Details

analyze2.0ms (0.1%)

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)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	39×	body	512	valid
8.0ms	76×	body	1024	valid
3.0ms	120×	body	128	valid
1.0ms	8×	body	2048	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify98.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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: 33.9b

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))
2.7b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms (0.4%)

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))

series54.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

40.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify73.0ms (2%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4936	794
1	4936	794

prune48.0ms (1.3%)

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 697 to 458 computations (34.3% saved)

localize6.0ms (0.2%)

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)))

rewrite27.0ms (0.7%)

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:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series66.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
21.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4917	1530
1	4917	1530

prune96.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	78	9	87

Merged error: 0.0b

Counts

87 → 9

Compiler

Compiled 1523 to 1082 computations (29% 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)))
0.3b	(*.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)))))

rewrite116.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`*-un-lft-identity_binary64_1783`
290×	`sqrt-prod_binary64_1799`
172×	`times-frac_binary64_1789`
144×	`add-sqr-sqrt_binary64_1805`
116×	`distribute-lft-out_binary64_1734`
88×	`add-cube-cbrt_binary64_1818`
43×	`swap-sqr_binary64_1750`
31×	`pow1_binary64_1844`
27×	`associate-l_binary64_1724` `sqrt-pow1_binary64_1801` `associate-r_binary64_1723`
16×	`unswap-sqr_binary64_1751`
14×	`associate-/r/_binary64_1729` `add-exp-log_binary64_1821`
12×	`associate-/r*_binary64_1727`
11×	`inv-pow_binary64_1868` `pow-flip_binary64_1857`
10×	`add-cbrt-cube_binary64_1819`
9×	`div-inv_binary64_1780` `pow-prod-up_binary64_1853` `pow1/2_binary64_1863` `rem-sqrt-square_binary64_1796`
7×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
6×	`associate-/l*_binary64_1728`
5×	`pow-sqr_binary64_1756` `sqrt-div_binary64_1800` `pow-prod-down_binary64_1854`
4×	`div-exp_binary64_1834` `add-log-exp_binary64_1822`
3×	`sqr-abs_binary64_1798`
2×	`1-exp_binary64_1827` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rec-exp_binary64_1833`
1×	`associate-r/_binary64_1725` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `pow-plus_binary64_1846` `associate-l/_binary64_1726` `*-commutative_binary64_1714` `frac-times_binary64_1793` `rem-square-sqrt_binary64_1795` `pow2_binary64_1864`

Counts

4 → 281

Calls

4 calls:

42.0ms	(*.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)))))
14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series148.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
34.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
34.0ms	(*.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)))))
28.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify109.0ms (3%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5033	6769

prune510.0ms (14.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	288	5	293
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	293	9	302

Merged error: 0.0b

Counts

302 → 9

Compiler

Compiled 7525 to 5505 computations (26.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.5b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)

rewrite52.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64_1783`
34×	`sqrt-prod_binary64_1799`
31×	`unpow-prod-down_binary64_1862`
19×	`add-sqr-sqrt_binary64_1805`
18×	`add-cube-cbrt_binary64_1818`
16×	`distribute-lft-out_binary64_1734` `pow-unpow_binary64_1860`
9×	`times-frac_binary64_1789`
7×	`add-exp-log_binary64_1821` `pow1_binary64_1844`
6×	`add-log-exp_binary64_1822`
5×	`pow-exp_binary64_1851`
4×	`add-cbrt-cube_binary64_1819` `pow-pow_binary64_1855`
3×	`sqr-pow_binary64_1755` `pow-to-exp_binary64_1852`
2×	`flip-+_binary64_1757` `pow1/2_binary64_1863` `sqrt-div_binary64_1800` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801`
1×	`+-commutative_binary64_1713` `div-inv_binary64_1780` `sum-log_binary64_1874` `rem-sqrt-square_binary64_1796` `sqrt-pow2_binary64_1802`

Counts

4 → 97

Calls

4 calls:

14.0ms	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
10.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series241.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
66.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
40.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
20.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify85.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4889	2570
1	4889	2570

prune140.0ms (3.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	109	9	118

Merged error: 0b

Counts

118 → 9

Compiler

Compiled 2274 to 1755 computations (22.8% saved)

regimes151.0ms (4.2%)

Compiler: Compiled 1789 to 1473 computations (17.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.4s (40.2%)

Algorithm

1×

intervals

Results

203.0ms	1944×	body	1024	valid
126.0ms	4389×	body	128	valid
76.0ms	982×	body	512	valid
28.0ms	219×	body	2048	valid
27.0ms	466×	body	256	valid

Compiler

Compiled 871 to 720 computations (17.3% saved)

Details

analyze2.0ms (0.1%)

sample26.0ms (0.7%)

simplify98.0ms (2.7%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite15.0ms (0.4%)

series54.0ms (1.5%)

simplify73.0ms (2%)

prune48.0ms (1.3%)

localize6.0ms (0.2%)

rewrite27.0ms (0.7%)

series66.0ms (1.8%)

simplify58.0ms (1.6%)

prune96.0ms (2.7%)

localize9.0ms (0.2%)

rewrite116.0ms (3.2%)

series148.0ms (4.1%)

simplify109.0ms (3%)

prune510.0ms (14.2%)

localize12.0ms (0.3%)

rewrite52.0ms (1.4%)

series241.0ms (6.7%)

simplify85.0ms (2.4%)

prune140.0ms (3.9%)

regimes151.0ms (4.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.4s (40.2%)

Profiling