Details

analyze2.5s (3.6%)

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 (2.2%)

Algorithm

1×

intervals

Results

1.4s	110×	body	8192	exit
99.0ms	256×	body	128	valid
6.0ms	369×	pre	128	true
1.0ms	3×	body	128	invalid

Compiler

Compiled 252 to 223 computations (11.5% saved)

simplify58.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

388×	`associate-+l+_binary64`
296×	`associate-+r+_binary64`
271×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`
224×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	156
1	160	147
2	606	119
3	3454	115
4	4863	115
5	4787	115

prune12.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

1.8b

Counts

3 → 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 596 to 508 computations (14.8% saved)

localize115.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
✓	2.5b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite195.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64`
53×	`distribute-lft-out_binary64`
44×	`frac-add_binary64`
44×	`add-log-exp_binary64`
31×	`sum-log_binary64`

Counts

4 → 107

Calls

4 calls:

148.0ms	(+.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)))
18.0ms	(+.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))

series53.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

41.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
9.0ms	(+.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)))
3.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify197.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-l_binary64`
422×	`fma-def_binary64`
368×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`
221×	`*-commutative_binary64`

Counts

143 → 230

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	542	9052
1	1578	8750
2	5010	8750

prune474.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	222	8	230
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	223	9	232

Error

0.3b

Counts

232 → 9

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 PI.f64 2))) (cbrt.f64 (sqrt.f64 (.f64 PI.f64 2)))) (cbrt.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)))))
▶	1.2b	(.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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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 (+.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)))))
	1.7b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 PI.f64) (sqrt.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)))))
	1.2b	(.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 (fma.f64 5893731530977871/590295810358705651712 (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312) 316912650056936879084143652025/316912650057057350374175801344)) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) (-.f64 6 z)))) (.f64 (-.f64 7 z) (fma.f64 -4992549864024149/36028797018963968 (.f64 (fma.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312) 316912650056936879084143652025/316912650057057350374175801344) (.f64 (.f64 (-.f64 2 z) (-.f64 3 z)) (.f64 (-.f64 4 z) (-.f64 5 z)))) (.f64 (-.f64 6 z) (fma.f64 7041008316161153/562949953421312 (.f64 (fma.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312) 316912650056936879084143652025/316912650057057350374175801344) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) (-.f64 4 z)))) (.f64 (-.f64 5 z) (fma.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312) 316912650056936879084143652025/316912650057057350374175801344)) (.f64 (-.f64 3 z) -6214088902520669/35184372088832) (.f64 (-.f64 4 z) (fma.f64 (fma.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312) 316912650056936879084143652025/316912650057057350374175801344) (.f64 (-.f64 2 z) 848079078717083/1099511627776) (.f64 (fma.f64 -5537752839100187/4398046511104 (fma.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312) 316912650056936879084143652025/316912650057057350374175801344) (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3)))) (-.f64 3 z))))))))))) (.f64 (-.f64 7 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312) 316912650056936879084143652025/316912650057057350374175801344)) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (*.f64 (-.f64 5 z) (-.f64 6 z)))))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.8b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (cbrt.f64 (.f64 (.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 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))) (.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)))))
	2.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (exp.f64 (+.f64 (+.f64 z -15/2) (log.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 PI.f64)))))) (+.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 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (fma.f64 -5537752839100187/4398046511104 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (.f64 (-.f64 2 z) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z))))) (.f64 (-.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)))))
	1.6b	(.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 777369958913643152449373/2951479051793528258560 (fma.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000 (fma.f64 z 58027045549583850709031327/132816557330708771635200 (.f64 (pow.f64 z 3) 888358207598286547306070409407/1464302544571064207278080000)))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Compiler

Compiled 21224 to 16739 computations (21.1% saved)

localize60.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))))

rewrite61.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`flip-+_binary64`
24×	`frac-sub_binary64`
24×	`flip3-+_binary64`
24×	`frac-times_binary64`
20×	`*-un-lft-identity_binary64`

Counts

2 → 85

Calls

2 calls:

34.0ms

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

21.0ms

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

series10.0ms (0%)

Counts

2 → 24

Calls

2 calls:

6.0ms

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

4.0ms

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

simplify206.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

847×	`fma-def_binary64`
370×	`associate-*l/_binary64`
221×	`fma-neg_binary64`
181×	`associate-l_binary64`
163×	`cancel-sign-sub-inv_binary64`

Counts

109 → 205

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	4943
1	645	4422
2	2275	4158
3	4890	4144
4	4996	4144
5	4881	4144

prune594.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	289	4	293
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	295	7	302

Error

0.2b

Counts

302 → 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 (+.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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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)))))
	1.6b	(.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 777369958913643152449373/2951479051793528258560 (fma.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000 (fma.f64 z 58027045549583850709031327/132816557330708771635200 (.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 (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 (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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)))))
	1.7b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 PI.f64) (sqrt.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)))))
	1.3b	(.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 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4)) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4))) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4))) (*.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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)))))
	2.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (exp.f64 (+.f64 (+.f64 z -15/2) (log.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 PI.f64)))))) (+.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 (fma.f64 (-.f64 2 z) (.f64 (-.f64 2 z) (.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z)))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z)))))) (.f64 (+.f64 17263820999676124423475388113594350996383117645/10889035741470030830827987437816582766592 (/.f64 -182489477154585031194980454210491189375598961469/170141183460469231731687303715884105728 (-.f64 1 z))) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (.f64 (-.f64 2 z) (-.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)))))

Compiler

Compiled 26701 to 21290 computations (20.3% saved)

localize72.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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))
✓	1.1b	(fma.f64 (-.f64 2 z) (.f64 (-.f64 2 z) (.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z)))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z)))))) (*.f64 (+.f64 17263820999676124423475388113594350996383117645/10889035741470030830827987437816582766592 (/.f64 -182489477154585031194980454210491189375598961469/170141183460469231731687303715884105728 (-.f64 1 z))) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))

rewrite53.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

228×	`add-sqr-sqrt_binary64`
220×	`*-un-lft-identity_binary64`
148×	`times-frac_binary64`
144×	`prod-diff_binary64`
134×	`add-cube-cbrt_binary64`

Counts

2 → 250

Calls

2 calls:

26.0ms

(*.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

0.0ms

(fma.f64 (-.f64 2 z) (*.f64 (-.f64 2 z) (*.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (*.f64 (-.f64 1 z) (-.f64 1 z)))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (*.f64 (-.f64 1 z) (-.f64 1 z)))))) (*.f64 (+.f64 17263820999676124423475388113594350996383117645/10889035741470030830827987437816582766592 (/.f64 -182489477154585031194980454210491189375598961469/170141183460469231731687303715884105728 (-.f64 1 z))) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))

series12.0ms (0%)

Counts

2 → 24

Calls

2 calls:

6.0ms

(fma.f64 (-.f64 2 z) (*.f64 (-.f64 2 z) (*.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (*.f64 (-.f64 1 z) (-.f64 1 z)))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (*.f64 (-.f64 1 z) (-.f64 1 z)))))) (*.f64 (+.f64 17263820999676124423475388113594350996383117645/10889035741470030830827987437816582766592 (/.f64 -182489477154585031194980454210491189375598961469/170141183460469231731687303715884105728 (-.f64 1 z))) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))

5.0ms

(*.f64 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

simplify346.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

386×	`associate-l_binary64`
376×	`associate-r_binary64`
327×	`*-commutative_binary64`
239×	`distribute-rgt-neg-out_binary64`
231×	`distribute-rgt-in_binary64`

Counts

274 → 534

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	530	14907
1	1109	11216
2	3558	7532
3	4667	7518
4	4733	7518

prune1.5s (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	709	1	710
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	709	8	717

Error

0.2b

Counts

717 → 8

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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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)))))
	1.6b	(.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 777369958913643152449373/2951479051793528258560 (fma.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000 (fma.f64 z 58027045549583850709031327/132816557330708771635200 (.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 (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 (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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)))))
	1.7b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 PI.f64) (sqrt.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)))))
	2.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 PI.f64 2))) (cbrt.f64 (sqrt.f64 (.f64 PI.f64 2)))) (cbrt.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 (fma.f64 (-.f64 2 z) (.f64 (-.f64 2 z) (.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z)))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z)))))) (.f64 (+.f64 17263820999676124423475388113594350996383117645/10889035741470030830827987437816582766592 (/.f64 -182489477154585031194980454210491189375598961469/170141183460469231731687303715884105728 (-.f64 1 z))) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (.f64 (-.f64 2 z) (-.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)))))
	1.3b	(.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 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4)) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4))) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 4))) (*.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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)))))
	2.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (exp.f64 (+.f64 (+.f64 z -15/2) (log.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 PI.f64)))))) (+.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 (fma.f64 (-.f64 2 z) (.f64 (-.f64 2 z) (.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z)))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z)))))) (.f64 (+.f64 17263820999676124423475388113594350996383117645/10889035741470030830827987437816582766592 (/.f64 -182489477154585031194980454210491189375598961469/170141183460469231731687303715884105728 (-.f64 1 z))) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (.f64 (-.f64 2 z) (-.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)))))

Compiler

Compiled 61855 to 49688 computations (19.7% saved)

localize61.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(+.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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
	1.0b	(.f64 (.f64 (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))
✓	3.1b	(-.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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))))

rewrite315.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

2161×	`*-un-lft-identity_binary64`
816×	`times-frac_binary64`
751×	`distribute-lft-out_binary64`
432×	`distribute-lft-out--_binary64`
55×	`fma-def_binary64`

Counts

2 → 224

Calls

2 calls:

224.0ms

(+.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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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)))

30.0ms

(-.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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))))

series19.0ms (0%)

Counts

2 → 24

Calls

2 calls:

14.0ms

(+.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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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)))

4.0ms

(-.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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))))

simplify556.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

358×	`distribute-rgt-in_binary64`
330×	`distribute-lft-in_binary64`
290×	`fma-def_binary64`
225×	`associate-l_binary64`
162×	`associate-r_binary64`

Counts

248 → 429

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	414	23976
1	1252	23174
2	4843	23162
3	4933	23162

prune867.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	777	4	781
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	781	8	789

Error

0.2b

Counts

789 → 8

Alt Table

Status	Error	Program
	2.1b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (exp.f64 (+.f64 (+.f64 z -15/2) (log.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64)))))) (+.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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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 316912650056936879084143652025/316912650057057350374175801344 (/.f64 3349966604360028729823972713705/4951760157141521099596496896 (-.f64 1 z))) (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) 3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (-.f64 (-.f64 (-.f64 (-.f64 (-.f64 (/.f64 (*.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 z)) (exp.f64 -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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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)))))
	1.6b	(.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 777369958913643152449373/2951479051793528258560 (fma.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000 (fma.f64 z 58027045549583850709031327/132816557330708771635200 (.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 (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 (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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)))))
	1.7b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 PI.f64) (sqrt.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)))))
	0.4b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 PI.f64) (sqrt.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 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 -5537752839100187/4398046511104 (-.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 (fma.f64 (-.f64 2 z) (.f64 (-.f64 2 z) (.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z)))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z)))))) (.f64 (+.f64 17263820999676124423475388113594350996383117645/10889035741470030830827987437816582766592 (/.f64 -182489477154585031194980454210491189375598961469/170141183460469231731687303715884105728 (-.f64 1 z))) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (.f64 (-.f64 2 z) (-.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)))))

Compiler

Compiled 34004 to 27296 computations (19.7% saved)

regimes1.8s (2.5%)

Accuracy

Total 0.2b remaining (36.4%)

Threshold costs 0.2b (36.4%)

Compiler

Compiled 52768 to 43448 computations (17.7% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

23×	`+-commutative_binary64`
15×	`sub-neg_binary64`
10×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	169
1	101	169
2	123	169
3	129	169
4	132	169
5	130	169

end2.0ms (0%)

Compiler: Compiled 110 to 91 computations (17.3% saved)

sample58.8s (83.5%)

Algorithm

1×

intervals

Results

53.6s	3821×	body	8192	exit
3.6s	8000×	body	128	valid
221.0ms	11898×	pre	128	true
38.0ms	77×	body	128	invalid

Compiler

Compiled 1058 to 877 computations (17.1% saved)

Details

analyze2.5s (3.6%)

sample1.5s (2.2%)

simplify58.0ms (0.1%)

prune12.0ms (0%)

localize115.0ms (0.2%)

rewrite195.0ms (0.3%)

series53.0ms (0.1%)

simplify197.0ms (0.3%)

prune474.0ms (0.7%)

localize60.0ms (0.1%)

rewrite61.0ms (0.1%)

series10.0ms (0%)

simplify206.0ms (0.3%)

prune594.0ms (0.8%)

localize72.0ms (0.1%)

rewrite53.0ms (0.1%)

series12.0ms (0%)

simplify346.0ms (0.5%)

prune1.5s (2.1%)

localize61.0ms (0.1%)

rewrite315.0ms (0.4%)

series19.0ms (0%)

simplify556.0ms (0.8%)

prune867.0ms (1.2%)

regimes1.8s (2.5%)

simplify8.0ms (0%)

end2.0ms (0%)

sample58.8s (83.5%)

Profiling