Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample23.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	68×	body	1024	valid
4.0ms	138×	body	128	valid
3.0ms	32×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify175.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

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: 29.2b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite67.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_1783`
88×	`times-frac_binary64_1789`
85×	`add-sqr-sqrt_binary64_1805`
37×	`add-cube-cbrt_binary64_1818`
34×	`cancel-sign-sub-inv_binary64_1749`
27×	`distribute-lft-out_binary64_1734`
22×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
11×	`associate-/r*_binary64_1727`
9×	`difference-of-sqr-1_binary64_1753`
7×	`add-cbrt-cube_binary64_1819` `associate-/l*_binary64_1728` `add-exp-log_binary64_1821`
6×	`associate-/r/_binary64_1729`
5×	`add-log-exp_binary64_1822`
3×	`flip3--_binary64_1787` `div-inv_binary64_1780` `flip--_binary64_1758` `pow1_binary64_1844`
2×	`associate-/l/_binary64_1730` `flip-+_binary64_1757` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `flip3-+_binary64_1786` `clear-num_binary64_1782`
1×	`diff-log_binary64_1875` `frac-sub_binary64_1792` `sub-neg_binary64_1776`

Counts

3 → 147

Calls

3 calls:

40.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series68.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

42.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
13.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
13.0ms	(/.f64 x (+.f64 x 1))

simplify81.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5658	2774

prune195.0ms (5.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	3	157

Merged error: 0.0b

Counts

157 → 3

Compiler

Compiled 3052 to 2150 computations (29.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
7.9b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))

rewrite52.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_1805`
69×	`*-un-lft-identity_binary64_1783`
56×	`times-frac_binary64_1789`
37×	`add-cube-cbrt_binary64_1818`
27×	`associate-r_binary64_1723`
19×	`add-exp-log_binary64_1821`
14×	`difference-of-squares_binary64_1752`
13×	`add-cbrt-cube_binary64_1819`
11×	`associate-/r*_binary64_1727`
7×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735` `pow1_binary64_1844`
6×	`associate-/r/_binary64_1729` `associate-/l*_binary64_1728` `frac-sub_binary64_1792` `add-log-exp_binary64_1822`
5×	`distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `div-exp_binary64_1834` `flip3-+_binary64_1786`
4×	`prod-exp_binary64_1832` `associate-l_binary64_1724` `associate-*l/_binary64_1726` `frac-times_binary64_1793`
3×	`flip3--_binary64_1787` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `unswap-sqr_binary64_1751` `flip--_binary64_1758`
2×	`associate-*r/_binary64_1725` `un-div-inv_binary64_1781` `cbrt-unprod_binary64_1816` `1-exp_binary64_1827` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rec-exp_binary64_1833`
1×	`inv-pow_binary64_1868` `pow-flip_binary64_1857` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `*-commutative_binary64_1714` `pow-prod-down_binary64_1854` `sub-neg_binary64_1776`

Counts

4 → 155

Calls

4 calls:

16.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
11.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series76.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
14.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
13.0ms	(/.f64 x (+.f64 x 1))
10.0ms	(/.f64 1 (-.f64 x 1))

simplify80.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5801	2543

prune187.0ms (5.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	167	3	170

Merged error: 0.0b

Counts

170 → 3

Compiler

Compiled 3522 to 2552 computations (27.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)
0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
18.1b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite46.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1783`
50×	`add-sqr-sqrt_binary64_1805`
34×	`cancel-sign-sub-inv_binary64_1749`
28×	`times-frac_binary64_1789`
26×	`add-cube-cbrt_binary64_1818`
22×	`cbrt-prod_binary64_1814`
11×	`pow1_binary64_1844`
8×	`difference-of-squares_binary64_1752` `pow1/3_binary64_1865`
7×	`distribute-lft-out_binary64_1734`
6×	`swap-sqr_binary64_1750` `add-exp-log_binary64_1821` `associate-l_binary64_1724` `add-log-exp_binary64_1822` `associate-r_binary64_1723`
4×	`add-cbrt-cube_binary64_1819` `difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735` `unswap-sqr_binary64_1751`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `pow-prod-up_binary64_1853` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854` `flip--_binary64_1758`
1×	`associate-r/_binary64_1725` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-plus_binary64_1846` `div-inv_binary64_1780` `diff-log_binary64_1875` `frac-sub_binary64_1792` `-commutative_binary64_1714` `sub-neg_binary64_1776` `pow2_binary64_1864`

Counts

4 → 108

Calls

4 calls:

24.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series318.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
87.0ms	(cbrt.f64 x)
85.0ms	(cbrt.f64 x)
48.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify74.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5026	1467

prune128.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	120	3	123

Merged error: 0.0b

Counts

123 → 3

Compiler

Compiled 2780 to 1561 computations (43.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.4b	(/.f64 3 (pow.f64 x 3))
0.7b	(/.f64 -1 (*.f64 x x))
7.2b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite93.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64_1783`
68×	`times-frac_binary64_1789`
44×	`add-sqr-sqrt_binary64_1805`
40×	`add-cube-cbrt_binary64_1818`
14×	`add-exp-log_binary64_1821` `unpow3_binary64_1849`
13×	`cancel-sign-sub-inv_binary64_1749` `associate-/r*_binary64_1727`
12×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
11×	`add-cbrt-cube_binary64_1819` `distribute-lft-out_binary64_1734` `add-log-exp_binary64_1822`
8×	`distribute-rgt-out_binary64_1736`
6×	`associate-/l*_binary64_1728` `div-inv_binary64_1780`
5×	`div-exp_binary64_1834`
4×	`sqr-pow_binary64_1755` `cube-mult_binary64_1813` `pow1_binary64_1844`
3×	`frac-sub_binary64_1792` `cbrt-undiv_binary64_1817`
2×	`difference-of-squares_binary64_1752` `frac-add_binary64_1791` `flip-+_binary64_1757` `distribute-lft-out--_binary64_1735` `distribute-rgt1-in_binary64_1739` `diff-log_binary64_1875` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `flip3-+_binary64_1786` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip--_binary64_1758` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `pow-exp_binary64_1851` `associate--r+_binary64_1719`

Counts

4 → 141

Calls

4 calls:

40.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
31.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
5.0ms	(/.f64 3 (pow.f64 x 3))
4.0ms	(/.f64 -1 (*.f64 x x))

series115.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
23.0ms	(/.f64 3 (pow.f64 x 3))
18.0ms	(/.f64 -1 (*.f64 x x))
17.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify78.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5045	2493

prune176.0ms (4.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	152	4	156

Merged error: 0b

Counts

156 → 4

Compiler

Compiled 3142 to 2183 computations (30.5% saved)

regimes167.0ms (4.6%)

Compiler: Compiled 1622 to 1256 computations (22.6% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	77
1	90	77

end0.0ms (0%)

sample1.4s (37.7%)

Algorithm

1×

intervals

Results

250.0ms	2047×	body	1024	valid
147.0ms	4282×	body	128	valid
90.0ms	931×	body	512	valid
34.0ms	540×	body	256	valid
31.0ms	200×	body	2048	valid

Compiler

Compiled 813 to 627 computations (22.9% saved)

Details

analyze4.0ms (0.1%)

sample23.0ms (0.6%)

simplify175.0ms (4.8%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

rewrite67.0ms (1.9%)

series68.0ms (1.9%)

simplify81.0ms (2.2%)

prune195.0ms (5.4%)

localize8.0ms (0.2%)

rewrite52.0ms (1.4%)

series76.0ms (2.1%)

simplify80.0ms (2.2%)

prune187.0ms (5.2%)

localize10.0ms (0.3%)

rewrite46.0ms (1.3%)

series318.0ms (8.8%)

simplify74.0ms (2.1%)

prune128.0ms (3.5%)

localize9.0ms (0.2%)

rewrite93.0ms (2.6%)

series115.0ms (3.2%)

simplify78.0ms (2.2%)

prune176.0ms (4.9%)

regimes167.0ms (4.6%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (37.7%)

Profiling