Details

analyze4.0ms (0.1%)

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)

simplify169.0ms (5.3%)

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 2 expressions with local error:

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

rewrite45.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

32.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
7.0ms	(/.f64 1 (-.f64 x 1))

series95.0ms (3%)

Counts

2 → 6

Calls

2 calls:

75.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
21.0ms	(/.f64 1 (-.f64 x 1))

simplify76.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4942	1114
1	4942	1114

prune93.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Merged error: 0b

Counts

74 → 4

Compiler

Compiled 1615 to 1227 computations (24% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.3b	(/.f64 1 (+.f64 -1 (*.f64 x x)))
14.1b	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

rewrite44.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_1821`
22×	`*-un-lft-identity_binary64_1799`
20×	`times-frac_binary64_1805`
19×	`add-cube-cbrt_binary64_1834`
16×	`add-exp-log_binary64_1837`
15×	`associate-l_binary64_1740`
10×	`add-cbrt-cube_binary64_1835`
7×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
6×	`pow1_binary64_1860`
5×	`add-log-exp_binary64_1838` `frac-add_binary64_1807`
4×	`div-exp_binary64_1850` `prod-exp_binary64_1848` `associate-r/_binary64_1741` `associate-/r/_binary64_1745` `frac-times_binary64_1809` `associate-r*_binary64_1739`
3×	`associate-/l_binary64_1744` `unswap-sqr_binary64_1767` `associate-/r_binary64_1743`
2×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `rec-exp_binary64_1849` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `cbrt-unprod_binary64_1832` `div-inv_binary64_1796` `associate-+l+_binary64_1732` `associate-*l/_binary64_1742`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `+-commutative_binary64_1729` `frac-2neg_binary64_1810` `pow-flip_binary64_1873` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870` `distribute-lft-out_binary64_1750` `inv-pow_binary64_1884`

Counts

3 → 95

Calls

3 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 1 (+.f64 -1 (*.f64 x x)))

series173.0ms (5.4%)

Counts

3 → 9

Calls

3 calls:

108.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
36.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
29.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

simplify71.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	6211	1770

prune113.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	104	4	108

Merged error: 0b

Counts

108 → 4

Compiler

Compiled 2338 to 1596 computations (31.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite104.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`*-un-lft-identity_binary64_1799`
54×	`distribute-lft-out_binary64_1750`
52×	`times-frac_binary64_1805`
24×	`cbrt-prod_binary64_1830`
19×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834`
18×	`unpow-prod-down_binary64_1878` `cube-prod_binary64_1827`
9×	`add-exp-log_binary64_1837`
7×	`add-cbrt-cube_binary64_1835`
6×	`pow1_binary64_1860` `add-log-exp_binary64_1838` `div-inv_binary64_1796` `cube-div_binary64_1828`
4×	`associate-/r*_binary64_1743` `flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`associate-/l*_binary64_1744` `pow-unpow_binary64_1876` `cbrt-div_binary64_1831` `frac-add_binary64_1807`
2×	`div-exp_binary64_1850` `cube-mult_binary64_1829` `associate-/r/_binary64_1745` `unpow3_binary64_1865` `sqr-pow_binary64_1771`
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` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `pow-flip_binary64_1873` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `pow-exp_binary64_1867` `pow-pow_binary64_1871` `rem-cube-cbrt_binary64_1822` `inv-pow_binary64_1884`

Counts

4 → 129

Calls

4 calls:

29.0ms	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
27.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
25.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
6.0ms	(/.f64 1 (+.f64 -1 x))

series243.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
72.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
60.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
17.0ms	(/.f64 1 (+.f64 -1 x))

simplify94.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4957	2805
1	4957	2805

prune161.0ms (5.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	141	4	145

Merged error: 0b

Counts

145 → 4

Compiler

Compiled 2792 to 2202 computations (21.1% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite150.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`cbrt-div_binary64_1831`
81×	`frac-times_binary64_1809`
80×	`*-un-lft-identity_binary64_1799`
51×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
48×	`frac-add_binary64_1807`
44×	`times-frac_binary64_1805`
35×	`add-sqr-sqrt_binary64_1821`
33×	`add-cube-cbrt_binary64_1834`
27×	`associate-*l/_binary64_1742`
26×	`pow1_binary64_1860`
22×	`distribute-lft-out_binary64_1750`
21×	`add-exp-log_binary64_1837`
15×	`associate-*r/_binary64_1741`
12×	`associate-/r_binary64_1743` `associate-r*_binary64_1739`
11×	`add-cbrt-cube_binary64_1835`
10×	`cbrt-prod_binary64_1830`
9×	`associate-/l*_binary64_1744` `pow1/3_binary64_1881` `pow-prod-up_binary64_1869`
6×	`div-exp_binary64_1850` `associate-/r/_binary64_1745` `pow-plus_binary64_1862`
5×	`pow-prod-down_binary64_1870`
4×	`add-log-exp_binary64_1838` `div-inv_binary64_1796`
3×	`pow-sqr_binary64_1772` `clear-num_binary64_1798` `prod-exp_binary64_1848` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `pow-flip_binary64_1873` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `cbrt-unprod_binary64_1832` `inv-pow_binary64_1884`
2×	`pow2_binary64_1880` `unswap-sqr_binary64_1767`
1×	`associate-l_binary64_1740` `*-commutative_binary64_1730` `pow3_binary64_1882` `rem-3cbrt-lft_binary64_1824`

Counts

4 → 216

Calls

4 calls:

91.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))))
6.0ms	(/.f64 1 (+.f64 -1 x))
6.0ms	(/.f64 1 (+.f64 -1 x))
6.0ms	(/.f64 1 (+.f64 -1 x))

series159.0ms (5%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))))
23.0ms	(/.f64 1 (+.f64 -1 x))
17.0ms	(/.f64 1 (+.f64 -1 x))
16.0ms	(/.f64 1 (+.f64 -1 x))

simplify106.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5022	9294

prune724.0ms (22.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	228	4	232

Merged error: 0b

Counts

232 → 4

Compiler

Compiled 11415 to 8663 computations (24.1% saved)

regimes25.0ms (0.8%)

Compiler: Compiled 184 to 148 computations (19.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms (0%)

sample476.0ms (15%)

Algorithm

1×

intervals

Results

263.0ms

8000×

body

128

valid

Compiler

Compiled 103 to 84 computations (18.4% saved)

Details

analyze4.0ms (0.1%)

sample13.0ms (0.4%)

simplify169.0ms (5.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite45.0ms (1.4%)

series95.0ms (3%)

simplify76.0ms (2.4%)

prune93.0ms (2.9%)

localize9.0ms (0.3%)

rewrite44.0ms (1.4%)

series173.0ms (5.4%)

simplify71.0ms (2.2%)

prune113.0ms (3.6%)

localize9.0ms (0.3%)

rewrite104.0ms (3.3%)

series243.0ms (7.7%)

simplify94.0ms (2.9%)

prune161.0ms (5.1%)

localize12.0ms (0.4%)

rewrite150.0ms (4.7%)

series159.0ms (5%)

simplify106.0ms (3.3%)

prune724.0ms (22.8%)

regimes25.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample476.0ms (15%)

Profiling