Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	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 12 to 10 computations (16.7% saved)

sample13.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify165.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

rewrite56.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_1783`
41×	`times-frac_binary64_1789`
40×	`add-sqr-sqrt_binary64_1805`
24×	`add-cube-cbrt_binary64_1818`
12×	`distribute-lft-out_binary64_1734`
11×	`associate-/r*_binary64_1727`
9×	`add-exp-log_binary64_1821`
8×	`difference-of-squares_binary64_1752`
7×	`add-cbrt-cube_binary64_1819`
6×	`associate-/l*_binary64_1728` `distribute-lft-out--_binary64_1735`
5×	`add-log-exp_binary64_1822`
4×	`associate-/r/_binary64_1729` `difference-of-sqr-1_binary64_1753` `pow1_binary64_1844`
3×	`div-inv_binary64_1780` `div-exp_binary64_1834`
2×	`flip-+_binary64_1757` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `flip3-+_binary64_1786` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `inv-pow_binary64_1868` `frac-add_binary64_1791` `1-exp_binary64_1827` `pow-flip_binary64_1857` `sum-log_binary64_1874` `flip--_binary64_1758` `rec-exp_binary64_1833`

Counts

3 → 100

Calls

3 calls:

34.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
7.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))

series105.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

62.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
24.0ms	(/.f64 x (+.f64 x 1))
19.0ms	(/.f64 1 (-.f64 x 1))

simplify93.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4913	1579
1	4913	1579

prune114.0ms (3.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	3	110

Merged error: 0b

Counts

110 → 3

Compiler

Compiled 1897 to 1393 computations (26.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(/.f64 x (+.f64 x 1))
0.2b	(/.f64 1 (+.f64 -1 (*.f64 x x)))
12.8b	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

rewrite57.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64_1783`
36×	`add-sqr-sqrt_binary64_1805`
32×	`times-frac_binary64_1789`
29×	`add-cube-cbrt_binary64_1818`
19×	`add-exp-log_binary64_1821`
15×	`associate-l_binary64_1724`
13×	`add-cbrt-cube_binary64_1819`
8×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
7×	`associate-/r*_binary64_1727` `pow1_binary64_1844`
6×	`associate-/r/_binary64_1729` `associate-/l*_binary64_1728` `add-log-exp_binary64_1822`
5×	`frac-add_binary64_1791` `distribute-lft-out_binary64_1734` `div-exp_binary64_1834`
4×	`associate-r/_binary64_1725` `prod-exp_binary64_1832` `frac-times_binary64_1793` `associate-r*_binary64_1723`
3×	`div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `unswap-sqr_binary64_1751`
2×	`distribute-lft-in_binary64_1732` `cbrt-unprod_binary64_1816` `1-exp_binary64_1827` `associate-+l+_binary64_1716` `associate-*l/_binary64_1726` `frac-2neg_binary64_1794` `distribute-rgt-in_binary64_1733` `clear-num_binary64_1782` `rec-exp_binary64_1833`
1×	`+-commutative_binary64_1713` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `*-commutative_binary64_1714` `sum-log_binary64_1874` `pow-prod-down_binary64_1854`

Counts

4 → 128

Calls

4 calls:

20.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
13.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
6.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
6.0ms	(/.f64 x (+.f64 x 1))

series194.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
34.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
32.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
24.0ms	(/.f64 x (+.f64 x 1))

simplify79.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	6853	2235

prune154.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	140	3	143

Merged error: 0b

Counts

143 → 3

Compiler

Compiled 3138 to 2112 computations (32.7% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
0.0b	(/.f64 x (+.f64 1 x))
0.0b	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
0.0b	(/.f64 1 (+.f64 -1 x))

rewrite91.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`*-un-lft-identity_binary64_1783`
56×	`times-frac_binary64_1789`
48×	`distribute-lft-out_binary64_1734`
28×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
24×	`cbrt-prod_binary64_1814`
18×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
11×	`add-exp-log_binary64_1821`
9×	`add-cbrt-cube_binary64_1819`
8×	`associate-/r*_binary64_1727`
6×	`associate-/l*_binary64_1728` `div-inv_binary64_1780` `cube-div_binary64_1812` `pow1_binary64_1844`
4×	`associate-/r/_binary64_1729` `flip-+_binary64_1757` `flip3-+_binary64_1786` `add-log-exp_binary64_1822`
3×	`pow-unpow_binary64_1860` `cbrt-div_binary64_1815` `div-exp_binary64_1834`
2×	`sqr-pow_binary64_1755` `cube-mult_binary64_1813` `frac-add_binary64_1791` `unpow3_binary64_1849` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`inv-pow_binary64_1868` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `1-exp_binary64_1827` `pow-flip_binary64_1857` `pow-pow_binary64_1855` `pow1/3_binary64_1865` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `rec-exp_binary64_1833`

Counts

4 → 144

Calls

4 calls:

30.0ms	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
29.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
6.0ms	(/.f64 1 (+.f64 -1 x))
6.0ms	(/.f64 x (+.f64 1 x))

series197.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
68.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
24.0ms	(/.f64 x (+.f64 1 x))
17.0ms	(/.f64 1 (+.f64 -1 x))

simplify93.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4953	2840
1	4953	2840

prune172.0ms (5.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	156	3	159

Merged error: 0b

Counts

159 → 3

Compiler

Compiled 3063 to 2378 computations (22.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (/.f64 (+.f64 1 x) x)))
0.0b	(/.f64 (+.f64 1 x) x)
0.0b	(/.f64 1 (-.f64 x 1))
0.1b	(/.f64 1 (/.f64 (+.f64 1 x) x))

rewrite120.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`*-un-lft-identity_binary64_1783` `times-frac_binary64_1789`
94×	`add-sqr-sqrt_binary64_1805`
78×	`add-cube-cbrt_binary64_1818`
26×	`distribute-lft-out_binary64_1734` `associate-/r*_binary64_1727`
21×	`add-exp-log_binary64_1821`
13×	`add-cbrt-cube_binary64_1819`
11×	`div-inv_binary64_1780`
10×	`associate-/l*_binary64_1728` `div-exp_binary64_1834`
8×	`difference-of-squares_binary64_1752`
7×	`distribute-lft-out--_binary64_1735`
6×	`add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`cbrt-undiv_binary64_1817`
4×	`difference-of-sqr-1_binary64_1753`
3×	`associate-/r/_binary64_1729` `1-exp_binary64_1827` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rec-exp_binary64_1833`
2×	`associate-/l/_binary64_1730` `inv-pow_binary64_1868` `flip-+_binary64_1757` `pow-flip_binary64_1857` `flip3-+_binary64_1786`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `frac-add_binary64_1791` `sum-log_binary64_1874` `flip--_binary64_1758`

Counts

4 → 192

Calls

4 calls:

77.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (/.f64 (+.f64 1 x) x)))
10.0ms	(/.f64 1 (/.f64 (+.f64 1 x) x))
7.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 (+.f64 1 x) x)

series165.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(/.f64 (+.f64 1 x) x)
60.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (/.f64 (+.f64 1 x) x)))
24.0ms	(/.f64 1 (/.f64 (+.f64 1 x) x))
18.0ms	(/.f64 1 (-.f64 x 1))

simplify102.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5255	3191

prune215.0ms (7.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	204	3	207

Merged error: 0b

Counts

207 → 3

Compiler

Compiled 3876 to 2888 computations (25.5% saved)

regimes57.0ms (2%)

Compiler: Compiled 558 to 460 computations (17.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	25
1	16	25

end0.0ms (0%)

sample639.0ms (21.8%)

Algorithm

1×

intervals

Results

241.0ms

8000×

body

128

valid

Compiler

Compiled 296 to 244 computations (17.6% saved)

Details

analyze5.0ms (0.2%)

sample13.0ms (0.4%)

simplify165.0ms (5.6%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

rewrite56.0ms (1.9%)

series105.0ms (3.6%)

simplify93.0ms (3.2%)

prune114.0ms (3.9%)

localize9.0ms (0.3%)

rewrite57.0ms (2%)

series194.0ms (6.6%)

simplify79.0ms (2.7%)

prune154.0ms (5.3%)

localize12.0ms (0.4%)

rewrite91.0ms (3.1%)

series197.0ms (6.7%)

simplify93.0ms (3.2%)

prune172.0ms (5.9%)

localize8.0ms (0.3%)

rewrite120.0ms (4.1%)

series165.0ms (5.6%)

simplify102.0ms (3.5%)

prune215.0ms (7.4%)

regimes57.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample639.0ms (21.8%)

Profiling