Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample27.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	66×	body	1024	valid
4.0ms	140×	body	128	valid
3.0ms	28×	body	512	valid
1.0ms	8×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify172.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 28.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
1.2b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_1815`
14×	`add-sqr-sqrt_binary64_1821` `*-un-lft-identity_binary64_1799`
6×	`cancel-sign-sub-inv_binary64_1765`
5×	`add-cube-cbrt_binary64_1834`
4×	`add-log-exp_binary64_1838` `difference-of-squares_binary64_1768`
3×	`pow1_binary64_1860` `distribute-lft-out--_binary64_1751`
2×	`sqrt-div_binary64_1816` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837` `distribute-lft-out_binary64_1750`
1×	`sub-neg_binary64_1792` `pow1/2_binary64_1879` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `sqrt-pow1_binary64_1817` `flip3-+_binary64_1802` `rem-sqrt-square_binary64_1812` `flip-+_binary64_1773`

Counts

2 → 40

Calls

2 calls:

14.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series98.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

72.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5005	794

prune101.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	3	47

Merged error: 0.2b

Counts

47 → 3

Compiler

Compiled 1311 to 956 computations (27.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1799`
24×	`sqrt-prod_binary64_1815`
21×	`distribute-lft-out_binary64_1750`
18×	`times-frac_binary64_1805`
16×	`add-sqr-sqrt_binary64_1821`
15×	`add-cube-cbrt_binary64_1834`
7×	`add-exp-log_binary64_1837`
6×	`associate-/r*_binary64_1743`
5×	`pow1_binary64_1860` `add-log-exp_binary64_1838` `add-cbrt-cube_binary64_1835`
3×	`associate-/l*_binary64_1744` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`sqrt-div_binary64_1816` `div-exp_binary64_1850` `associate-/r/_binary64_1745`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `+-commutative_binary64_1729` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `pow1/2_binary64_1879` `pow-flip_binary64_1873` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812` `inv-pow_binary64_1884`

Counts

3 → 75

Calls

3 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series135.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

65.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
41.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
28.0ms	(sqrt.f64 (+.f64 x 1))

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4944	1516
1	4944	1516

prune238.0ms (4.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	80	7	87

Merged error: 0.0b

Counts

87 → 7

Compiler

Compiled 3663 to 2827 computations (22.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite136.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`*-un-lft-identity_binary64_1799`
290×	`sqrt-prod_binary64_1815`
172×	`times-frac_binary64_1805`
144×	`add-sqr-sqrt_binary64_1821`
116×	`distribute-lft-out_binary64_1750`
88×	`add-cube-cbrt_binary64_1834`
43×	`swap-sqr_binary64_1766`
31×	`pow1_binary64_1860`
27×	`associate-l_binary64_1740` `sqrt-pow1_binary64_1817` `associate-r_binary64_1739`
16×	`unswap-sqr_binary64_1767`
14×	`associate-/r/_binary64_1745` `add-exp-log_binary64_1837`
12×	`associate-/r*_binary64_1743`
11×	`pow-flip_binary64_1873` `inv-pow_binary64_1884`
10×	`add-cbrt-cube_binary64_1835`
9×	`pow1/2_binary64_1879` `pow-prod-up_binary64_1869` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812`
7×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
6×	`associate-/l*_binary64_1744`
5×	`sqrt-div_binary64_1816` `pow-sqr_binary64_1772` `pow-prod-down_binary64_1870`
4×	`div-exp_binary64_1850` `add-log-exp_binary64_1838`
3×	`sqr-abs_binary64_1814`
2×	`clear-num_binary64_1798` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833`
1×	`pow2_binary64_1880` `prod-exp_binary64_1848` `associate-r/_binary64_1741` `cbrt-unprod_binary64_1832` `-commutative_binary64_1730` `sqrt-unprod_binary64_1819` `rem-square-sqrt_binary64_1811` `pow-plus_binary64_1862` `frac-times_binary64_1809` `associate-*l/_binary64_1742`

Counts

4 → 281

Calls

4 calls:

50.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
15.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
13.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series303.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
68.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
68.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
59.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify129.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4932	6672
1	4932	6672

prune689.0ms (13.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	286	7	293
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	289	11	300

Merged error: 0.0b

Counts

300 → 11

Compiler

Compiled 10363 to 7846 computations (24.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite150.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

702×	`sqrt-prod_binary64_1815`
655×	`*-un-lft-identity_binary64_1799`
461×	`times-frac_binary64_1805`
264×	`distribute-lft-out_binary64_1750`
197×	`add-sqr-sqrt_binary64_1821`
192×	`add-cube-cbrt_binary64_1834`
30×	`associate-/l*_binary64_1744`
26×	`associate-/r/_binary64_1745`
15×	`associate-/r*_binary64_1743`
14×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
13×	`div-inv_binary64_1796`
12×	`pow1_binary64_1860`
10×	`sqrt-pow1_binary64_1817` `add-exp-log_binary64_1837`
8×	`add-cbrt-cube_binary64_1835`
6×	`sqrt-div_binary64_1816`
4×	`pow-div_binary64_1874` `add-log-exp_binary64_1838` `pow1/2_binary64_1879` `pow-flip_binary64_1873` `rem-sqrt-square_binary64_1812` `inv-pow_binary64_1884`
3×	`div-exp_binary64_1850`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `cbrt-undiv_binary64_1833`
1×	`rec-exp_binary64_1849` `1-exp_binary64_1843` `associate-/l/_binary64_1746` `sqrt-undiv_binary64_1820`

Counts

4 → 401

Calls

4 calls:

34.0ms	(/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
14.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series333.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
88.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
72.0ms	(/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
65.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify186.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

413 → 413

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5234	17279

prune1.4s (26.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	410	3	413
Fresh	3	5	8
Picked	0	1	1
Done	1	1	2
Total	414	10	424

Merged error: 0b

Counts

424 → 10

Compiler

Compiled 16704 to 12327 computations (26.2% saved)

regimes29.0ms (0.6%)

Compiler: Compiled 262 to 208 computations (20.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample902.0ms (17.3%)

Algorithm

1×

intervals

Results

227.0ms	2032×	body	1024	valid
131.0ms	4289×	body	128	valid
83.0ms	993×	body	512	valid
28.0ms	205×	body	2048	valid
26.0ms	481×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 286 to 230 computations (19.6% saved)

Details

analyze3.0ms (0%)

sample27.0ms (0.5%)

simplify172.0ms (3.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite21.0ms (0.4%)

series98.0ms (1.9%)

simplify63.0ms (1.2%)

prune101.0ms (1.9%)

localize6.0ms (0.1%)

rewrite31.0ms (0.6%)

series135.0ms (2.6%)

simplify68.0ms (1.3%)

prune238.0ms (4.6%)

localize9.0ms (0.2%)

rewrite136.0ms (2.6%)

series303.0ms (5.8%)

simplify129.0ms (2.5%)

prune689.0ms (13.2%)

localize12.0ms (0.2%)

rewrite150.0ms (2.9%)

series333.0ms (6.4%)

simplify186.0ms (3.6%)

prune1.4s (26.3%)

regimes29.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample902.0ms (17.3%)

Profiling