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)

sample111.0ms (1.9%)

Algorithm

1×

intervals

Results

85.0ms	141×	body	2048	valid
15.0ms	64×	body	1024	valid
4.0ms	27×	body	512	valid
1.0ms	12×	body	256	valid
1.0ms	12×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify250.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

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: 27.5b

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)
1.9b	(+.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)

series77.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

61.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
16.0ms	(-.f64 (exp.f64 x) 2)

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4904	654
1	4904	654

prune100.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	4	46

Merged error: 0.0b

Counts

46 → 4

Compiler

Compiled 1367 to 894 computations (34.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite36.0ms (0.6%)

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)))

series358.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
65.0ms	(*.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))))
50.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4979	1259
1	4979	1259

prune114.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

Compiler

Compiled 2068 to 1461 computations (29.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
1.9b	(log.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))))
1.9b	(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_1799`
10×	`add-log-exp_binary64_1838`
9×	`add-sqr-sqrt_binary64_1821`
7×	`add-cube-cbrt_binary64_1834`
6×	`log-pow_binary64_1888` `cancel-sign-sub-inv_binary64_1765`
5×	`exp-prod_binary64_1851`
4×	`pow1_binary64_1860` `log-prod_binary64_1885` `associate-+r+_binary64_1731` `distribute-lft-out_binary64_1750` `frac-add_binary64_1807`
3×	`exp-diff_binary64_1847` `flip--_binary64_1774` `add-cbrt-cube_binary64_1835` `flip3--_binary64_1803` `add-exp-log_binary64_1837` `distribute-lft-out--_binary64_1751`
2×	`sum-log_binary64_1890` `sub-neg_binary64_1792` `neg-sub0_binary64_1794` `associate-+r-_binary64_1733` `diff-log_binary64_1891` `exp-neg_binary64_1846`
1×	`exp-sum_binary64_1845` `+-commutative_binary64_1729` `difference-of-squares_binary64_1768` `flip3-+_binary64_1802` `rem-log-exp_binary64_1840` `log-div_binary64_1886` `flip-+_binary64_1773`

Counts

3 → 58

Calls

3 calls:

11.0ms	(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))
10.0ms	(log.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))))
5.0ms	(-.f64 (exp.f64 x) 2)

series349.0ms (5.9%)

Counts

3 → 9

Calls

3 calls:

273.0ms	(log.f64 (exp.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))))
63.0ms	(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))
14.0ms	(-.f64 (exp.f64 x) 2)

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4939	1021
1	4939	1021

prune60.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	67	5	72

Merged error: 0.0b

Counts

72 → 5

Compiler

Compiled 1084 to 616 computations (43.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))
0.0b	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
0.0b	(pow.f64 (exp.f64 x) 3)
2.3b	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1821`
14×	`*-un-lft-identity_binary64_1799`
12×	`add-cube-cbrt_binary64_1834`
9×	`pow1_binary64_1860` `add-cbrt-cube_binary64_1835`
7×	`associate-r_binary64_1739`
6×	`add-log-exp_binary64_1838` `associate-l_binary64_1740` `add-exp-log_binary64_1837`
4×	`associate-*r/_binary64_1741` `pow-pow_binary64_1871`
3×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `pow-unpow_binary64_1876` `unpow-prod-down_binary64_1878` `exp-prod_binary64_1851` `flip3-+_binary64_1802` `cube-prod_binary64_1827` `flip-+_binary64_1773`
2×	`prod-exp_binary64_1848` `unswap-sqr_binary64_1767` `associate-+r+_binary64_1731` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `cube-mult_binary64_1829` `pow-to-exp_binary64_1868` `unpow3_binary64_1865` `pow-exp_binary64_1867` `sqr-pow_binary64_1771` `distribute-lft-out_binary64_1750` `rem-cube-cbrt_binary64_1822`

Counts

4 → 84

Calls

4 calls:

9.0ms	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))
7.0ms	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
4.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))
4.0ms	(pow.f64 (exp.f64 x) 3)

series287.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))
80.0ms	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
38.0ms	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))
37.0ms	(pow.f64 (exp.f64 x) 3)

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5020	1516

prune177.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	95	6	101

Merged error: 0.0b

Counts

101 → 6

Compiler

Compiled 3909 to 2341 computations (40.1% saved)

regimes17.0ms (0.3%)

Compiler: Compiled 149 to 103 computations (30.9% 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%)

sample3.6s (60.2%)

Algorithm

1×

intervals

Results

2.4s	4139×	body	2048	valid
517.0ms	2031×	body	1024	valid
139.0ms	1002×	body	512	valid
45.0ms	507×	body	256	valid
15.0ms	321×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 179 to 130 computations (27.4% saved)

Details

analyze4.0ms (0.1%)

sample111.0ms (1.9%)

simplify250.0ms (4.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite18.0ms (0.3%)

series77.0ms (1.3%)

simplify62.0ms (1.1%)

prune100.0ms (1.7%)

localize9.0ms (0.2%)

rewrite36.0ms (0.6%)

series358.0ms (6.1%)

simplify80.0ms (1.3%)

prune114.0ms (1.9%)

localize8.0ms (0.1%)

rewrite30.0ms (0.5%)

series349.0ms (5.9%)

simplify79.0ms (1.3%)

prune60.0ms (1%)

localize13.0ms (0.2%)

rewrite34.0ms (0.6%)

series287.0ms (4.9%)

simplify71.0ms (1.2%)

prune177.0ms (3%)

regimes17.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.6s (60.2%)

Profiling