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
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample26.0ms (1%)

Algorithm

1×

intervals

Results

12.0ms	77×	body	1024	valid
4.0ms	49×	body	512	valid
2.0ms	99×	body	128	valid
1.0ms	25×	body	256	valid
1.0ms	6×	body	2048	valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify105.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9

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

Error

39.0b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
2.7b	(-.f64 (exp.f64 x) 1)

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1805`
30×	`*-un-lft-identity_binary64_1783`
21×	`times-frac_binary64_1789`
15×	`add-cube-cbrt_binary64_1818`
10×	`difference-of-squares_binary64_1752`
7×	`associate-/l*_binary64_1728`
5×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-log-exp_binary64_1822`
3×	`cancel-sign-sub-inv_binary64_1749` `associate-/r*_binary64_1727`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `flip--_binary64_1758` `pow1_binary64_1844`
1×	`div-sub_binary64_1788` `div-inv_binary64_1780` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `sub-neg_binary64_1776`

Counts

2 → 64

Calls

2 calls:

7.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
4.0ms	(-.f64 (exp.f64 x) 1)

series50.0ms (1.9%)

Counts

2 → 12

Calls

2 calls:

33.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
17.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 134 to 114 computations (14.9% saved)

simplify63.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1147
1	249	1094
2	556	1082
3	1324	1076
4	4324	1076
5	4961	1076

prune73.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	6	77

Error

0.0b

Counts

77 → 6

Compiler

Compiled 967 to 541 computations (44.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.0b	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
0.3b	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
0.3b	(*.f64 x 1/24)

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1805`
10×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
9×	`associate-l_binary64_1724` `associate-r_binary64_1723`
6×	`add-log-exp_binary64_1822`
4×	`associate-*r/_binary64_1725`
3×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`
2×	`distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733`
1×	`+-commutative_binary64_1713` `sum-log_binary64_1874`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
5.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
4.0ms	(*.f64 x 1/24)
3.0ms	(+.f64 1/6 (*.f64 x 1/24))

series125.0ms (4.7%)

Counts

4 → 20

Calls

4 calls:

50.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
31.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
27.0ms	(+.f64 1/6 (*.f64 x 1/24))
16.0ms	(*.f64 x 1/24)

Compiler

Compiled 398 to 347 computations (12.8% saved)

simplify84.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1170
1	315	1089
2	1055	1083
3	3490	1083
4	4315	1083
5	4984	1083
6	4884	1083

prune88.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	93	6	99

Error

0.0b

Counts

99 → 6

Compiler

Compiled 1655 to 1283 computations (22.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (exp.f64 x) x)
2.4b	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))

rewrite24.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_1805`
33×	`*-un-lft-identity_binary64_1783`
32×	`times-frac_binary64_1789`
19×	`add-cube-cbrt_binary64_1818`
13×	`cancel-sign-sub-inv_binary64_1749`
7×	`div-inv_binary64_1780`
6×	`difference-of-squares_binary64_1752`
5×	`distribute-lft-out--_binary64_1735`
4×	`add-cbrt-cube_binary64_1819` `add-log-exp_binary64_1822`
3×	`associate-/l_binary64_1728` `add-exp-log_binary64_1821` `associate-/r_binary64_1727` `distribute-rgt-out--_binary64_1737`
2×	`pow1_binary64_1844`
1×	`flip3--_binary64_1787` `sub-div_binary64_1790` `diff-log_binary64_1875` `frac-sub_binary64_1792` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

2 → 67

Calls

2 calls:

15.0ms	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
4.0ms	(/.f64 (exp.f64 x) x)

series60.0ms (2.3%)

Counts

2 → 12

Calls

2 calls:

33.0ms	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
26.0ms	(/.f64 (exp.f64 x) x)

Compiler

Compiled 142 to 121 computations (14.8% saved)

simplify71.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	1010
1	329	987
2	833	972
3	2421	961
4	4433	961
5	5008	961

prune52.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	80	5	85

Error

0.0b

Counts

85 → 5

Compiler

Compiled 1004 to 483 computations (51.9% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)) x)
0.0b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
0.0b	(pow.f64 (-.f64 (exp.f64 x) 1) 3)
2.7b	(-.f64 (exp.f64 x) 1)

rewrite48.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`add-sqr-sqrt_binary64_1805`
100×	`cbrt-prod_binary64_1814`
90×	`*-un-lft-identity_binary64_1783`
69×	`times-frac_binary64_1789`
51×	`add-cube-cbrt_binary64_1818`
42×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
26×	`difference-of-squares_binary64_1752`
23×	`associate-/l*_binary64_1728`
13×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
7×	`add-exp-log_binary64_1821`
6×	`add-cbrt-cube_binary64_1819` `sqr-pow_binary64_1755` `cube-mult_binary64_1813` `unpow3_binary64_1849` `cube-div_binary64_1812` `add-log-exp_binary64_1822`
5×	`pow1_binary64_1844`
4×	`flip3--_binary64_1787` `cbrt-div_binary64_1815` `flip--_binary64_1758`
3×	`pow-unpow_binary64_1860` `cancel-sign-sub-inv_binary64_1749` `associate-/r*_binary64_1727`
2×	`associate-/l/_binary64_1730`
1×	`rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `div-inv_binary64_1780` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `pow-pow_binary64_1855` `pow1/3_binary64_1865` `clear-num_binary64_1782` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `pow-exp_binary64_1851`

Counts

4 → 191

Calls

4 calls:

11.0ms	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)) x)
6.0ms	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
6.0ms	(pow.f64 (-.f64 (exp.f64 x) 1) 3)
5.0ms	(-.f64 (exp.f64 x) 1)

series115.0ms (4.4%)

Counts

4 → 24

Calls

4 calls:

47.0ms	(pow.f64 (-.f64 (exp.f64 x) 1) 3)
33.0ms	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)) x)
18.0ms	(-.f64 (exp.f64 x) 1)
17.0ms	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))

Compiler

Compiled 326 to 278 computations (14.7% saved)

simplify91.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	220	3677
1	374	3474
2	1136	3444
3	4822	3444
4	5020	3444

prune167.0ms (6.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	215	5	220

Error

0.0b

Counts

220 → 5

Compiler

Compiled 3029 to 1826 computations (39.7% saved)

regimes99.0ms (3.8%)

Accuracy

Total 0.6b remaining (97.9%)

Threshold costs 0.6b (97.9%)

Compiler

Compiled 682 to 529 computations (22.4% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	33
1	20	33
2	28	33
3	32	33
4	40	33
5	39	33
6	37	33

end0.0ms (0%)

sample1.2s (46.5%)

Algorithm

1×

intervals

Results

407.0ms	2686×	body	1024	valid
111.0ms	1311×	body	512	valid
77.0ms	3088×	body	128	valid
51.0ms	283×	body	2048	valid
38.0ms	632×	body	256	valid

Compiler

Compiled 371 to 283 computations (23.7% saved)

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9

Details

analyze4.0ms (0.1%)

sample26.0ms (1%)

simplify105.0ms (4%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite15.0ms (0.6%)

series50.0ms (1.9%)

simplify63.0ms (2.4%)

prune73.0ms (2.7%)

localize8.0ms (0.3%)

rewrite22.0ms (0.8%)

series125.0ms (4.7%)

simplify84.0ms (3.2%)

prune88.0ms (3.3%)

localize5.0ms (0.2%)

rewrite24.0ms (0.9%)

series60.0ms (2.3%)

simplify71.0ms (2.7%)

prune52.0ms (2%)

localize6.0ms (0.2%)

rewrite48.0ms (1.8%)

series115.0ms (4.4%)

simplify91.0ms (3.4%)

prune167.0ms (6.3%)

regimes99.0ms (3.8%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (46.5%)

Profiling

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9