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)

sample12.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify179.0ms (7.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

prune2.0ms (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)

localize6.0ms (0.2%)

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))

rewrite58.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_1799`
41×	`times-frac_binary64_1805`
40×	`add-sqr-sqrt_binary64_1821`
24×	`add-cube-cbrt_binary64_1834`
12×	`distribute-lft-out_binary64_1750`
11×	`associate-/r*_binary64_1743`
9×	`add-exp-log_binary64_1837`
8×	`difference-of-squares_binary64_1768`
7×	`add-cbrt-cube_binary64_1835`
6×	`associate-/l*_binary64_1744` `distribute-lft-out--_binary64_1751`
5×	`add-log-exp_binary64_1838`
4×	`pow1_binary64_1860` `associate-/r/_binary64_1745` `difference-of-sqr-1_binary64_1769`
3×	`div-exp_binary64_1850` `div-inv_binary64_1796`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `cbrt-undiv_binary64_1833` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `rec-exp_binary64_1849` `pow-flip_binary64_1873` `1-exp_binary64_1843` `flip--_binary64_1774` `flip3--_binary64_1803` `frac-add_binary64_1807` `inv-pow_binary64_1884`

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))

series109.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

62.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
25.0ms	(/.f64 x (+.f64 x 1))
21.0ms	(/.f64 1 (-.f64 x 1))

simplify95.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4913	1579
1	4913	1579

prune116.0ms (4.6%)

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 2046 to 1518 computations (25.8% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite79.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`*-un-lft-identity_binary64_1799`
40×	`times-frac_binary64_1805`
28×	`distribute-lft-out_binary64_1750`
23×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834`
10×	`add-exp-log_binary64_1837`
9×	`add-log-exp_binary64_1838` `exp-prod_binary64_1851`
8×	`associate-/r*_binary64_1743` `add-cbrt-cube_binary64_1835`
6×	`associate-/l*_binary64_1744`
5×	`pow1_binary64_1860`
4×	`associate-/r/_binary64_1745` `div-inv_binary64_1796`
3×	`div-exp_binary64_1850` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`sum-log_binary64_1890` `clear-num_binary64_1798` `frac-2neg_binary64_1810` `cbrt-undiv_binary64_1833` `rem-exp-log_binary64_1839`
1×	`exp-sum_binary64_1845` `+-commutative_binary64_1729` `rec-exp_binary64_1849` `pow-flip_binary64_1873` `1-exp_binary64_1843` `frac-add_binary64_1807` `inv-pow_binary64_1884`

Counts

4 → 107

Calls

4 calls:

29.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
28.0ms	(exp.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))
6.0ms	(/.f64 1 (+.f64 -1 x))
6.0ms	(/.f64 x (+.f64 1 x))

series191.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(exp.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))
60.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
24.0ms	(/.f64 x (+.f64 1 x))
18.0ms	(/.f64 1 (+.f64 -1 x))

simplify89.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4924	1686
1	4924	1686

prune132.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	119	3	122

Merged error: 0b

Counts

122 → 3

Compiler

Compiled 2235 to 1710 computations (23.5% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 -1 x))
0.0b	(+.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3)) (/.f64 x (+.f64 x 1)))
0.1b	(pow.f64 (/.f64 1 (+.f64 -1 x)) 3)
19.5b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3))

rewrite95.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64_1799`
60×	`times-frac_binary64_1805`
47×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834`
42×	`cbrt-prod_binary64_1830`
36×	`unpow-prod-down_binary64_1878` `cube-prod_binary64_1827`
17×	`distribute-lft-out_binary64_1750`
13×	`add-exp-log_binary64_1837`
10×	`associate-/r/_binary64_1745`
9×	`add-cbrt-cube_binary64_1835`
7×	`pow1_binary64_1860`
6×	`add-log-exp_binary64_1838` `flip3-+_binary64_1802` `flip-+_binary64_1773`
5×	`div-inv_binary64_1796`
4×	`div-exp_binary64_1850` `associate-/r*_binary64_1743` `pow-exp_binary64_1867`
3×	`associate-/l*_binary64_1744` `pow-unpow_binary64_1876` `pow-pow_binary64_1871` `cube-div_binary64_1828`
2×	`cube-mult_binary64_1829` `rec-exp_binary64_1849` `pow-flip_binary64_1873` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `unpow3_binary64_1865` `sqr-pow_binary64_1771` `cbrt-div_binary64_1831` `rem-cube-cbrt_binary64_1822` `inv-pow_binary64_1884`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `+-commutative_binary64_1729` `rem-cbrt-cube_binary64_1823` `pow1/3_binary64_1881` `pow-to-exp_binary64_1868` `frac-2neg_binary64_1810` `frac-add_binary64_1807`

Counts

4 → 162

Calls

4 calls:

54.0ms	(+.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3)) (/.f64 x (+.f64 x 1)))
9.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3))
9.0ms	(pow.f64 (/.f64 1 (+.f64 -1 x)) 3)
6.0ms	(/.f64 1 (+.f64 -1 x))

series126.0ms (5%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(+.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3)) (/.f64 x (+.f64 x 1)))
24.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3))
23.0ms	(pow.f64 (/.f64 1 (+.f64 -1 x)) 3)
20.0ms	(/.f64 1 (+.f64 -1 x))

simplify82.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4988	2384
1	4988	2384

prune195.0ms (7.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	174	3	177

Merged error: 0b

Counts

177 → 3

Compiler

Compiled 3202 to 2516 computations (21.4% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 1 (+.f64 -1 x))
0.0b	(+.f64 (log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x)))) (/.f64 x (+.f64 x 1)))
3.5b	(log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x))))

rewrite62.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64_1799`
36×	`times-frac_binary64_1805`
32×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834`
20×	`log-pow_binary64_1888`
18×	`exp-prod_binary64_1851`
13×	`distribute-lft-out_binary64_1750`
10×	`add-exp-log_binary64_1837`
8×	`associate-/r*_binary64_1743` `add-cbrt-cube_binary64_1835`
7×	`pow1_binary64_1860`
6×	`log-prod_binary64_1885` `associate-/l*_binary64_1744` `associate-/r/_binary64_1745`
5×	`add-log-exp_binary64_1838`
4×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`div-exp_binary64_1850` `div-inv_binary64_1796` `associate-+l+_binary64_1732`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `cbrt-undiv_binary64_1833`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `rec-exp_binary64_1849` `pow-flip_binary64_1873` `1-exp_binary64_1843` `rem-log-exp_binary64_1840` `inv-pow_binary64_1884`

Counts

4 → 116

Calls

4 calls:

32.0ms	(+.f64 (log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x)))) (/.f64 x (+.f64 x 1)))
8.0ms	(log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x))))
6.0ms	(/.f64 1 (+.f64 -1 x))
6.0ms	(/.f64 x (+.f64 x 1))

series168.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(+.f64 (log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x)))) (/.f64 x (+.f64 x 1)))
38.0ms	(log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x))))
23.0ms	(/.f64 x (+.f64 x 1))
16.0ms	(/.f64 1 (+.f64 -1 x))

simplify98.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4907	1699
1	4907	1699

prune133.0ms (5.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	128	3	131

Merged error: 0b

Counts

131 → 3

Compiler

Compiled 2366 to 1814 computations (23.3% saved)

regimes10.0ms (0.4%)

Compiler: Compiled 42 to 36 computations (14.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	20
1	15	20

end0.0ms (0%)

sample434.0ms (17.3%)

Algorithm

1×

intervals

Results

240.0ms

8000×

body

128

valid

Compiler

Compiled 65 to 56 computations (13.8% saved)

Details

analyze4.0ms (0.2%)

sample12.0ms (0.5%)

simplify179.0ms (7.1%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite58.0ms (2.3%)

series109.0ms (4.3%)

simplify95.0ms (3.8%)

prune116.0ms (4.6%)

localize10.0ms (0.4%)

rewrite79.0ms (3.1%)

series191.0ms (7.6%)

simplify89.0ms (3.6%)

prune132.0ms (5.3%)

localize12.0ms (0.5%)

rewrite95.0ms (3.8%)

series126.0ms (5%)

simplify82.0ms (3.3%)

prune195.0ms (7.8%)

localize10.0ms (0.4%)

rewrite62.0ms (2.5%)

series168.0ms (6.7%)

simplify98.0ms (3.9%)

prune133.0ms (5.3%)

regimes10.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample434.0ms (17.3%)

Profiling