Details

analyze2.0ms (0%)

Algorithm

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)

sample25.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	62×	body	1024	valid
5.0ms	136×	body	128	valid
4.0ms	34×	body	512	valid
2.0ms	24×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify101.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune3.0ms (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

23.2b

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))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
4.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite74.0ms (0.9%)

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:

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))

series79.0ms (1%)

Counts

4 → 18

Calls

4 calls:

32.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
19.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
15.0ms	(sqrt.f64 (+.f64 x 1))
12.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 370 to 323 computations (12.7% saved)

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4860	3341
1	4860	3341

prune251.0ms (3.2%)

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

22.5b

Counts

208 → 12

Compiler

Compiled 3664 to 2733 computations (25.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 1 (sqrt.f64 x))
0.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
4.1b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite223.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

1332×	`*-un-lft-identity_binary64_1783`
1249×	`times-frac_binary64_1789`
725×	`add-sqr-sqrt_binary64_1805`
429×	`distribute-lft-out_binary64_1734`
304×	`sqrt-prod_binary64_1799`
293×	`add-cube-cbrt_binary64_1818`
180×	`distribute-lft-out--_binary64_1735`
168×	`div-inv_binary64_1780`
162×	`difference-of-squares_binary64_1752`
29×	`associate-/r*_binary64_1727`
28×	`associate-/l*_binary64_1728`
18×	`cancel-sign-sub-inv_binary64_1749`
14×	`add-exp-log_binary64_1821`
10×	`add-cbrt-cube_binary64_1819`
8×	`pow1_binary64_1844`
7×	`associate-/r/_binary64_1729`
6×	`pow-flip_binary64_1857` `add-log-exp_binary64_1822`
5×	`div-exp_binary64_1834`
3×	`associate-/l/_binary64_1730` `flip-+_binary64_1757` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `flip3-+_binary64_1786` `clear-num_binary64_1782`
2×	`flip3--_binary64_1787` `inv-pow_binary64_1868` `1-exp_binary64_1827` `pow1/2_binary64_1863` `frac-sub_binary64_1792` `sqrt-div_binary64_1800` `sqrt-pow1_binary64_1801` `flip--_binary64_1758` `rec-exp_binary64_1833`
1×	`div-sub_binary64_1788` `frac-add_binary64_1791` `diff-log_binary64_1875` `sub-neg_binary64_1776`

Counts

4 → 554

Calls

4 calls:

68.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
20.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

series107.0ms (1.3%)

Counts

4 → 24

Calls

4 calls:

36.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
31.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
22.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
18.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 698 to 595 computations (14.8% saved)

simplify245.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

578 → 578

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4931	21944
1	4931	21944

prune1.8s (22.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	575	3	578
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	585	5	590

Error

4.8b

Counts

590 → 5

Compiler

Compiled 17943 to 14012 computations (21.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 1 (sqrt.f64 x))
0.7b	(/.f64 1 (*.f64 x (+.f64 1 x)))
5.3b	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite111.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

417×	`times-frac_binary64_1789`
399×	`*-un-lft-identity_binary64_1783`
164×	`distribute-lft-out_binary64_1734`
148×	`sqrt-prod_binary64_1799`
141×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
61×	`div-inv_binary64_1780`
42×	`add-exp-log_binary64_1821`
41×	`associate-/r/_binary64_1729`
36×	`associate-*r/_binary64_1725`
30×	`associate-/r*_binary64_1727`
22×	`add-cbrt-cube_binary64_1819`
20×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
19×	`div-exp_binary64_1834`
18×	`associate-/l*_binary64_1728`
11×	`pow1_binary64_1844`
9×	`cbrt-undiv_binary64_1817`
8×	`pow-flip_binary64_1857`
6×	`prod-exp_binary64_1832` `1-exp_binary64_1827` `rec-exp_binary64_1833`
4×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `add-log-exp_binary64_1822`
3×	`inv-pow_binary64_1868`
2×	`cbrt-unprod_binary64_1816` `pow1/2_binary64_1863` `sqrt-div_binary64_1800` `sqrt-pow1_binary64_1801`
1×	`associate-/l/_binary64_1730` `frac-add_binary64_1791` `pow-prod-down_binary64_1854`

Counts

4 → 319

Calls

4 calls:

50.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
7.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

series119.0ms (1.5%)

Counts

4 → 24

Calls

4 calls:

47.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
36.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
22.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
14.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 672 to 568 computations (15.5% saved)

simplify162.0ms (2%)

Algorithm

1×	egg-herbie

Counts

343 → 343

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4975	9277
1	4975	9277

prune689.0ms (8.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	334	9	343
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	338	10	348

Error

0.0b

Counts

348 → 10

Compiler

Compiled 9106 to 6887 computations (24.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
0.6b	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

rewrite126.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`*-un-lft-identity_binary64_1783`
88×	`times-frac_binary64_1789`
59×	`add-sqr-sqrt_binary64_1805`
57×	`add-cube-cbrt_binary64_1818`
40×	`sqrt-prod_binary64_1799`
36×	`add-exp-log_binary64_1821`
22×	`add-cbrt-cube_binary64_1819`
21×	`distribute-lft-out_binary64_1734`
19×	`associate-/l*_binary64_1728`
16×	`div-exp_binary64_1834` `associate-r_binary64_1723`
15×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
14×	`associate-/r*_binary64_1727`
13×	`associate-/r/_binary64_1729`
12×	`frac-times_binary64_1793`
10×	`pow1_binary64_1844`
9×	`div-inv_binary64_1780`
8×	`cbrt-undiv_binary64_1817`
6×	`associate-*r/_binary64_1725` `frac-add_binary64_1791` `pow-flip_binary64_1857`
5×	`prod-exp_binary64_1832`
4×	`1-exp_binary64_1827` `associate-l_binary64_1724` `associate-*l/_binary64_1726` `rec-exp_binary64_1833` `add-log-exp_binary64_1822`
3×	`cbrt-unprod_binary64_1816` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
2×	`inv-pow_binary64_1868` `pow1/2_binary64_1863` `sqrt-div_binary64_1800` `sqrt-pow1_binary64_1801`
1×	`associate-/l/_binary64_1730` `distribute-lft-in_binary64_1732` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`

Counts

4 → 202

Calls

4 calls:

47.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
43.0ms	(*.f64 (+.f64 x 1) (+.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))

series99.0ms (1.2%)

Counts

4 → 15

Calls

4 calls:

38.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
25.0ms	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
21.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
14.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 464 to 387 computations (16.6% saved)

simplify105.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4953	3910
1	4953	3910

prune321.0ms (4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	214	3	217
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	220	7	227

Error

0.0b

Counts

227 → 7

Compiler

Compiled 5172 to 3770 computations (27.1% saved)

regimes339.0ms (4.3%)

Accuracy

Total 0.3b remaining (99.7%)

Threshold costs 0.3b (99.7%)

Compiler

Compiled 4576 to 3756 computations (17.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	48
1	20	48

end0.0ms (0%)

sample2.8s (35.5%)

Algorithm

1×

intervals

Results

348.0ms	2293×	body	1024	valid
164.0ms	4172×	body	128	valid
109.0ms	1011×	body	512	valid
43.0ms	524×	body	256	valid

Compiler

Compiled 2333 to 1915 computations (17.9% saved)

Details

analyze2.0ms (0%)

sample25.0ms (0.3%)

simplify101.0ms (1.3%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite74.0ms (0.9%)

series79.0ms (1%)

simplify98.0ms (1.2%)

prune251.0ms (3.2%)

localize12.0ms (0.1%)

rewrite223.0ms (2.8%)

series107.0ms (1.3%)

simplify245.0ms (3.1%)

prune1.8s (22.7%)

localize11.0ms (0.1%)

rewrite111.0ms (1.4%)

series119.0ms (1.5%)

simplify162.0ms (2%)

prune689.0ms (8.7%)

localize11.0ms (0.1%)

rewrite126.0ms (1.6%)

series99.0ms (1.2%)

simplify105.0ms (1.3%)

prune321.0ms (4%)

regimes339.0ms (4.3%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.8s (35.5%)

Profiling