Details

analyze1.7s (2.9%)

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 127 to 112 computations (11.8% saved)

sample1.5s (2.6%)

Algorithm

1×

intervals

Results

1.4s	127×	body	8192	exit
77.0ms	256×	body	128	valid
7.0ms	385×	pre	128	true
1.0ms	2×	body	128	invalid

Compiler

Compiled 252 to 223 computations (11.5% saved)

simplify56.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

388×	`associate-+l+_binary64`
318×	`exp-sum_binary64`
296×	`associate-+r+_binary64`
271×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	156
1	160	147
2	604	119
3	3400	115
4	4793	115
5	4804	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

Error

1.8b

Counts

2 → 2

Alt Table

Status	Error	Program
	1.8b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -5537752839100187/4398046511104 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 848079078717083/1099511627776 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -6214088902520669/35184372088832 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 7041008316161153/562949953421312 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -4992549864024149/36028797018963968 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 5893731530977871/590295810358705651712 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 5688119651184367/37778931862957161709568 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
▶	1.8b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Status

Error

Program

1.8b

(*.f64 (/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -5537752839100187/4398046511104 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 848079078717083/1099511627776 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -6214088902520669/35184372088832 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 7041008316161153/562949953421312 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -4992549864024149/36028797018963968 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 5893731530977871/590295810358705651712 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 5688119651184367/37778931862957161709568 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))

▶

1.8b

(*.f64 (/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Compiler

Compiled 473 to 403 computations (14.8% saved)

localize57.0ms (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))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite255.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

19×	`*-un-lft-identity_binary64`
18×	`add-log-exp_binary64`
10×	`add-exp-log_binary64`
9×	`sum-log_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `distribute-lft-out_binary64`
8×	`frac-add_binary64`

Counts

4 → 70

Calls

4 calls:

32.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
28.0ms	(+.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))

Compiler

Compiled 5592 to 4335 computations (22.5% saved)

series169.0ms (0.3%)

Error

1.2b

Counts

4 → 30

Calls

4 calls:

54.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
29.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
28.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.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))

Compiler

Compiled 4381 to 3504 computations (20% saved)

simplify110.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

935×	`distribute-rgt-in_binary64`
340×	`associate-l_binary64`
335×	`associate-r_binary64`
249×	`cancel-sign-sub-inv_binary64`
233×	`*-commutative_binary64`

Counts

100 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	3381
1	811	3152
2	2922	2977
3	5759	2977

prune158.0ms (0.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Error

1.1b

Counts

80 → 5

Alt Table

Status	Error	Program
	1.9b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 26993877973793301/562949953421312 (.f64 z (+.f64 6363719339736815/17592186044416 (.f64 18265191518573817/35184372088832 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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	2.0b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 PI.f64))) (cbrt.f64 (sqrt.f64 (.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 PI.f64)))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.8b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (sqrt.f64 PI.f64) (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (sqrt.f64 2) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))))) (+.f64 (+.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
▶	1.2b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.2b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (*.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Compiler

Compiled 5830 to 4534 computations (22.2% saved)

localize65.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 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))
3.0b	(-.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)))

rewrite1.1s (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

183×	`times-frac_binary64`
162×	`*-un-lft-identity_binary64`
156×	`add-sqr-sqrt_binary64`
111×	`cancel-sign-sub-inv_binary64`
76×	`add-cube-cbrt_binary64`

Counts

4 → 207

Calls

4 calls:

64.0ms	(-.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)))
32.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 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))

Compiler

Compiled 19164 to 15163 computations (20.9% saved)

series224.0ms (0.4%)

Error

1.1b

Counts

4 → 30

Calls

4 calls:

57.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
35.0ms	(-.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)))
35.0ms	(*.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))

Compiler

Compiled 5625 to 4552 computations (19.1% saved)

simplify240.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-*l/_binary64`
192×	`associate-/l/_binary64`
184×	`*-commutative_binary64`
180×	`distribute-rgt-in_binary64`
177×	`distribute-lft-in_binary64`

Counts

237 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	637	8385
1	1955	7660
2	4958	7609
3	4960	7609

prune437.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	202	5	207

Error

0.2b

Counts

207 → 5

Alt Table

Status	Error	Program
	1.3b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.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 (neg.f64 (/.f64 (*.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)) (-.f64 2 z))) (/.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (-.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.9b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 26993877973793301/562949953421312 (.f64 z (+.f64 6363719339736815/17592186044416 (.f64 18265191518573817/35184372088832 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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
▶	0.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.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 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))) (neg.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	0.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 (log.f64 (+.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.2b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (*.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Compiler

Compiled 13142 to 10357 computations (21.2% saved)

localize75.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 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))
3.0b	(+.f64 (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))) (neg.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))))

rewrite610.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

25×	`flip3-+_binary64` `flip-+_binary64`
24×	`frac-times_binary64` `frac-add_binary64`
23×	`*-un-lft-identity_binary64`
17×	`associate-l/_binary64` `associate-r/_binary64`
16×	`pow1_binary64` `distribute-neg-frac_binary64`

Counts

4 → 110

Calls

4 calls:

31.0ms	(+.f64 (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))) (neg.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))))
25.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 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))

Compiler

Compiled 14017 to 11313 computations (19.3% saved)

series217.0ms (0.4%)

Error

0.2b

Counts

4 → 30

Calls

4 calls:

62.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
40.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
34.0ms	(+.f64 (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))) (neg.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6135 to 4994 computations (18.6% saved)

simplify278.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

521×	`associate-l_binary64`
506×	`associate-r_binary64`
329×	`*-commutative_binary64`
304×	`cancel-sign-sub-inv_binary64`
164×	`distribute-rgt-in_binary64`

Counts

140 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	354	7083
1	1004	5975
2	3705	5694
3	4888	5680
4	4991	5680
5	4922	5680

prune321.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	118	5	123

Error

0.2b

Counts

123 → 5

Alt Table

Status	Error	Program
	1.3b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.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 (neg.f64 (/.f64 (*.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)) (-.f64 2 z))) (/.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (-.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.9b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 26993877973793301/562949953421312 (.f64 z (+.f64 6363719339736815/17592186044416 (.f64 18265191518573817/35184372088832 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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
✓	0.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.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 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))) (neg.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
▶	0.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 (log.f64 (+.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.2b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (*.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Compiler

Compiled 9942 to 7942 computations (20.1% saved)

localize69.0ms (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	(sqrt.f64 (*.f64 PI.f64 2))
1.0b	(exp.f64 (*.f64 2 (log.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))))
3.0b	(-.f64 (exp.f64 (*.f64 2 (log.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))

rewrite793.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

189×	`times-frac_binary64`
173×	`add-sqr-sqrt_binary64`
152×	`*-un-lft-identity_binary64`
111×	`cancel-sign-sub-inv_binary64`
74×	`add-cube-cbrt_binary64`

Counts

4 → 182

Calls

4 calls:

96.0ms	(-.f64 (exp.f64 (*.f64 2 (log.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.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)))
13.0ms	(exp.f64 (*.f64 2 (log.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 15904 to 12582 computations (20.9% saved)

series203.0ms (0.3%)

Error

0.2b

Counts

4 → 30

Calls

4 calls:

57.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
34.0ms	(exp.f64 (*.f64 2 (log.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))))
34.0ms	(-.f64 (exp.f64 (*.f64 2 (log.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 5569 to 4510 computations (19% saved)

simplify160.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

448×	`associate-*l/_binary64`
418×	`associate-l_binary64`
415×	`associate-*r/_binary64`
192×	`associate-/l/_binary64`
157×	`*-commutative_binary64`

Counts

212 → 187

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	603	6966
1	1740	6353
2	5015	6353

prune352.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	187	5	192

Error

0.2b

Counts

192 → 5

Alt Table

Status	Error	Program
	2.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (exp.f64 (.f64 2 (log.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))) (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)) (-.f64 2 z))) (/.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (-.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	0.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (exp.f64 (.f64 2 (log.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))) (.f64 (/.f64 -30666706506962181608371823434969/19342813113834066795298816 (-.f64 8 (pow.f64 z 3))) (/.f64 (+.f64 4 (*.f64 z (+.f64 z 2))) (-.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.3b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.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 (neg.f64 (/.f64 (*.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)) (-.f64 2 z))) (/.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (-.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.9b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 26993877973793301/562949953421312 (.f64 z (+.f64 6363719339736815/17592186044416 (.f64 18265191518573817/35184372088832 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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	0.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.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 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))) (neg.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.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))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Compiler

Compiled 10747 to 8454 computations (21.3% saved)

regimes2.0s (3.4%)

Accuracy

Total 0.1b remaining (31.7%)

Threshold costs 0.1b (31.7%)

Compiler

Compiled 41940 to 34586 computations (17.5% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

24×	`+-commutative_binary64`
16×	`sub-neg_binary64`
10×	`*-commutative_binary64`
4×	`neg-mul-1_binary64` `neg-sub0_binary64`
3×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	156
1	99	156
2	123	156
3	134	156
4	139	156
5	140	156
6	137	156

end3.0ms (0%)

Compiler: Compiled 102 to 84 computations (17.6% saved)

sample48.0s (81.1%)

Algorithm

1×

intervals

Results

44.1s	3980×	body	8192	exit
2.3s	8000×	body	128	valid
229.0ms	12073×	pre	128	true
29.0ms	93×	body	128	invalid

Compiler

Compiled 738 to 617 computations (16.4% saved)

Details

analyze1.7s (2.9%)

sample1.5s (2.6%)

simplify56.0ms (0.1%)

prune13.0ms (0%)

localize57.0ms (0.1%)

rewrite255.0ms (0.4%)

series169.0ms (0.3%)

simplify110.0ms (0.2%)

prune158.0ms (0.3%)

localize65.0ms (0.1%)

rewrite1.1s (1.9%)

series224.0ms (0.4%)

simplify240.0ms (0.4%)

prune437.0ms (0.7%)

localize75.0ms (0.1%)

rewrite610.0ms (1%)

series217.0ms (0.4%)

simplify278.0ms (0.5%)

prune321.0ms (0.5%)

localize69.0ms (0.1%)

rewrite793.0ms (1.3%)

series203.0ms (0.3%)

simplify160.0ms (0.3%)

prune352.0ms (0.6%)

regimes2.0s (3.4%)

simplify10.0ms (0%)

end3.0ms (0%)

sample48.0s (81.1%)

Profiling