Details

analyze4.0ms (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 (0.5%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify101.0ms (4.2%)

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)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite55.0ms (2.3%)

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))
5.0ms	(/.f64 x (+.f64 x 1))

series54.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
13.0ms	(/.f64 x (+.f64 x 1))
10.0ms	(/.f64 1 (-.f64 x 1))

simplify85.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5162	1579

prune118.0ms (4.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	4	110

Merged error: 0b

Counts

110 → 4

Compiler

Compiled 1931 to 1421 computations (26.4% saved)

localize10.0ms (0.4%)

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))
0.1b	(/.f64 1 (+.f64 -1 (*.f64 x x)))
17.5b	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

rewrite48.0ms (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:

16.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
12.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))
5.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))

series96.0ms (4%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
21.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
15.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
12.0ms	(/.f64 x (+.f64 x 1))

simplify102.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4975	2244
1	4975	2244

prune160.0ms (6.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	140	4	144

Merged error: 0b

Counts

144 → 4

Compiler

Compiled 3178 to 2146 computations (32.5% saved)

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (+.f64 -1 x)) (cbrt.f64 (+.f64 -1 x)))
0.3b	(cbrt.f64 (-.f64 x 1))
0.3b	(cbrt.f64 (+.f64 -1 x))
0.3b	(cbrt.f64 (+.f64 -1 x))

rewrite31.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`cbrt-prod_binary64_1814`
36×	`*-un-lft-identity_binary64_1783`
27×	`add-sqr-sqrt_binary64_1805`
18×	`cbrt-div_binary64_1815`
15×	`add-cube-cbrt_binary64_1818`
11×	`pow1_binary64_1844`
9×	`swap-sqr_binary64_1750` `pow1/3_binary64_1865`
8×	`distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `flip3-+_binary64_1786`
7×	`associate-l_binary64_1724` `associate-r_binary64_1723`
6×	`add-exp-log_binary64_1821`
4×	`add-cbrt-cube_binary64_1819` `frac-times_binary64_1793` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
2×	`associate-r/_binary64_1725` `difference-of-squares_binary64_1752` `pow-prod-up_binary64_1853` `associate-l/_binary64_1726` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
1×	`flip3--_binary64_1787` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `difference-of-sqr-1_binary64_1753` `pow-plus_binary64_1846` `distribute-lft-out--_binary64_1735` `*-commutative_binary64_1714` `flip--_binary64_1758` `pow2_binary64_1864`

Counts

4 → 98

Calls

4 calls:

12.0ms	(*.f64 (cbrt.f64 (+.f64 -1 x)) (cbrt.f64 (+.f64 -1 x)))
3.0ms	(cbrt.f64 (+.f64 -1 x))
3.0ms	(cbrt.f64 (-.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 -1 x))

series130.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(*.f64 (cbrt.f64 (+.f64 -1 x)) (cbrt.f64 (+.f64 -1 x)))
32.0ms	(cbrt.f64 (+.f64 -1 x))
31.0ms	(cbrt.f64 (-.f64 x 1))
30.0ms	(cbrt.f64 (+.f64 -1 x))

simplify79.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5099	1633

prune166.0ms (6.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Merged error: 0b

Counts

114 → 4

Compiler

Compiled 3084 to 2409 computations (21.9% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite70.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`*-un-lft-identity_binary64_1783`
40×	`times-frac_binary64_1789`
28×	`distribute-lft-out_binary64_1734`
23×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
10×	`add-exp-log_binary64_1821`
9×	`exp-prod_binary64_1835` `add-log-exp_binary64_1822`
8×	`add-cbrt-cube_binary64_1819` `associate-/r*_binary64_1727`
6×	`associate-/l*_binary64_1728`
5×	`pow1_binary64_1844`
4×	`associate-/r/_binary64_1729` `div-inv_binary64_1780`
3×	`flip-+_binary64_1757` `div-exp_binary64_1834` `flip3-+_binary64_1786`
2×	`rem-exp-log_binary64_1823` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `clear-num_binary64_1782`
1×	`+-commutative_binary64_1713` `inv-pow_binary64_1868` `exp-sum_binary64_1829` `frac-add_binary64_1791` `1-exp_binary64_1827` `pow-flip_binary64_1857` `rec-exp_binary64_1833`

Counts

4 → 107

Calls

4 calls:

26.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
25.0ms	(exp.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))
6.0ms	(/.f64 1 (+.f64 -1 x))
5.0ms	(/.f64 x (+.f64 1 x))

series95.0ms (4%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(exp.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))
28.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
13.0ms	(/.f64 x (+.f64 1 x))
10.0ms	(/.f64 1 (+.f64 -1 x))

simplify126.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4914	1686
1	4914	1686

prune126.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	120	3	123

Merged error: 0b

Counts

123 → 3

Compiler

Compiled 2208 to 1687 computations (23.6% saved)

regimes52.0ms (2.2%)

Compiler: Compiled 530 to 424 computations (20% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	46
1	20	46

end0.0ms (0%)

sample648.0ms (27%)

Algorithm

1×

intervals

Results

248.0ms

8000×

body

128

valid

Compiler

Compiled 294 to 238 computations (19% saved)

Details

analyze4.0ms (0.2%)

sample13.0ms (0.5%)

simplify101.0ms (4.2%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

rewrite55.0ms (2.3%)

series54.0ms (2.2%)

simplify85.0ms (3.5%)

prune118.0ms (4.9%)

localize10.0ms (0.4%)

rewrite48.0ms (2%)

series96.0ms (4%)

simplify102.0ms (4.2%)

prune160.0ms (6.7%)

localize13.0ms (0.6%)

rewrite31.0ms (1.3%)

series130.0ms (5.4%)

simplify79.0ms (3.3%)

prune166.0ms (6.9%)

localize10.0ms (0.4%)

rewrite70.0ms (2.9%)

series95.0ms (4%)

simplify126.0ms (5.3%)

prune126.0ms (5.2%)

regimes52.0ms (2.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample648.0ms (27%)

Profiling