Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample102.0ms (1.6%)

Algorithm

1×

intervals

Results

74.0ms	131×	body	2048	valid
14.0ms	56×	body	1024	valid
5.0ms	35×	body	512	valid
2.0ms	19×	body	256	valid
1.0ms	15×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify240.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5087	13

prune2.0ms (0%)

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

Merged error: 30.6b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
5.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_1799`
9×	`add-log-exp_binary64_1838`
6×	`add-sqr-sqrt_binary64_1821` `cancel-sign-sub-inv_binary64_1765`
4×	`add-cube-cbrt_binary64_1834` `associate-+l+_binary64_1732` `frac-add_binary64_1807`
3×	`flip--_binary64_1774` `flip3--_binary64_1803`
2×	`pow1_binary64_1860` `exp-diff_binary64_1847` `sum-log_binary64_1890` `sub-neg_binary64_1792` `neg-sub0_binary64_1794` `diff-log_binary64_1891` `add-cbrt-cube_binary64_1835` `exp-neg_binary64_1846` `add-exp-log_binary64_1837` `distribute-lft-out_binary64_1750` `distribute-lft-out--_binary64_1751`
1×	`+-commutative_binary64_1729` `difference-of-squares_binary64_1768` `flip3-+_binary64_1802` `associate-+l-_binary64_1734` `flip-+_binary64_1773`

Counts

2 → 39

Calls

2 calls:

10.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
5.0ms	(-.f64 (exp.f64 x) 2)

series71.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
14.0ms	(-.f64 (exp.f64 x) 2)

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4904	654
1	4904	654

prune144.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	3	46

Merged error: 0.0b

Counts

46 → 3

Compiler

Compiled 2072 to 1379 computations (33.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
0.1b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1821`
14×	`add-exp-log_binary64_1837` `associate-r_binary64_1739`
11×	`add-log-exp_binary64_1838`
10×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
8×	`unpow-prod-down_binary64_1878` `add-cbrt-cube_binary64_1835`
6×	`prod-exp_binary64_1848` `unswap-sqr_binary64_1767` `associate-l_binary64_1740`
4×	`pow1_binary64_1860` `sum-log_binary64_1890` `sqr-pow_binary64_1771`
2×	`+-commutative_binary64_1729` `pow-to-exp_binary64_1868` `cbrt-unprod_binary64_1832` `pow-exp_binary64_1867` `*-commutative_binary64_1730` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`associate-+r+_binary64_1731`

Counts

4 → 74

Calls

4 calls:

9.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
6.0ms	(*.f64 1/12 (pow.f64 x 4))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
6.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))

series355.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
62.0ms	(*.f64 1/360 (pow.f64 x 6))
59.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
52.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4979	1259
1	4979	1259

prune116.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0b

Counts

89 → 4

Compiler

Compiled 2101 to 1479 computations (29.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))))
28.8b	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
28.8b	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
28.8b	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))

rewrite65.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1830`
23×	`add-sqr-sqrt_binary64_1821`
18×	`cbrt-div_binary64_1831`
15×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
11×	`pow1_binary64_1860`
9×	`pow1/3_binary64_1881` `flip3-+_binary64_1802` `flip-+_binary64_1773`
6×	`associate-l_binary64_1740` `add-exp-log_binary64_1837` `swap-sqr_binary64_1766` `associate-r_binary64_1739`
4×	`add-log-exp_binary64_1838` `unswap-sqr_binary64_1767` `add-cbrt-cube_binary64_1835` `frac-times_binary64_1809`
2×	`pow-sqr_binary64_1772` `associate-r/_binary64_1741` `pow-prod-up_binary64_1869` `pow-prod-down_binary64_1870` `associate-l/_binary64_1742`
1×	`pow2_binary64_1880` `prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `pow-plus_binary64_1862`

Counts

4 → 87

Calls

4 calls:

21.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))))
8.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
8.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
8.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))

series571.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))))
142.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
140.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
127.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))

simplify105.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4920	4267
1	4920	4267

prune365.0ms (5.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	99	4	103

Merged error: 0b

Counts

103 → 4

Compiler

Compiled 6275 to 4542 computations (27.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
0.0b	(-.f64 (exp.f64 x) 2)
0.1b	(pow.f64 (exp.f64 x) -2)
4.9b	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1821` `cancel-sign-sub-inv_binary64_1765`
17×	`*-un-lft-identity_binary64_1799`
13×	`add-cube-cbrt_binary64_1834`
10×	`add-log-exp_binary64_1838`
8×	`associate--l+_binary64_1736`
7×	`unpow-prod-down_binary64_1878`
5×	`pow1_binary64_1860` `sub-neg_binary64_1792` `difference-of-squares_binary64_1768`
4×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837` `pow-pow_binary64_1871`
3×	`pow-unpow_binary64_1876` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `sqr-pow_binary64_1771` `exp-prod_binary64_1851`
2×	`distribute-lft-out--_binary64_1751`
1×	`pow-to-exp_binary64_1868` `pow-exp_binary64_1867`

Counts

4 → 81

Calls

4 calls:

18.0ms	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2))
6.0ms	(pow.f64 (exp.f64 x) -2)
5.0ms	(-.f64 (exp.f64 x) 2)
5.0ms	(-.f64 (exp.f64 x) 2)

series215.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2))
49.0ms	(pow.f64 (exp.f64 x) -2)
17.0ms	(-.f64 (exp.f64 x) 2)
13.0ms	(-.f64 (exp.f64 x) 2)

simplify101.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4891	1150
1	4891	1150

prune128.0ms (2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	93	4	97

Merged error: 0b

Counts

97 → 4

Compiler

Compiled 2767 to 1564 computations (43.5% saved)

regimes14.0ms (0.2%)

Compiler: Compiled 119 to 85 computations (28.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms (0%)

sample3.4s (54.3%)

Algorithm

1×

intervals

Results

2.4s	4138×	body	2048	valid
493.0ms	1926×	body	1024	valid
138.0ms	1004×	body	512	valid
47.0ms	534×	body	256	valid
18.0ms	398×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 149 to 112 computations (24.8% saved)

Details

analyze4.0ms (0.1%)

sample102.0ms (1.6%)

simplify240.0ms (3.8%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite18.0ms (0.3%)

series71.0ms (1.1%)

simplify58.0ms (0.9%)

prune144.0ms (2.3%)

localize10.0ms (0.2%)

rewrite34.0ms (0.5%)

series355.0ms (5.7%)

simplify74.0ms (1.2%)

prune116.0ms (1.9%)

localize15.0ms (0.2%)

rewrite65.0ms (1%)

series571.0ms (9.1%)

simplify105.0ms (1.7%)

prune365.0ms (5.8%)

localize11.0ms (0.2%)

rewrite43.0ms (0.7%)

series215.0ms (3.4%)

simplify101.0ms (1.6%)

prune128.0ms (2%)

regimes14.0ms (0.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.4s (54.3%)

Profiling