l*_binary64_1728`
5×	`cbrt-unprod_binary64_1816`
4×	`add-log-exp_binary64_1822` `inv-pow_binary64_1868` `div-inv_binary64_1780`
3×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
2×	`*-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`sqrt-unprod_binary64_1803` `distribute-lft-out_binary64_1734` `frac-times_binary64_1793` `un-div-inv_binary64_1781` `associate-*l/_binary64_1726`

Counts

4 → 213

Calls

4 calls:

29.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
9.0ms	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 6289 to 4291 computations (31.8% saved)

series124.0ms (1.5%)

Error

Counts

4 → 18

Calls

4 calls:

41.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
28.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
27.0ms	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
14.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 732 to 593 computations (19% saved)

simplify111.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4925	5154
1	4925	5154

prune508.0ms (6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	229	2	231
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	232	7	239

Error

Counts

239 → 7

Compiler

Compiled 5723 to 3821 computations (33.2% saved)

regimes660.0ms (7.7%)

Accuracy

Total 0.2b remaining (99%)

Threshold costs 0.2b (99%)

Compiler

Compiled 8501 to 6729 computations (20.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	26
1	17	26

end0.0ms (0%)

sample4.5s (53%)

Algorithm

1×

intervals

Results

349.0ms	2268×	body	1024	valid
168.0ms	4184×	body	128	valid
117.0ms	1069×	body	512	valid
42.0ms	479×	body	256	valid

Compiler

Compiled 4210 to 3330 computations (20.9% saved)

Details

analyze110.0ms (1.3%)

sample30.0ms (0.4%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite326.0ms (3.8%)

series68.0ms (0.8%)

simplify107.0ms (1.3%)

prune219.0ms (2.6%)

localize7.0ms (0.1%)

rewrite166.0ms (2%)

series127.0ms (1.5%)

simplify70.0ms (0.8%)

prune115.0ms (1.3%)

localize11.0ms (0.1%)

rewrite333.0ms (3.9%)

series120.0ms (1.4%)

simplify98.0ms (1.1%)

prune237.0ms (2.8%)

localize10.0ms (0.1%)

rewrite426.0ms (5%)

series124.0ms (1.5%)

simplify111.0ms (1.3%)

prune508.0ms (6%)

regimes660.0ms (7.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.5s (53%)

Profiling