Details

analyze1.8s (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 127 to 112 computations (11.8% saved)

sample1.5s (1.7%)

Algorithm

1×

intervals

Results

1.4s	122×	body	8192	exit
83.0ms	256×	body	128	valid
7.0ms	380×	pre	128	true
1.0ms	2×	body	128	invalid

Compiler

Compiled 252 to 223 computations (11.5% saved)

simplify55.0ms (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

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

1.8b

Counts

2 → 1

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 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 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 225 to 183 computations (18.7% saved)

localize59.0ms (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 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 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)))

rewrite245.0ms (0.3%)

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:

39.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
22.0ms	(+.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)

series164.0ms (0.2%)

Error

1.2b

Counts

4 → 30

Calls

4 calls:

53.0ms	(.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 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 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))

Compiler

Compiled 4381 to 3504 computations (20% saved)

simplify111.0ms (0.1%)

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	5760	2977

prune168.0ms (0.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	7	79

Error

1.1b

Counts

79 → 7

Alt Table

Status	Error	Program
	1.9b	(.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)))))
▶	1.2b	(.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)))))
	2.5b	(.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 (exp.f64 (log.f64 (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.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)))))
	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 (sqrt.f64 (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))) (sqrt.f64 (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.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)))))
	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 (cbrt.f64 (pow.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 3)) (/.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)))))
	2.5b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (-.f64 (.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 (exp.f64 -15/2) (+.f64 (.f64 (sqrt.f64 15/2) (sqrt.f64 2)) (.f64 127/225 (.f64 (.f64 z z) (.f64 (sqrt.f64 15/2) (sqrt.f64 2)))))) (.f64 (exp.f64 -15/2) (+.f64 (.f64 14/15 (.f64 z (.f64 (sqrt.f64 15/2) (sqrt.f64 2)))) (.f64 1/2 (.f64 (.f64 z z) (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))))))))) (.f64 (sqrt.f64 PI.f64) (.f64 (exp.f64 -15/2) (+.f64 (.f64 (sqrt.f64 15/2) (.f64 (.f64 z (sqrt.f64 2)) (log.f64 15/2))) (.f64 14/15 (.f64 (.f64 z z) (.f64 (sqrt.f64 15/2) (*.f64 (sqrt.f64 2) (log.f64 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)))))
	2.1b	(.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 (cbrt.f64 (pow.f64 (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) 3)) (/.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 6264 to 4898 computations (21.8% saved)

localize64.0ms (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 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)))

rewrite961.0ms (1.1%)

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:

65.0ms	(-.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))))
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 19164 to 15163 computations (20.9% saved)

series208.0ms (0.2%)

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)))
34.0ms	(-.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)))
34.0ms	(*.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)

simplify235.0ms (0.3%)

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	4961	7609

prune550.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	203	6	209

Error

0.2b

Counts

209 → 6

Alt Table

Status	Error	Program
▶	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)))))
	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 316912650056936879084143652025/316912650057057350374175801344 (/.f64 3349966604360028729823972713705/4951760157141521099596496896 (-.f64 1 z))) (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) 3349966604360028729823972713705/4951760157141521099596496896) (-.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 (-.f64 2 z) (.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z))))) (.f64 (.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 -30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)))) (.f64 (-.f64 2 z) (.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 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)))))
	1.8b	(.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 (cbrt.f64 (pow.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 3)) (/.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 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64))) (exp.f64 z)) (exp.f64 -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 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)))))

Compiler

Compiled 13448 to 10611 computations (21.1% saved)

localize70.0ms (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 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 (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))))))

rewrite828.0ms (0.9%)

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:

29.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
28.0ms	(+.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))))))
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)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 14017 to 11313 computations (19.3% saved)

series213.0ms (0.2%)

Error

0.2b

Counts

4 → 30

Calls

4 calls:

61.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
39.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
35.0ms	(+.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)

simplify282.0ms (0.3%)

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	4923	5680

prune303.0ms (0.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	119	5	124

Error

0.2b

Counts

124 → 5

Alt Table

Status	Error	Program
	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 316912650056936879084143652025/316912650057057350374175801344 (/.f64 3349966604360028729823972713705/4951760157141521099596496896 (-.f64 1 z))) (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) 3349966604360028729823972713705/4951760157141521099596496896) (-.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 (pow.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) 6) (pow.f64 (/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))) 3)) (+.f64 (pow.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) 4) (+.f64 (pow.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))) 4) (*.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4) (/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.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)))))
▶	0.8b	(.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 (exp.f64 (log.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4) (/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.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)))))
	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 (cbrt.f64 (pow.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 3)) (/.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 (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)))))

Compiler

Compiled 10154 to 8122 computations (20% saved)

localize75.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
1.6b	(exp.f64 (log.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4) (/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))))
3.1b	(-.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4) (/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))

rewrite21.2s (23.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

7856×	`times-frac_binary64`
5218×	`add-sqr-sqrt_binary64`
4892×	`*-un-lft-identity_binary64`
3625×	`sqrt-prod_binary64`
2660×	`add-cube-cbrt_binary64`

Counts

4 → 3120

Calls

4 calls:

877.0ms	(-.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4) (/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))
796.0ms	(exp.f64 (log.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4) (/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))))
83.0ms	(/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 201134 to 160238 computations (20.3% saved)

series161.0ms (0.2%)

Error

0.2b

Counts

4 → 28

Calls

4 calls:

41.0ms	(exp.f64 (log.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4) (/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))))
35.0ms	(/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z)))
29.0ms	(-.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4) (/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.f64 2 z))) (sqrt.f64 (-.f64 2 z))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 4643 to 3783 computations (18.5% saved)

simplify2.6s (2.9%)

Algorithm

1×	egg-herbie

Rules

971×	`associate-/l/_binary64`
454×	`neg-mul-1_binary64` `neg-sub0_binary64`
452×	`distribute-lft-neg-out_binary64`
451×	`distribute-neg-frac_binary64`
103×	`/-rgt-identity_binary64`

Counts

3148 → 2749

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2378	161992
1	5484	161992

prune8.8s (9.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	2748	1	2749
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	2749	5	2754

Error

0.2b

Counts

2754 → 5

Alt Table

Status	Error	Program
	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 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4)) (/.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (sqrt.f64 (-.f64 2 z)))) (sqrt.f64 (sqrt.f64 (-.f64 2 z))))) (-.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4)) (/.f64 (/.f64 (sqrt.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z))) (sqrt.f64 (sqrt.f64 (-.f64 2 z)))) (sqrt.f64 (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)))))
	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 316912650056936879084143652025/316912650057057350374175801344 (/.f64 3349966604360028729823972713705/4951760157141521099596496896 (-.f64 1 z))) (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) 3349966604360028729823972713705/4951760157141521099596496896) (-.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)))))
	0.8b	(.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 (exp.f64 (log.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4) (/.f64 (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (sqrt.f64 (-.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)))))
	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 (cbrt.f64 (pow.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 3)) (/.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 (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)))))

Compiler

Compiled 112548 to 89234 computations (20.7% saved)

regimes2.4s (2.7%)

Accuracy

Total 0.2b remaining (35.1%)

Threshold costs 0.2b (35.1%)

Compiler

Compiled 46518 to 38376 computations (17.5% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Rules

27×	`+-commutative_binary64`
18×	`sub-neg_binary64`
15×	`*-commutative_binary64`
7×	`neg-mul-1_binary64` `neg-sub0_binary64`
5×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	179
1	110	177
2	140	177
3	154	177
4	165	177
5	168	177
6	169	177
7	165	177

end3.0ms (0%)

Compiler: Compiled 115 to 95 computations (17.4% saved)

sample46.4s (51.9%)

Algorithm

1×

intervals

Results

42.5s	3866×	body	8192	exit
2.4s	8000×	body	128	valid
211.0ms	11957×	pre	128	true
30.0ms	91×	body	128	invalid

Compiler

Compiled 776 to 650 computations (16.2% saved)

Details

analyze1.8s (2%)

sample1.5s (1.7%)

simplify55.0ms (0.1%)

prune8.0ms (0%)

localize59.0ms (0.1%)

rewrite245.0ms (0.3%)

series164.0ms (0.2%)

simplify111.0ms (0.1%)

prune168.0ms (0.2%)

localize64.0ms (0.1%)

rewrite961.0ms (1.1%)

series208.0ms (0.2%)

simplify235.0ms (0.3%)

prune550.0ms (0.6%)

localize70.0ms (0.1%)

rewrite828.0ms (0.9%)

series213.0ms (0.2%)

simplify282.0ms (0.3%)

prune303.0ms (0.3%)

localize75.0ms (0.1%)

rewrite21.2s (23.6%)

series161.0ms (0.2%)

simplify2.6s (2.9%)

prune8.8s (9.8%)

regimes2.4s (2.7%)

simplify11.0ms (0%)

end3.0ms (0%)

sample46.4s (51.9%)

Profiling