Details

analyze1.8s (3.2%)

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 (2.8%)

Algorithm

1×

intervals

Results

1.4s	125×	body	8192	exit
80.0ms	256×	body	128	valid
8.0ms	384×	pre	128	true
1.0ms	3×	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

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

Error

1.7b

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 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 (.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)))))

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)))))

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)))))

Compiler

Compiled 473 to 403 computations (14.8% saved)

localize55.0ms (0.1%)

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)))

rewrite396.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

45×	`*-un-lft-identity_binary64`
44×	`add-log-exp_binary64` `frac-add_binary64`
31×	`sum-log_binary64` `distribute-lft-out_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `flip-+_binary64`

Counts

4 → 86

Calls

4 calls:

91.0ms	(+.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)))
22.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
15.0ms	(.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 9154 to 7239 computations (20.9% saved)

series140.0ms (0.3%)

Error

0.3b

Counts

4 → 20

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)))
21.0ms	(+.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)))
19.0ms	(+.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 3139 to 2501 computations (20.3% saved)

simplify166.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

638×	`associate-l_binary64`
503×	`associate-r_binary64`
368×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`
214×	`*-commutative_binary64`

Counts

106 → 84

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	503	8587
1	1390	8274
2	5176	8274

prune229.0ms (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	80	6	86

Error

0.2b

Counts

86 → 6

Alt Table

Status	Error	Program
	1.8b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (cbrt.f64 (pow.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64)))) 3)) (+.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)))))
	1.9b	(.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 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 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z)) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) 848079078717083/1099511627776)))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832))))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (.f64 (-.f64 2 z) (-.f64 3 z)) (.f64 (-.f64 4 z) 7041008316161153/562949953421312))))) (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968))))) (.f64 5893731530977871/590295810358705651712 (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) (-.f64 6 z)))))) (.f64 (-.f64 7 z) (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) (-.f64 6 z)))))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
▶	0.5b	(.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 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.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 (exp.f64 (log.f64 (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 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 26993877973793301/562949953421312 (.f64 6363719339736815/17592186044416 z)) (.f64 18265191518573817/35184372088832 (*.f64 z 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 8914 to 7084 computations (20.5% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
0.4b	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
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))

rewrite188.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
10×	`prod-exp_binary64`

Counts

4 → 78

Calls

4 calls:

15.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
6.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
6.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 4016 to 2669 computations (33.5% saved)

series114.0ms (0.2%)

Error

0.1b

Counts

4 → 13

Calls

4 calls:

50.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
16.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
15.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 2109 to 1665 computations (21.1% saved)

simplify137.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

393×	`associate-l_binary64`
362×	`associate-r_binary64`
300×	`associate-/l*_binary64`
217×	`cancel-sign-sub-inv_binary64`
206×	`*-commutative_binary64`

Counts

91 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	2234
1	591	2004
2	2145	1898
3	4603	1898
4	4994	1898
5	4943	1898

prune117.0ms (0.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	49	7	56

Error

0.1b

Counts

56 → 7

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 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 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z)) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) 848079078717083/1099511627776)))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832))))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (.f64 (-.f64 2 z) (-.f64 3 z)) (.f64 (-.f64 4 z) 7041008316161153/562949953421312))))) (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968))))) (.f64 5893731530977871/590295810358705651712 (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) (-.f64 6 z)))))) (.f64 (-.f64 7 z) (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) (-.f64 6 z)))))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
▶	0.3b	(.f64 (+.f64 (/.f64 1 z) (.f64 1/6 (.f64 z (pow.f64 PI.f64 2)))) (.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 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (*.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.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 (exp.f64 (log.f64 (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))))))))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	0.5b	(.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 892/3375 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 z 3)))))) (.f64 (exp.f64 -15/2) (+.f64 (.f64 14/15 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) z))) (.f64 127/225 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (.f64 z z)))))))) (-.f64 (.f64 (sqrt.f64 PI.f64) (.f64 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))) (+.f64 (.f64 7/15 (.f64 (exp.f64 -15/2) (pow.f64 z 3))) (.f64 1/2 (.f64 (exp.f64 -15/2) (.f64 z z)))))) (.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (log.f64 15/2))) (+.f64 (.f64 14/15 (.f64 (exp.f64 -15/2) (.f64 z z))) (.f64 127/225 (.f64 (exp.f64 -15/2) (pow.f64 z 3))))) (.f64 (exp.f64 -15/2) (+.f64 (.f64 1/6 (.f64 (pow.f64 z 3) (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 3))))) (.f64 (sqrt.f64 15/2) (.f64 (.f64 (sqrt.f64 2) z) (log.f64 15/2))))))))) (+.f64 (+.f64 (+.f64 (+.f64 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (*.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.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 26993877973793301/562949953421312 (.f64 6363719339736815/17592186044416 z)) (.f64 18265191518573817/35184372088832 (*.f64 z 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)))))
	43.2b	(.f64 (cbrt.f64 (pow.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) 3)) (.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 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	0.9b	(.f64 (.f64 (sqrt.f64 PI.f64) (/.f64 (sqrt.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 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (*.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Compiler

Compiled 3404 to 2572 computations (24.4% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
0.4b	(.f64 1/6 (.f64 z (pow.f64 PI.f64 2)))
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))

rewrite244.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

25×	`add-exp-log_binary64`
19×	`add-cbrt-cube_binary64`
17×	`prod-exp_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`

Counts

4 → 70

Calls

4 calls:

15.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
6.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
5.0ms	(.f64 1/6 (.f64 z (pow.f64 PI.f64 2)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3745 to 2849 computations (23.9% saved)

series112.0ms (0.2%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

51.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
15.0ms	(.f64 1/6 (.f64 z (pow.f64 PI.f64 2)))
13.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 2085 to 1694 computations (18.8% saved)

simplify106.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-l_binary64`
425×	`associate-r_binary64`
325×	`associate-+l+_binary64`
227×	`*-commutative_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

82 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	1945
1	580	1722
2	2219	1616
3	4681	1616
4	4945	1616

prune144.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	50	7	57

Error

0.1b

Counts

57 → 7

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 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 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z)) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) 848079078717083/1099511627776)))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832))))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (.f64 (-.f64 2 z) (-.f64 3 z)) (.f64 (-.f64 4 z) 7041008316161153/562949953421312))))) (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968))))) (.f64 5893731530977871/590295810358705651712 (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) (-.f64 6 z)))))) (.f64 (-.f64 7 z) (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) (-.f64 6 z)))))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
✓	0.3b	(.f64 (+.f64 (/.f64 1 z) (.f64 1/6 (.f64 z (pow.f64 PI.f64 2)))) (.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 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (*.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.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 (exp.f64 (log.f64 (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))))))))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
▶	0.5b	(.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 892/3375 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 z 3)))))) (.f64 (exp.f64 -15/2) (+.f64 (.f64 14/15 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) z))) (.f64 127/225 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (.f64 z z)))))))) (-.f64 (.f64 (sqrt.f64 PI.f64) (.f64 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))) (+.f64 (.f64 7/15 (.f64 (exp.f64 -15/2) (pow.f64 z 3))) (.f64 1/2 (.f64 (exp.f64 -15/2) (.f64 z z)))))) (.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (log.f64 15/2))) (+.f64 (.f64 14/15 (.f64 (exp.f64 -15/2) (.f64 z z))) (.f64 127/225 (.f64 (exp.f64 -15/2) (pow.f64 z 3))))) (.f64 (exp.f64 -15/2) (+.f64 (.f64 1/6 (.f64 (pow.f64 z 3) (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 3))))) (.f64 (sqrt.f64 15/2) (.f64 (.f64 (sqrt.f64 2) z) (log.f64 15/2))))))))) (+.f64 (+.f64 (+.f64 (+.f64 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (*.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.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 26993877973793301/562949953421312 (.f64 6363719339736815/17592186044416 z)) (.f64 18265191518573817/35184372088832 (*.f64 z 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)))))
	43.2b	(.f64 (cbrt.f64 (pow.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) 3)) (.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 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	0.9b	(.f64 (.f64 (sqrt.f64 PI.f64) (/.f64 (sqrt.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 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (*.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Compiler

Compiled 3450 to 2737 computations (20.7% saved)

localize333.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.0b	(pow.f64 (log.f64 15/2) 2)
1.0b	(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))
1.0b	(.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2)))
1.0b	(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 3))

rewrite741.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

43×	`add-sqr-sqrt_binary64`
25×	`add-exp-log_binary64`
24×	`associate-r_binary64`
18×	`associate-l_binary64`
17×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `sqrt-prod_binary64`

Counts

4 → 116

Calls

4 calls:

10.0ms	(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 3))
9.0ms	(.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2)))
8.0ms	(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))
2.0ms	(pow.f64 (log.f64 15/2) 2)

Compiler

Compiled 15949 to 13018 computations (18.4% saved)

series1.0ms (0%)

Error

0.1b

Counts

4 → 0

Calls

4 calls:

0.0ms	(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 3))
0.0ms	(.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2)))
0.0ms	(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))
0.0ms	(pow.f64 (log.f64 15/2) 2)

Compiler

Compiled 0 to 0 computations (0% saved)

simplify132.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

485×	`associate-/l/_binary64`
383×	`*-commutative_binary64`
366×	`sqr-pow_binary64`
316×	`log-prod_binary64`
264×	`distribute-rgt-in_binary64`

Counts

116 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1796
1	258	1560
2	828	1520
3	1535	1520
4	2813	1520
5	4874	1520
6	4871	1520

prune299.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	87	7	94

Error

0.1b

Counts

94 → 7

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 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 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z)) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) 848079078717083/1099511627776)))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832))))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (.f64 (-.f64 2 z) (-.f64 3 z)) (.f64 (-.f64 4 z) 7041008316161153/562949953421312))))) (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968))))) (.f64 5893731530977871/590295810358705651712 (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) (-.f64 6 z)))))) (.f64 (-.f64 7 z) (.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) (-.f64 6 z)))))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	0.3b	(.f64 (+.f64 (/.f64 1 z) (.f64 1/6 (.f64 z (pow.f64 PI.f64 2)))) (.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 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (*.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.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 (exp.f64 (log.f64 (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))))))))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	0.5b	(.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 892/3375 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 z 3)))))) (.f64 (exp.f64 -15/2) (+.f64 (.f64 14/15 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) z))) (.f64 127/225 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (.f64 z z)))))))) (-.f64 (.f64 (sqrt.f64 PI.f64) (.f64 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))) (+.f64 (.f64 7/15 (.f64 (exp.f64 -15/2) (pow.f64 z 3))) (.f64 1/2 (.f64 (exp.f64 -15/2) (.f64 z z)))))) (.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (log.f64 15/2))) (+.f64 (.f64 14/15 (.f64 (exp.f64 -15/2) (.f64 z z))) (.f64 127/225 (.f64 (exp.f64 -15/2) (pow.f64 z 3))))) (.f64 (exp.f64 -15/2) (+.f64 (.f64 1/6 (.f64 (pow.f64 z 3) (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 3))))) (.f64 (sqrt.f64 15/2) (.f64 (.f64 (sqrt.f64 2) z) (log.f64 15/2))))))))) (+.f64 (+.f64 (+.f64 (+.f64 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (*.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.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 26993877973793301/562949953421312 (.f64 6363719339736815/17592186044416 z)) (.f64 18265191518573817/35184372088832 (*.f64 z 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)))))
	43.2b	(.f64 (cbrt.f64 (pow.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) 3)) (.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 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	0.9b	(.f64 (.f64 (sqrt.f64 PI.f64) (/.f64 (sqrt.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 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)) (*.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Compiler

Compiled 8188 to 6668 computations (18.6% saved)

regimes978.0ms (1.8%)

Accuracy

Total 0.7b remaining (87.2%)

Threshold costs 0.7b (87.2%)

Compiler

Compiled 20136 to 16108 computations (20% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
9×	`+-commutative_binary64`
4×	`sub-neg_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	84
1	66	84
2	72	84
3	74	84
4	75	84
5	74	84

end2.0ms (0%)

Compiler: Compiled 55 to 44 computations (20% saved)

sample47.5s (85.4%)

Algorithm

1×

intervals

Results

43.3s	3881×	body	8192	exit
2.5s	8000×	body	128	valid
244.0ms	11967×	pre	128	true
28.0ms	86×	body	128	invalid

Compiler

Compiled 938 to 772 computations (17.7% saved)

Details

analyze1.8s (3.2%)

sample1.5s (2.8%)

simplify55.0ms (0.1%)

prune16.0ms (0%)

localize55.0ms (0.1%)

rewrite396.0ms (0.7%)

series140.0ms (0.3%)

simplify166.0ms (0.3%)

prune229.0ms (0.4%)

localize35.0ms (0.1%)

rewrite188.0ms (0.3%)

series114.0ms (0.2%)

simplify137.0ms (0.2%)

prune117.0ms (0.2%)

localize41.0ms (0.1%)

rewrite244.0ms (0.4%)

series112.0ms (0.2%)

simplify106.0ms (0.2%)

prune144.0ms (0.3%)

localize333.0ms (0.6%)

rewrite741.0ms (1.3%)

series1.0ms (0%)

simplify132.0ms (0.2%)

prune299.0ms (0.5%)

regimes978.0ms (1.8%)

simplify6.0ms (0%)

end2.0ms (0%)

sample47.5s (85.4%)

Profiling