Details

analyze100.0ms (1.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11
0	1	1
1	1	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)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms	64×	body	1024	valid
4.0ms	127×	body	128	valid
3.0ms	38×	body	512	valid
1.0ms	11×	body	2048	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify10.0ms (0.2%)

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

Error

31.5b

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))
1.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite61.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

30.9b

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×	`add-log-exp_binary64_1822` `difference-of-squares_binary64_1752`
3×	`pow1_binary64_1844` `distribute-lft-out--_binary64_1735`
2×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `distribute-lft-out_binary64_1734` `sqrt-div_binary64_1800`
1×	`diff-log_binary64_1875` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `flip3-+_binary64_1786` `flip-+_binary64_1757` `rem-sqrt-square_binary64_1796`

Counts

2 → 40

Calls

2 calls:

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

Compiler

Compiled 571 to 370 computations (35.2% saved)

series49.0ms (0.9%)

Error

30.7b

Counts

2 → 9

Calls

2 calls:

27.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 245 to 193 computations (21.2% saved)

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4932	589
1	4932	589

prune45.0ms (0.8%)

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

Error

0.1b

Counts

50 → 4

Compiler

Compiled 583 to 383 computations (34.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite115.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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×	`pow1_binary64_1844` `add-log-exp_binary64_1822` `add-cbrt-cube_binary64_1819`
3×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-/l*_binary64_1728`
2×	`div-exp_binary64_1834` `associate-/r/_binary64_1729` `sqrt-div_binary64_1800`
1×	`inv-pow_binary64_1868` `pow-flip_binary64_1857` `1-exp_binary64_1827` `rec-exp_binary64_1833` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `sum-log_binary64_1874` `+-commutative_binary64_1713` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`

Counts

3 → 75

Calls

3 calls:

10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 1268 to 926 computations (27% saved)

series54.0ms (1%)

Error

0.1b

Counts

3 → 12

Calls

3 calls:

18.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(sqrt.f64 (+.f64 1 x))
14.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 268 to 232 computations (13.4% saved)

simplify90.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4859	1227
1	4859	1227

prune92.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	2	0	2
Picked	0	1	1
Done	1	0	1
Total	82	9	91

Error

0.0b

Counts

91 → 9

Compiler

Compiled 1342 to 984 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite335.0ms (6.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

110×	`sqrt-prod_binary64_1799`
70×	`add-sqr-sqrt_binary64_1805`
46×	`*-un-lft-identity_binary64_1783`
40×	`sqrt-pow1_binary64_1801`
32×	`pow1_binary64_1844` `sqrt-div_binary64_1800`
28×	`add-cube-cbrt_binary64_1818`
20×	`pow1/2_binary64_1863`
18×	`swap-sqr_binary64_1750`
12×	`rem-sqrt-square_binary64_1796`
10×	`add-exp-log_binary64_1821` `associate-l_binary64_1724` `associate-r_binary64_1723`
9×	`pow-prod-up_binary64_1853` `flip3-+_binary64_1786` `flip-+_binary64_1757` `unswap-sqr_binary64_1751` `times-frac_binary64_1789`
8×	`add-cbrt-cube_binary64_1819` `distribute-lft-out_binary64_1734`
5×	`pow-prod-down_binary64_1854` `pow-sqr_binary64_1756`
4×	`add-log-exp_binary64_1822` `sqr-abs_binary64_1798` `frac-times_binary64_1793`
3×	`associate-/l_binary64_1728` `associate-/r_binary64_1727`
2×	`associate-l/_binary64_1726` `associate-r/_binary64_1725` `div-exp_binary64_1834` `associate-/r/_binary64_1729`
1×	`pow2_binary64_1864` `pow-plus_binary64_1846` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `sqrt-unprod_binary64_1803` `rem-square-sqrt_binary64_1795` `*-commutative_binary64_1714` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `1-exp_binary64_1827` `rec-exp_binary64_1833` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780`

Counts

4 → 169

Calls

4 calls:

20.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
20.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
7.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 4294 to 3383 computations (21.2% saved)

series160.0ms (3%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

47.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
46.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
19.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
19.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))

Compiler

Compiled 1145 to 963 computations (15.9% saved)

simplify89.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4867	2436
1	4867	2436

prune229.0ms (4.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	197	8	205

Error

0.0b

Counts

205 → 8

Compiler

Compiled 3611 to 2734 computations (24.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3)) (sqrt.f64 x)))
0.2b	(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3))
0.3b	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3)

rewrite608.0ms (11.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

225×	`sqrt-prod_binary64_1799`
114×	`add-sqr-sqrt_binary64_1805`
48×	`*-un-lft-identity_binary64_1783`
46×	`sqrt-div_binary64_1800`
42×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
40×	`unswap-sqr_binary64_1751`
36×	`add-cube-cbrt_binary64_1818`
32×	`associate-r_binary64_1723`
14×	`add-exp-log_binary64_1821`
13×	`sqrt-pow1_binary64_1801` `associate-l_binary64_1724`
12×	`pow1_binary64_1844`
9×	`add-cbrt-cube_binary64_1819` `flip3-+_binary64_1786` `flip-+_binary64_1757` `times-frac_binary64_1789`
8×	`cube-div_binary64_1812`
7×	`pow-pow_binary64_1855`
6×	`distribute-lft-out_binary64_1734` `sqr-pow_binary64_1755`
5×	`pow1/2_binary64_1863`
4×	`add-log-exp_binary64_1822` `frac-times_binary64_1793`
3×	`pow-unpow_binary64_1860` `prod-exp_binary64_1832` `associate-/l_binary64_1728` `associate-/r_binary64_1727`
2×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `unpow3_binary64_1849` `cube-mult_binary64_1813` `associate-l/_binary64_1726` `associate-r/_binary64_1725` `div-exp_binary64_1834` `associate-/r/_binary64_1729` `rem-sqrt-square_binary64_1796`
1×	`rem-cube-cbrt_binary64_1806` `sqrt-pow2_binary64_1802` `pow-prod-up_binary64_1853` `cbrt-unprod_binary64_1816` `*-commutative_binary64_1714` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `1-exp_binary64_1827` `rec-exp_binary64_1833` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780`

Counts

4 → 213

Calls

4 calls:

27.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3))
20.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3)) (sqrt.f64 x)))
8.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3)
8.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 7051 to 5865 computations (16.8% saved)

series193.0ms (3.6%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

71.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3)
53.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
19.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3)) (sqrt.f64 x)))
18.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3))

Compiler

Compiled 1264 to 1082 computations (14.4% saved)

simplify112.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4911	3926
1	4911	3926

prune366.0ms (6.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	239	9	248

Error

0.0b

Counts

248 → 9

Compiler

Compiled 5235 to 4152 computations (20.7% saved)

regimes256.0ms (4.8%)

Accuracy

Total 0.1b remaining (91.1%)

Threshold costs 0.1b (91.1%)

Compiler

Compiled 3057 to 2480 computations (18.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample2.2s (42.2%)

Algorithm

1×

intervals

Results

214.0ms	1948×	body	1024	valid
128.0ms	4263×	body	128	valid
86.0ms	1053×	body	512	valid
31.0ms	516×	body	256	valid
30.0ms	220×	body	2048	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 1506 to 1225 computations (18.7% saved)

Details

analyze100.0ms (1.9%)

sample24.0ms (0.4%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite61.0ms (1.2%)

series49.0ms (0.9%)

simplify37.0ms (0.7%)

prune45.0ms (0.8%)

localize6.0ms (0.1%)

rewrite115.0ms (2.2%)

series54.0ms (1%)

simplify90.0ms (1.7%)

prune92.0ms (1.7%)

localize10.0ms (0.2%)

rewrite335.0ms (6.3%)

series160.0ms (3%)

simplify89.0ms (1.7%)

prune229.0ms (4.3%)

localize11.0ms (0.2%)

rewrite608.0ms (11.5%)

series193.0ms (3.6%)

simplify112.0ms (2.1%)

prune366.0ms (6.9%)

regimes256.0ms (4.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (42.2%)

Profiling