Details

analyze1.8s (1.7%)

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)

sample2.3s (2.2%)

Algorithm

1×

intervals

Results

2.2s	103×	body	8192	exit
83.0ms	256×	body	128	valid
7.0ms	362×	pre	128	true
1.0ms	3×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify205.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

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)

localize58.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.6b	(-.f64 (-.f64 1 z) 1)
5.6b	(-.f64 (-.f64 1 z) 1)
5.6b	(-.f64 (-.f64 1 z) 1)
5.6b	(-.f64 (-.f64 1 z) 1)

rewrite53.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1762`
24×	`add-log-exp_binary64_1798`
20×	`add-sqr-sqrt_binary64_1783`
12×	`diff-log_binary64_1851` `distribute-lft-out--_binary64_1716`
8×	`difference-of-squares_binary64_1731` `sub-neg_binary64_1755`
4×	`flip3--_binary64_1766` `difference-of-sqr-1_binary64_1732` `flip--_binary64_1737` `add-cube-cbrt_binary64_1794` `associate--l+_binary64_1701` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820` `associate--l-_binary64_1702`

Counts

4 → 76

Calls

4 calls:

9.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)

series70.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(-.f64 (-.f64 1 z) 1)
18.0ms	(-.f64 (-.f64 1 z) 1)
17.0ms	(-.f64 (-.f64 1 z) 1)
17.0ms	(-.f64 (-.f64 1 z) 1)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4902	660
1	4902	660

prune849.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	88	2	90

Merged error: 1.8b

Counts

90 → 2

Compiler

Compiled 11046 to 9300 computations (15.8% saved)

localize55.0ms (0.1%)

Local error

Found 4 expressions with local error:

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	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite172.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_1762`
44×	`add-log-exp_binary64_1798` `frac-add_binary64_1770`
31×	`distribute-lft-out_binary64_1715` `sum-log_binary64_1850`
10×	`add-exp-log_binary64_1797`
9×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `add-cbrt-cube_binary64_1795` `pow1_binary64_1820`
7×	`prod-exp_binary64_1808`
5×	`add-sqr-sqrt_binary64_1783` `add-cube-cbrt_binary64_1794`
4×	`associate-r_binary64_1704`
3×	`cbrt-unprod_binary64_1792`
2×	`pow-prod-down_binary64_1830` `+-commutative_binary64_1694` `sqrt-pow1_binary64_1779` `associate-+l+_binary64_1697`
1×	`pow-sub_binary64_1835` `associate-l/_binary64_1707` `pow-exp_binary64_1827` `sqrt-prod_binary64_1777` `associate-r/_binary64_1706` `exp-sum_binary64_1805` `-commutative_binary64_1695` `pow-to-exp_binary64_1828` `associate-l*_binary64_1705` `pow1/2_binary64_1839`

Counts

4 → 86

Calls

4 calls:

106.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
24.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series305.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

182.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
95.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
27.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify112.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4971	7992
1	4971	7992

prune760.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	87	9	96
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	89	9	98

Merged error: 0.3b

Counts

98 → 9

Compiler

Compiled 11717 to 9228 computations (21.2% saved)

localize101.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

rewrite163.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-log-exp_binary64_1798` `*-un-lft-identity_binary64_1762`
12×	`distribute-lft-out_binary64_1715` `sum-log_binary64_1850`
8×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `frac-add_binary64_1770`
4×	`+-commutative_binary64_1694` `add-sqr-sqrt_binary64_1783` `add-cube-cbrt_binary64_1794` `add-cbrt-cube_binary64_1795` `associate-+r+_binary64_1696` `add-exp-log_binary64_1797` `pow1_binary64_1820`

Counts

4 → 68

Calls

4 calls:

30.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
27.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
26.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
26.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series134.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
33.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
33.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
32.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4977	2204
1	4977	2204

prune3.8s (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	80	9	89

Merged error: 0.3b

Counts

89 → 9

Compiler

Compiled 32939 to 27209 computations (17.4% saved)

localize63.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
1.0b	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
3.1b	(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))

rewrite471.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

1530×	`*-un-lft-identity_binary64_1762`
579×	`times-frac_binary64_1768`
533×	`distribute-lft-out_binary64_1715`
304×	`distribute-lft-out--_binary64_1716`
26×	`add-log-exp_binary64_1798`
25×	`frac-add_binary64_1770`
17×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
16×	`add-sqr-sqrt_binary64_1783`
15×	`sum-log_binary64_1850`
14×	`pow1_binary64_1820`
8×	`frac-times_binary64_1772` `frac-sub_binary64_1771` `add-cube-cbrt_binary64_1794`
6×	`swap-sqr_binary64_1729` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
5×	`associate-+l-_binary64_1699`
4×	`associate-l/_binary64_1707` `associate-r/_binary64_1706` `associate-l_binary64_1705` `associate-r_binary64_1704`
3×	`difference-of-squares_binary64_1731`
2×	`pow-prod-down_binary64_1830` `distribute-rgt-in_binary64_1714` `sqrt-pow1_binary64_1779` `distribute-lft-in_binary64_1713` `associate--l+_binary64_1701`
1×	`pow-sqr_binary64_1735` `flip3--_binary64_1766` `diff-log_binary64_1851` `div-sub_binary64_1767` `pow-prod-up_binary64_1829` `prod-exp_binary64_1808` `pow-plus_binary64_1822` `unswap-sqr_binary64_1730` `+-commutative_binary64_1694` `sqrt-prod_binary64_1777` `cbrt-unprod_binary64_1792` `flip--_binary64_1737` `sub-neg_binary64_1755` `*-commutative_binary64_1695` `associate-+l+_binary64_1697` `pow2_binary64_1840` `pow1/2_binary64_1839`

Counts

4 → 202

Calls

4 calls:

282.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
60.0ms	(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
27.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series499.0ms (0.5%)

Counts

4 → 10

Calls

4 calls:

416.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
57.0ms	(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
25.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify232.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4902	19967
1	4902	19967

prune2.5s (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	212	9	221

Merged error: 0.3b

Counts

221 → 9

Compiler

Compiled 25147 to 19982 computations (20.5% saved)

regimes584.0ms (0.5%)

Compiler: Compiled 7996 to 6688 computations (16.4% saved)

bsearch0.0ms (0%)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	205	589
1	205	589

end0.0ms (0%)

sample1.5min (85.5%)

Algorithm

1×

intervals

Results

1.4min	4013×	body	8192	exit
2.6s	8000×	body	128	valid
250.0ms	12097×	pre	128	true
29.0ms	84×	body	128	invalid

Compiler

Compiled 4390 to 3673 computations (16.3% saved)

Details

analyze1.8s (1.7%)

sample2.3s (2.2%)

simplify205.0ms (0.2%)

prune16.0ms (0%)

localize58.0ms (0.1%)

rewrite53.0ms (0%)

series70.0ms (0.1%)

simplify78.0ms (0.1%)

prune849.0ms (0.8%)

localize55.0ms (0.1%)

rewrite172.0ms (0.2%)

series305.0ms (0.3%)

simplify112.0ms (0.1%)

prune760.0ms (0.7%)

localize101.0ms (0.1%)

rewrite163.0ms (0.2%)

series134.0ms (0.1%)

simplify79.0ms (0.1%)

prune3.8s (3.6%)

localize63.0ms (0.1%)

rewrite471.0ms (0.4%)

series499.0ms (0.5%)

simplify232.0ms (0.2%)

prune2.5s (2.3%)

regimes584.0ms (0.5%)

bsearch0.0ms (0%)

simplify9.0ms (0%)

end0.0ms (0%)

sample1.5min (85.5%)

Profiling