Details

analyze1.8s (1.2%)

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)

sample3.6s (2.4%)

Algorithm

1×

intervals

Results

3.5s	164×	body	8192	exit
85.0ms	256×	body	128	valid
9.0ms	421×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify215.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4776	115
1	4776	115

prune13.0ms (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)

localize59.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite176.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_2099`
44×	`add-log-exp_binary64_2135` `frac-add_binary64_2107`
31×	`distribute-lft-out_binary64_2052` `sum-log_binary64_2187`
10×	`add-exp-log_binary64_2134`
9×	`flip3-+_binary64_2102` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `flip-+_binary64_2073`
7×	`prod-exp_binary64_2145`
5×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131`
4×	`associate-r_binary64_2041`
3×	`cbrt-unprod_binary64_2129`
2×	`associate-+l+_binary64_2034` `+-commutative_binary64_2031` `pow-prod-down_binary64_2167` `sqrt-pow1_binary64_2116`
1×	`associate-l_binary64_2042` `associate-r/_binary64_2043` `pow-exp_binary64_2164` `-commutative_binary64_2032` `associate-*l/_binary64_2044` `pow-to-exp_binary64_2165` `pow-sub_binary64_2172` `pow1/2_binary64_2176` `exp-sum_binary64_2142` `sqrt-prod_binary64_2114`

Counts

4 → 86

Calls

4 calls:

103.0ms	(+.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)))
17.0ms	(.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))

series322.0ms (0.2%)

Counts

4 → 10

Calls

4 calls:

198.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
93.0ms	(+.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)))
31.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify110.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4971	7992
1	4971	7992

prune775.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	90	8	98

Merged error: 0.3b

Counts

98 → 8

Compiler

Compiled 11711 to 9219 computations (21.3% saved)

localize100.0ms (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))))

rewrite165.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-log-exp_binary64_2135` `*-un-lft-identity_binary64_2099`
12×	`distribute-lft-out_binary64_2052` `sum-log_binary64_2187`
8×	`flip3-+_binary64_2102` `flip-+_binary64_2073` `frac-add_binary64_2107`
4×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `+-commutative_binary64_2031` `add-exp-log_binary64_2134` `associate-+r+_binary64_2033`

Counts

4 → 68

Calls

4 calls:

28.0ms	(+.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))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series130.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

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

simplify84.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4977	2204
1	4977	2204

prune4.2s (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	80	8	88

Merged error: 0.3b

Counts

88 → 8

Compiler

Compiled 32933 to 27200 computations (17.4% saved)

localize87.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (.f64 (-.f64 7 z) (+.f64 (.f64 (-.f64 6 z) (+.f64 (.f64 (-.f64 5 z) (+.f64 (.f64 (-.f64 4 z) (+.f64 (.f64 (+.f64 (.f64 (-.f64 2 z) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z)))) (.f64 -5537752839100187/4398046511104 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))) (-.f64 3 z)) (.f64 (.f64 (-.f64 2 z) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 848079078717083/1099511627776))) (.f64 -6214088902520669/35184372088832 (.f64 (.f64 (-.f64 2 z) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (-.f64 3 z))))) (.f64 7041008316161153/562949953421312 (.f64 (-.f64 4 z) (.f64 (.f64 (-.f64 2 z) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (-.f64 3 z)))))) (.f64 -4992549864024149/36028797018963968 (.f64 (-.f64 5 z) (.f64 (-.f64 4 z) (.f64 (.f64 (-.f64 2 z) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (-.f64 3 z))))))) (.f64 5893731530977871/590295810358705651712 (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (-.f64 4 z) (.f64 (*.f64 (-.f64 2 z) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (-.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))
2.8b	(+.f64 (.f64 (-.f64 2 z) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z)))) (.f64 -5537752839100187/4398046511104 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))

rewrite2.3min (92.1%)

Algorithm

1×	rewrite-expression-head

Calls

3 calls:

62.0ms

(+.f64 (*.f64 (-.f64 2 z) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z)))) (*.f64 -5537752839100187/4398046511104 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))

20.0ms

(*.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))

Details

analyze1.8s (1.2%)

sample3.6s (2.4%)

simplify215.0ms (0.1%)

prune13.0ms (0%)

localize59.0ms (0%)

rewrite176.0ms (0.1%)

series322.0ms (0.2%)

simplify110.0ms (0.1%)

prune775.0ms (0.5%)

localize100.0ms (0.1%)

rewrite165.0ms (0.1%)

series130.0ms (0.1%)

simplify84.0ms (0.1%)

prune4.2s (2.8%)

localize87.0ms (0.1%)

rewrite2.3min (92.1%)

Profiling