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)

sample20.0ms (0.3%)

Algorithm

1×

intervals

Results

6.0ms	62×	body	1024	valid
4.0ms	141×	body	128	valid
2.0ms	22×	body	512	valid
1.0ms	11×	body	2048	valid
1.0ms	20×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify99.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune6.0ms (0.1%)

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: 28.8b

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

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_1799`
14×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
6×	`cancel-sign-sub-inv_binary64_1749`
5×	`add-cube-cbrt_binary64_1818`
4×	`difference-of-squares_binary64_1752` `add-log-exp_binary64_1822`
3×	`distribute-lft-out--_binary64_1735` `pow1_binary64_1844`
2×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `distribute-lft-out_binary64_1734` `sqrt-div_binary64_1800`
1×	`flip3--_binary64_1787` `flip-+_binary64_1757` `pow1/2_binary64_1863` `diff-log_binary64_1875` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

2 → 40

Calls

2 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series44.0ms (0.6%)

Counts

2 → 9

Calls

2 calls:

29.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
15.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 168 to 140 computations (16.7% saved)

simplify89.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4802	589
1	4802	589

prune45.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	4	50

Merged error: 0.2b

Counts

50 → 4

Compiler

Compiled 591 to 388 computations (34.3% 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)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1783`
24×	`sqrt-prod_binary64_1799`
21×	`distribute-lft-out_binary64_1734`
18×	`times-frac_binary64_1789`
16×	`add-sqr-sqrt_binary64_1805`
15×	`add-cube-cbrt_binary64_1818`
7×	`add-exp-log_binary64_1821`
6×	`associate-/r*_binary64_1727`
5×	`add-cbrt-cube_binary64_1819` `add-log-exp_binary64_1822` `pow1_binary64_1844`
3×	`associate-/l*_binary64_1728` `flip-+_binary64_1757` `flip3-+_binary64_1786`
2×	`associate-/r/_binary64_1729` `sqrt-div_binary64_1800` `div-exp_binary64_1834`
1×	`+-commutative_binary64_1713` `inv-pow_binary64_1868` `1-exp_binary64_1827` `div-inv_binary64_1780` `pow-flip_binary64_1857` `pow1/2_binary64_1863` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`

Counts

3 → 75

Calls

3 calls:

10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series44.0ms (0.6%)

Counts

3 → 12

Calls

3 calls:

16.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
15.0ms	(sqrt.f64 (+.f64 x 1))
13.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 178 to 164 computations (7.9% saved)

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4911	1227
1	4911	1227

prune90.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	81	10	91

Merged error: 0.1b

Counts

91 → 10

Compiler

Compiled 1342 to 981 computations (26.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite140.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64_1783`
700×	`sqrt-prod_binary64_1799`
594×	`times-frac_binary64_1789`
280×	`distribute-lft-out_binary64_1734`
254×	`add-sqr-sqrt_binary64_1805`
252×	`add-cube-cbrt_binary64_1818`
36×	`associate-/l*_binary64_1728`
28×	`sqrt-div_binary64_1800`
24×	`associate-/r/_binary64_1729`
18×	`associate-/r*_binary64_1727`
17×	`add-exp-log_binary64_1821`
14×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
12×	`div-inv_binary64_1780`
11×	`add-cbrt-cube_binary64_1819`
8×	`div-exp_binary64_1834` `pow1_binary64_1844`
4×	`cbrt-undiv_binary64_1817` `add-log-exp_binary64_1822`
3×	`pow-flip_binary64_1857` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
2×	`1-exp_binary64_1827` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`
1×	`associate-/l/_binary64_1730` `inv-pow_binary64_1868`

Counts

4 → 453

Calls

4 calls:

34.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series88.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
25.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
19.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
19.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 392 to 352 computations (10.2% saved)

simplify223.0ms (3%)

Algorithm

1×	egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4875	14766
1	4875	14766

prune930.0ms (12.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	460	5	465
Fresh	4	3	7
Picked	1	0	1
Done	1	1	2
Total	466	9	475

Merged error: 0b

Counts

475 → 9

Compiler

Compiled 11606 to 8545 computations (26.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite182.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

887×	`*-un-lft-identity_binary64_1783`
880×	`sqrt-prod_binary64_1799`
774×	`times-frac_binary64_1789`
334×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
316×	`distribute-lft-out_binary64_1734`
216×	`cbrt-prod_binary64_1814`
36×	`associate-/l*_binary64_1728`
30×	`associate-/r/_binary64_1729` `sqrt-div_binary64_1800`
21×	`associate-/r*_binary64_1727`
17×	`add-exp-log_binary64_1821` `flip-+_binary64_1757` `flip3-+_binary64_1786`
15×	`div-inv_binary64_1780`
11×	`add-cbrt-cube_binary64_1819`
8×	`div-exp_binary64_1834`
7×	`pow1_binary64_1844`
6×	`cbrt-div_binary64_1815`
5×	`pow-flip_binary64_1857`
4×	`cbrt-undiv_binary64_1817` `sqrt-pow1_binary64_1801` `pow1/3_binary64_1865` `add-log-exp_binary64_1822`
2×	`pow-div_binary64_1858` `1-exp_binary64_1827` `pow1/2_binary64_1863` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rec-exp_binary64_1833`
1×	`associate-/l/_binary64_1730` `inv-pow_binary64_1868`

Counts

4 → 553

Calls

4 calls:

37.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
8.0ms	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series127.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
36.0ms	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
29.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
25.0ms	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 724 to 622 computations (14.1% saved)

simplify294.0ms (4%)

Algorithm

1×	egg-herbie

Counts

565 → 565

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4878	28200
1	4878	28200

prune2.8s (38%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	565	0	565
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	565	9	574

Merged error: 0b

Counts

574 → 9

Compiler

Compiled 26146 to 19496 computations (25.4% saved)

regimes208.0ms (2.8%)

Compiler: Compiled 2732 to 2180 computations (20.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.8s (24.5%)

Algorithm

1×

intervals

Results

211.0ms	1981×	body	1024	valid
126.0ms	4332×	body	128	valid
78.0ms	963×	body	512	valid
34.0ms	211×	body	2048	valid
27.0ms	513×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 1355 to 1082 computations (20.1% saved)

Details

analyze3.0ms (0%)

sample20.0ms (0.3%)

simplify99.0ms (1.3%)

prune6.0ms (0.1%)

localize5.0ms (0.1%)

rewrite14.0ms (0.2%)

series44.0ms (0.6%)

simplify89.0ms (1.2%)

prune45.0ms (0.6%)

localize6.0ms (0.1%)

rewrite28.0ms (0.4%)

series44.0ms (0.6%)

simplify78.0ms (1%)

prune90.0ms (1.2%)

localize12.0ms (0.2%)

rewrite140.0ms (1.9%)

series88.0ms (1.2%)

simplify223.0ms (3%)

prune930.0ms (12.5%)

localize15.0ms (0.2%)

rewrite182.0ms (2.4%)

series127.0ms (1.7%)

simplify294.0ms (4%)

prune2.8s (38%)

regimes208.0ms (2.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (24.5%)

Profiling