Details

analyze2.0s (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

Compiler

Compiled 126 to 112 computations (11.1% saved)

sample2.8s (2.9%)

Algorithm

1×

intervals

Results

2.7s	122×	body	8192	exit
92.0ms	256×	body	128	valid
9.0ms	379×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify220.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4776	115
1	4776	115

prune16.0ms (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: 1.8b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize62.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.7b	(-.f64 (-.f64 1 z) 1)
6.7b	(-.f64 (-.f64 1 z) 1)
6.7b	(-.f64 (-.f64 1 z) 1)
6.7b	(-.f64 (-.f64 1 z) 1)

rewrite66.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_1783`
28×	`add-sqr-sqrt_binary64_1805`
24×	`cancel-sign-sub-inv_binary64_1749` `add-log-exp_binary64_1822`
16×	`associate--l+_binary64_1720`
12×	`add-cube-cbrt_binary64_1818` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875`
8×	`difference-of-squares_binary64_1752` `sub-neg_binary64_1776`
4×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `difference-of-sqr-1_binary64_1753` `associate--l-_binary64_1721` `flip--_binary64_1758` `pow1_binary64_1844`

Counts

4 → 100

Calls

4 calls:

10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)

series83.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(-.f64 (-.f64 1 z) 1)
22.0ms	(-.f64 (-.f64 1 z) 1)
18.0ms	(-.f64 (-.f64 1 z) 1)
18.0ms	(-.f64 (-.f64 1 z) 1)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4806	704
1	4806	704

prune1.4s (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	112	2	114

Merged error: 1.8b

Counts

114 → 2

Compiler

Compiled 13990 to 11821 computations (15.5% saved)

localize60.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.5b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite105.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_1783`
18×	`add-log-exp_binary64_1822`
10×	`add-exp-log_binary64_1821`
9×	`add-cbrt-cube_binary64_1819` `distribute-lft-out_binary64_1734` `sum-log_binary64_1874` `pow1_binary64_1844`
8×	`frac-add_binary64_1791`
7×	`prod-exp_binary64_1832`
5×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `flip-+_binary64_1757` `flip3-+_binary64_1786`
4×	`associate-r_binary64_1723`
3×	`cbrt-unprod_binary64_1816`
2×	`+-commutative_binary64_1713` `associate-+l+_binary64_1716` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854`
1×	`associate-r/_binary64_1725` `exp-sum_binary64_1829` `pow-sub_binary64_1859` `pow1/2_binary64_1863` `associate-l_binary64_1724` `associate-l/_binary64_1726` `sqrt-prod_binary64_1799` `*-commutative_binary64_1714` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 70

Calls

4 calls:

38.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
32.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
19.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series281.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

208.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
41.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
32.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify67.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5515	2608

prune472.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	75	7	82

Merged error: 1.1b

Counts

82 → 7

Compiler

Compiled 7295 to 5643 computations (22.6% saved)

localize61.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
1.0b	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite170.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1783`
27×	`add-log-exp_binary64_1822`
16×	`distribute-lft-out_binary64_1734` `sum-log_binary64_1874`
10×	`add-exp-log_binary64_1821`
9×	`add-cbrt-cube_binary64_1819` `pow1_binary64_1844`
8×	`frac-add_binary64_1791`
7×	`prod-exp_binary64_1832`
5×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `flip-+_binary64_1757` `flip3-+_binary64_1786`
4×	`associate-r_binary64_1723`
3×	`cbrt-unprod_binary64_1816`
2×	`+-commutative_binary64_1713` `associate-+l+_binary64_1716` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854`
1×	`associate-r/_binary64_1725` `exp-sum_binary64_1829` `pow-sub_binary64_1859` `pow1/2_binary64_1863` `associate-l_binary64_1724` `associate-l/_binary64_1726` `sqrt-prod_binary64_1799` `*-commutative_binary64_1714` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 74

Calls

4 calls:

74.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
59.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
19.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series305.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

207.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
56.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
41.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5306	3267

prune502.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Merged error: 0.2b

Counts

91 → 8

Compiler

Compiled 7918 to 6138 computations (22.5% saved)

localize63.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
1.0b	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b	(.f64 (.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 PI.f64)

rewrite169.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_1783`
27×	`add-log-exp_binary64_1822`
18×	`add-exp-log_binary64_1821`
16×	`distribute-lft-out_binary64_1734` `prod-exp_binary64_1832` `sum-log_binary64_1874`
13×	`add-cbrt-cube_binary64_1819`
8×	`frac-add_binary64_1791`
7×	`add-sqr-sqrt_binary64_1805` `pow1_binary64_1844`
6×	`add-cube-cbrt_binary64_1818` `cbrt-unprod_binary64_1816`
5×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
4×	`associate-r_binary64_1723`
3×	`sqrt-prod_binary64_1799`
2×	`+-commutative_binary64_1713` `associate-+l+_binary64_1716` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`associate-r/_binary64_1725` `exp-sum_binary64_1829` `pow-sub_binary64_1859` `pow1/2_binary64_1863` `associate-l_binary64_1724` `associate-l/_binary64_1726` `*-commutative_binary64_1714` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796`

Counts

4 → 80

Calls

4 calls:

75.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
53.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
21.0ms	(.f64 (.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms	(sqrt.f64 PI.f64)

series305.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

205.0ms	(.f64 (.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
57.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
43.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
0.0ms	(sqrt.f64 PI.f64)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4967	3414
1	4967	3414

prune561.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	90	8	98

Merged error: 0.2b

Counts

98 → 8

Compiler

Compiled 7705 to 5846 computations (24.1% saved)

regimes382.0ms (0.4%)

Compiler: Compiled 4872 to 4098 computations (15.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	117
1	105	117

end0.0ms (0%)

sample1.4min (89.4%)

Algorithm

1×

intervals

Results

1.4min	3824×	body	8192	exit
2.8s	8000×	body	128	valid
239.0ms	11907×	pre	128	true
35.0ms	83×	body	128	invalid

Compiler

Compiled 2513 to 2113 computations (15.9% saved)

Details

analyze2.0s (2%)

sample2.8s (2.9%)

simplify220.0ms (0.2%)

prune16.0ms (0%)

localize62.0ms (0.1%)

rewrite66.0ms (0.1%)

series83.0ms (0.1%)

simplify78.0ms (0.1%)

prune1.4s (1.4%)

localize60.0ms (0.1%)

rewrite105.0ms (0.1%)

series281.0ms (0.3%)

simplify67.0ms (0.1%)

prune472.0ms (0.5%)

localize61.0ms (0.1%)

rewrite170.0ms (0.2%)

series305.0ms (0.3%)

simplify74.0ms (0.1%)

prune502.0ms (0.5%)

localize63.0ms (0.1%)

rewrite169.0ms (0.2%)

series305.0ms (0.3%)

simplify98.0ms (0.1%)

prune561.0ms (0.6%)

regimes382.0ms (0.4%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.4min (89.4%)

Profiling