Details

analyze168.0ms (1.9%)

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)

sample57.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	70×	body	1024	valid
14.0ms	37×	body	512	valid
10.0ms	130×	body	128	valid
3.0ms	19×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune4.0ms (0.1%)

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

22.9b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize15.0ms (0.2%)

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))
3.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite131.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

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×	`associate-/r*_binary64_1727` `distribute-lft-out--_binary64_1735`
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×	`associate-/l*_binary64_1728` `pow-flip_binary64_1857` `sqrt-div_binary64_1800` `add-log-exp_binary64_1822`
4×	`associate-/r/_binary64_1729` `div-exp_binary64_1834`
3×	`flip-+_binary64_1757` `pow1/2_binary64_1863` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801`
2×	`inv-pow_binary64_1868` `1-exp_binary64_1827` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rec-exp_binary64_1833`
1×	`flip3--_binary64_1787` `diff-log_binary64_1875` `frac-sub_binary64_1792` `rem-sqrt-square_binary64_1796` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 189

Calls

4 calls:

67.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
17.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(/.f64 1 (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))

series149.0ms (1.7%)

Counts

4 → 18

Calls

4 calls:

47.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
44.0ms	(sqrt.f64 (+.f64 x 1))
35.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
23.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 370 to 323 computations (12.7% saved)

simplify174.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4860	3341
1	4860	3341

prune443.0ms (5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	195	12	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	196	12	208

Error

22.2b

Counts

208 → 12

Compiler

Compiled 3646 to 2719 computations (25.4% saved)

localize16.0ms (0.2%)

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))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.8b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite104.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

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

Counts

4 → 113

Calls

4 calls:

40.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
19.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
18.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 1 x))

series239.0ms (2.7%)

Counts

4 → 16

Calls

4 calls:

109.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
57.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
42.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
30.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 503 to 398 computations (20.9% saved)

simplify113.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5146	2109

prune271.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	136	5	141

Error

0.3b

Counts

141 → 5

Compiler

Compiled 2612 to 1691 computations (35.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite138.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`*-un-lft-identity_binary64_1783`
78×	`times-frac_binary64_1789`
55×	`sqrt-prod_binary64_1799`
49×	`add-sqr-sqrt_binary64_1805`
42×	`distribute-lft-out_binary64_1734`
40×	`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`
10×	`pow1_binary64_1844`
8×	`associate-/r/_binary64_1729`
7×	`associate-/r_binary64_1727` `cbrt-undiv_binary64_1817` `associate-r*_binary64_1723`
6×	`flip-+_binary64_1757` `associate-l_binary64_1724` `sqrt-div_binary64_1800` `flip3-+_binary64_1786`
5×	`prod-exp_binary64_1832`
4×	`associate-*r/_binary64_1725` `div-inv_binary64_1780` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
3×	`cbrt-unprod_binary64_1816` `1-exp_binary64_1827` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854` `rec-exp_binary64_1833`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`associate-/l/_binary64_1730` `inv-pow_binary64_1868` `sqrt-unprod_binary64_1803` `pow-flip_binary64_1857` `*-commutative_binary64_1714` `rem-sqrt-square_binary64_1796`

Counts

4 → 168

Calls

4 calls:

42.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
23.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
21.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
7.0ms	(sqrt.f64 (+.f64 1 x))

series204.0ms (2.3%)

Counts

4 → 17

Calls

4 calls:

81.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
57.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
33.0ms	(sqrt.f64 (+.f64 1 x))
33.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 458 to 377 computations (17.7% saved)

simplify182.0ms (2%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4974	3645
1	4974	3645

prune467.0ms (5.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	177	8	185
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	179	11	190

Error

Counts

190 → 11

Compiler

Compiled 4322 to 2994 computations (30.7% saved)

localize19.0ms (0.2%)

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))))))
0.2b	(/.f64 1 (sqrt.f64 x))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite146.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

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×	`associate-*r/_binary64_1725` `flip-+_binary64_1757` `flip3-+_binary64_1786`
10×	`1-exp_binary64_1827` `associate-/r*_binary64_1727` `sqrt-div_binary64_1800` `rec-exp_binary64_1833`
8×	`frac-add_binary64_1791`
7×	`distribute-rgt-out_binary64_1736`
6×	`associate-/l*_binary64_1728` `pow-flip_binary64_1857` `cbrt-undiv_binary64_1817` `pow-prod-down_binary64_1854`
5×	`cbrt-unprod_binary64_1816`
4×	`inv-pow_binary64_1868` `div-inv_binary64_1780` `add-log-exp_binary64_1822`
3×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
2×	`*-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`un-div-inv_binary64_1781` `distribute-lft-out_binary64_1734` `sqrt-unprod_binary64_1803` `associate-*l/_binary64_1726` `frac-times_binary64_1793`

Counts

4 → 213

Calls

4 calls:

54.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
19.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
16.0ms	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
12.0ms	(/.f64 1 (sqrt.f64 x))

series203.0ms (2.3%)

Counts

4 → 16

Calls

4 calls:

66.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
56.0ms	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
50.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
31.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 468 to 399 computations (14.7% saved)

simplify204.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	5017	5104

prune543.0ms (6.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	233	7	240

Error

Counts

240 → 7

Compiler

Compiled 5673 to 3795 computations (33.1% saved)

regimes479.0ms (5.4%)

Accuracy

Total 0.2b remaining (98%)

Threshold costs 0.2b (98%)

Compiler

Compiled 2990 to 2398 computations (19.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	26
1	17	26

end0.0ms (0%)

sample4.4s (49.4%)

Algorithm

1×

intervals

Results

677.0ms	2253×	body	1024	valid
329.0ms	4239×	body	128	valid
229.0ms	1001×	body	512	valid
74.0ms	507×	body	256	valid

Compiler

Compiled 1527 to 1226 computations (19.7% saved)

Details

analyze168.0ms (1.9%)

sample57.0ms (0.6%)

simplify19.0ms (0.2%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

rewrite131.0ms (1.5%)

series149.0ms (1.7%)

simplify174.0ms (1.9%)

prune443.0ms (5%)

localize16.0ms (0.2%)

rewrite104.0ms (1.2%)

series239.0ms (2.7%)

simplify113.0ms (1.3%)

prune271.0ms (3%)

localize18.0ms (0.2%)

rewrite138.0ms (1.5%)

series204.0ms (2.3%)

simplify182.0ms (2%)

prune467.0ms (5.2%)

localize19.0ms (0.2%)

rewrite146.0ms (1.6%)

series203.0ms (2.3%)

simplify204.0ms (2.3%)

prune543.0ms (6.1%)

regimes479.0ms (5.4%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.4s (49.4%)

Profiling