Details

analyze7.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample25.0ms (0.7%)

Algorithm

1×

intervals

Results

7.0ms	46×	body	1024	valid
6.0ms	53×	body	512	valid
5.0ms	133×	body	128	valid
2.0ms	24×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify108.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune3.0ms (0.1%)

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

11.9b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
3.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite93.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_1783`
74×	`times-frac_binary64_1789`
72×	`add-sqr-sqrt_binary64_1805`
39×	`add-cube-cbrt_binary64_1818`
26×	`cancel-sign-sub-inv_binary64_1749`
18×	`distribute-lft-out--_binary64_1735`
17×	`distribute-lft-out_binary64_1734`
14×	`difference-of-squares_binary64_1752` `associate-+l+_binary64_1716`
12×	`add-exp-log_binary64_1821`
11×	`associate-/r*_binary64_1727` `add-log-exp_binary64_1822`
10×	`div-inv_binary64_1780`
8×	`add-cbrt-cube_binary64_1819`
6×	`associate-/l*_binary64_1728` `pow1_binary64_1844`
4×	`associate-/r/_binary64_1729` `difference-of-sqr-1_binary64_1753` `div-exp_binary64_1834`
3×	`flip3--_binary64_1787` `frac-add_binary64_1791` `flip--_binary64_1758`
2×	`inv-pow_binary64_1868` `1-exp_binary64_1827` `flip-+_binary64_1757` `pow-flip_binary64_1857` `diff-log_binary64_1875` `frac-sub_binary64_1792` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `flip3-+_binary64_1786` `clear-num_binary64_1782` `sub-neg_binary64_1776` `rec-exp_binary64_1833`
1×	`+-commutative_binary64_1713` `associate-+l-_binary64_1718`

Counts

4 → 161

Calls

4 calls:

48.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series85.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
14.0ms	(/.f64 1 (-.f64 x 1))
14.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
9.0ms	(/.f64 1 (+.f64 x 1))

simplify94.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4963	2797
1	4963	2797

prune231.0ms (6.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	3	174

Error

0.5b

Counts

174 → 3

Compiler

Compiled 3618 to 2904 computations (19.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 1 (+.f64 1 x)))
0.0b	(sqrt.f64 (/.f64 1 (+.f64 1 x)))
0.2b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
9.4b	(+.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 (/.f64 1 (+.f64 1 x)))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite108.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

150×	`sqrt-prod_binary64_1799`
138×	`*-un-lft-identity_binary64_1783`
127×	`add-sqr-sqrt_binary64_1805`
117×	`times-frac_binary64_1789`
67×	`add-cube-cbrt_binary64_1818`
31×	`swap-sqr_binary64_1750` `pow1_binary64_1844`
30×	`sqrt-pow1_binary64_1801`
26×	`distribute-lft-out_binary64_1734`
21×	`associate-l_binary64_1724` `associate-r_binary64_1723`
16×	`unswap-sqr_binary64_1751`
14×	`associate-+l+_binary64_1716`
13×	`cancel-sign-sub-inv_binary64_1749`
12×	`associate-/r/_binary64_1729` `rem-sqrt-square_binary64_1796`
10×	`inv-pow_binary64_1868` `div-inv_binary64_1780` `pow-flip_binary64_1857` `pow1/2_binary64_1863` `sqrt-div_binary64_1800`
9×	`pow-prod-up_binary64_1853` `add-log-exp_binary64_1822`
7×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
5×	`frac-add_binary64_1791` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
3×	`frac-sub_binary64_1792` `sqr-abs_binary64_1798`
2×	`associate-r/_binary64_1725` `associate-l/_binary64_1726` `sum-log_binary64_1874` `frac-times_binary64_1793`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `pow-plus_binary64_1846` `associate-+l-_binary64_1718` `diff-log_binary64_1875` `*-commutative_binary64_1714` `rem-square-sqrt_binary64_1795` `flip--_binary64_1758` `sub-neg_binary64_1776` `pow2_binary64_1864`

Counts

4 → 228

Calls

4 calls:

36.0ms	(+.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 (/.f64 1 (+.f64 1 x)))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
32.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
6.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 x)))
6.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 x)))

series96.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(+.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 (/.f64 1 (+.f64 1 x)))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
21.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 x)))
16.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 x)))
10.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 (/.f64 1 (+.f64 1 x))))

simplify99.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4999	4132
1	4999	4132

prune412.0ms (11.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	240	3	243

Error

0.5b

Counts

243 → 3

Compiler

Compiled 6372 to 5235 computations (17.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(*.f64 x (+.f64 1 x))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
17.0b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`associate-*r/_binary64_1725`
19×	`flip3--_binary64_1787` `flip--_binary64_1758`
16×	`add-sqr-sqrt_binary64_1805` `frac-add_binary64_1791`
13×	`*-un-lft-identity_binary64_1783`
12×	`frac-times_binary64_1793`
10×	`flip-+_binary64_1757` `associate-l_binary64_1724` `flip3-+_binary64_1786`
8×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `add-log-exp_binary64_1822` `pow1_binary64_1844`
7×	`associate-r_binary64_1723`
6×	`distribute-lft-in_binary64_1732` `associate-*l/_binary64_1726` `distribute-rgt-in_binary64_1733`
5×	`cancel-sign-sub-inv_binary64_1749` `sub-neg_binary64_1776`
4×	`associate-+l+_binary64_1716`
2×	`associate-+r+_binary64_1715` `difference-of-squares_binary64_1752` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `*-commutative_binary64_1714` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`
1×	`+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `sum-log_binary64_1874`

Counts

4 → 102

Calls

4 calls:

12.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
9.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
6.0ms	(*.f64 x (+.f64 1 x))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series57.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(*.f64 x (+.f64 1 x))
16.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
12.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
4.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify60.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5123	3216

prune178.0ms (4.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	116	1	117

Error

0.5b

Counts

117 → 1

Compiler

Compiled 3927 to 2715 computations (30.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (pow.f64 x 3) x)
0.5b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64_1805`
32×	`*-un-lft-identity_binary64_1783`
27×	`times-frac_binary64_1789`
20×	`difference-of-squares_binary64_1752`
17×	`add-cube-cbrt_binary64_1818`
9×	`associate-/r*_binary64_1727`
5×	`sqr-pow_binary64_1755` `unpow3_binary64_1849` `unpow-prod-down_binary64_1862` `distribute-lft-out--_binary64_1735` `distribute-rgt-out--_binary64_1737` `cube-prod_binary64_1811`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `cancel-sign-sub-inv_binary64_1749`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `flip--_binary64_1758` `pow1_binary64_1844`
1×	`div-inv_binary64_1780` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `sub-neg_binary64_1776`

Counts

2 → 73

Calls

2 calls:

9.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))
7.0ms	(-.f64 (pow.f64 x 3) x)

series65.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

42.0ms	(-.f64 (pow.f64 x 3) x)
23.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))

simplify88.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4973	1321
1	4973	1321

prune73.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	4	80

Error

Counts

80 → 4

Compiler

Compiled 1124 to 815 computations (27.5% saved)

regimes147.0ms (4%)

Accuracy

Total 0.1b remaining (93.7%)

Threshold costs 0.1b (93.7%)

Compiler

Compiled 1808 to 1506 computations (16.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	13
1	18	13

end0.0ms (0%)

sample1.6s (42.2%)

Algorithm

1×

intervals

Results

188.0ms	4534×	body	128	valid
186.0ms	1264×	body	1024	valid
166.0ms	1480×	body	512	valid
54.0ms	722×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 922 to 768 computations (16.7% saved)

Details

analyze7.0ms (0.2%)

sample25.0ms (0.7%)

simplify108.0ms (2.9%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite93.0ms (2.5%)

series85.0ms (2.3%)

simplify94.0ms (2.6%)

prune231.0ms (6.3%)

localize12.0ms (0.3%)

rewrite108.0ms (2.9%)

series96.0ms (2.6%)

simplify99.0ms (2.7%)

prune412.0ms (11.2%)

localize12.0ms (0.3%)

rewrite42.0ms (1.1%)

series57.0ms (1.5%)

simplify60.0ms (1.6%)

prune178.0ms (4.8%)

localize5.0ms (0.1%)

rewrite22.0ms (0.6%)

series65.0ms (1.8%)

simplify88.0ms (2.4%)

prune73.0ms (2%)

regimes147.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.6s (42.2%)

Profiling