Details

analyze1.8s (3.4%)

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)

sample1.2s (2.2%)

Algorithm

1×

intervals

Results

1.1s	99×	body	8192	exit
77.0ms	256×	body	128	valid
6.0ms	357×	pre	128	true
1.0ms	2×	body	128	invalid

Compiler

Compiled 252 to 223 computations (11.5% saved)

simplify52.0ms (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

prune14.0ms (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 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -5537752839100187/4398046511104 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 848079078717083/1099511627776 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -6214088902520669/35184372088832 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 7041008316161153/562949953421312 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -4992549864024149/36028797018963968 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 5893731530977871/590295810358705651712 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 5688119651184367/37778931862957161709568 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.8b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))

Status

Error

Program

▶

1.8b

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

1.8b

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

Compiler

Compiled 473 to 403 computations (14.8% saved)

localize71.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.0b	(-.f64 (-.f64 1 z) 1)
7.0b	(-.f64 (-.f64 1 z) 1)
7.0b	(-.f64 (-.f64 1 z) 1)
7.0b	(-.f64 (-.f64 1 z) 1)

rewrite504.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

36×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
24×	`add-log-exp_binary64` `cancel-sign-sub-inv_binary64`
16×	`associate--l+_binary64`
12×	`diff-log_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`

Counts

4 → 100

Calls

4 calls:

9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 11373 to 9694 computations (14.8% saved)

series101.0ms (0.2%)

Error

1.7b

Counts

4 → 12

Calls

4 calls:

22.0ms	(-.f64 (-.f64 1 z) 1)
21.0ms	(-.f64 (-.f64 1 z) 1)
21.0ms	(-.f64 (-.f64 1 z) 1)
20.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 3413 to 3009 computations (11.8% saved)

simplify104.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-in_binary64`
454×	`distribute-lft-in_binary64`
434×	`distribute-neg-in_binary64`
412×	`neg-mul-1_binary64`
305×	`associate-+l+_binary64`

Counts

112 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	1032
1	96	772
2	189	728
3	755	720
4	3363	704
5	4647	704
6	4856	704

prune227.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	100	2	102

Error

1.7b

Counts

102 → 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 6275 to 5272 computations (16% saved)

localize56.0ms (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)))

rewrite440.0ms (0.8%)

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:

97.0ms	(+.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)))
23.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 9154 to 7239 computations (20.9% saved)

series178.0ms (0.3%)

Error

0.3b

Counts

4 → 30

Calls

4 calls:

59.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
33.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
31.0ms	(+.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)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3901 to 3104 computations (20.4% 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`
219×	`*-commutative_binary64`

Counts

116 → 94

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	522	8765
1	1442	8452
2	5256	8452

prune245.0ms (0.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	88	8	96

Error

0.2b

Counts

96 → 8

Alt Table

Status	Error	Program
	1.9b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 PI.f64))) (cbrt.f64 (sqrt.f64 (.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 PI.f64)))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.7b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64))) (.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))) (cbrt.f64 (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 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)))))
	1.7b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 PI.f64))) (exp.f64 z)) (exp.f64 -15/2)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 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)))))
▶	1.0b	(.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)))))
	1.1b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
✓	1.8b	(.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 9493 to 7536 computations (20.6% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.3b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 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))

rewrite193.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
14×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`

Counts

4 → 77

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
4.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
4.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3952 to 2629 computations (33.5% saved)

series121.0ms (0.2%)

Error

0.1b

Counts

4 → 13

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)))
20.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
11.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 2109 to 1657 computations (21.4% saved)

simplify108.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

353×	`associate-l_binary64`
343×	`associate-r_binary64`
315×	`associate-+l+_binary64`
301×	`associate-/l*_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

90 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	2158
1	569	1943
2	2051	1846
3	4888	1846
4	4965	1846

prune135.0ms (0.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	47	11	58

Error

0.1b

Counts

58 → 11

Alt Table

Status	Error	Program
	43.8b	(.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)))))
	1.9b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64))) (.f64 (cbrt.f64 (exp.f64 (+.f64 -15/2 z))) (cbrt.f64 (exp.f64 (+.f64 -15/2 z))))) (cbrt.f64 (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)))))
	1.7b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64))) (.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))) (cbrt.f64 (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)))))
	1.0b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64))) (exp.f64 z)) (exp.f64 -15/2)) (+.f64 (+.f64 (+.f64 (+.f64 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 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)))))
	1.4b	(.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)))))
	1.1b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
✓	1.8b	(.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)))))
▶	0.9b	(.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)))))
✓	1.8b	(.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)))))
	1.0b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (sqrt.f64 PI.f64) (.f64 (exp.f64 (+.f64 -15/2 z)) (.f64 (sqrt.f64 2) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))))) (+.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 3766 to 2838 computations (24.6% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 z (pow.f64 PI.f64 2))
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 (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

25×	`add-exp-log_binary64`
17×	`prod-exp_binary64`
16×	`add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`

Counts

4 → 78

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
6.0ms	(.f64 1/6 (.f64 z (pow.f64 PI.f64 2)))
6.0ms	(*.f64 z (pow.f64 PI.f64 2))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 4231 to 3202 computations (24.3% saved)

series113.0ms (0.2%)

Error

0.1b

Counts

4 → 12

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)))
16.0ms	(.f64 1/6 (.f64 z (pow.f64 PI.f64 2)))
14.0ms	(*.f64 z (pow.f64 PI.f64 2))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 2032 to 1646 computations (19% saved)

simplify129.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

409×	`associate-r_binary64`
403×	`associate-l_binary64`
325×	`associate-+l+_binary64`
215×	`cancel-sign-sub-inv_binary64`
214×	`*-commutative_binary64`

Counts

90 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	2096
1	555	1820
2	2120	1718
3	4598	1717
4	4988	1717
5	4956	1717

prune155.0ms (0.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	60	10	70

Error

0.1b

Counts

70 → 10

Alt Table

Status	Error	Program
	43.8b	(.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)))))
	1.7b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64))) (.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))) (cbrt.f64 (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 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)))))
	0.9b	(.f64 (+.f64 (/.f64 1 z) (.f64 1/6 (.f64 z (pow.f64 PI.f64 2)))) (.f64 (.f64 (.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64))) (exp.f64 z)) (exp.f64 -15/2)) (+.f64 (+.f64 (+.f64 (+.f64 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)))))
	1.4b	(.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)))))
	1.1b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z))) (-.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z))) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
	1.8b	(.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)))))
	1.0b	(.f64 (+.f64 (/.f64 1 z) (.f64 1/6 (.f64 z (pow.f64 PI.f64 2)))) (.f64 (-.f64 (.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 (exp.f64 -15/2) (+.f64 (.f64 (sqrt.f64 15/2) (sqrt.f64 2)) (.f64 127/225 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (.f64 z z)))))) (.f64 (exp.f64 -15/2) (+.f64 (.f64 14/15 (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) z))) (.f64 1/2 (.f64 (.f64 z z) (.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))))))))) (.f64 (sqrt.f64 PI.f64) (.f64 (exp.f64 -15/2) (+.f64 (.f64 (sqrt.f64 15/2) (.f64 (.f64 (sqrt.f64 2) z) (log.f64 15/2))) (.f64 14/15 (.f64 (.f64 (sqrt.f64 15/2) (.f64 (.f64 (sqrt.f64 2) z) (log.f64 15/2))) z)))))) (+.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)))))
	1.0b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (sqrt.f64 PI.f64) (.f64 (exp.f64 (+.f64 -15/2 z)) (.f64 (sqrt.f64 2) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))))) (+.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 3442 to 2692 computations (21.8% saved)

regimes1.6s (3.1%)

Accuracy

Total 0.5b remaining (84.1%)

Threshold costs 0.5b (84.1%)

Compiler

Compiled 33586 to 27424 computations (18.3% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	133
1	98	133
2	111	133
3	113	133
4	114	133
5	113	133

end3.0ms (0%)

Compiler: Compiled 84 to 70 computations (16.7% saved)

sample45.2s (84.8%)

Algorithm

1×

intervals

Results

41.0s	3724×	body	8192	exit
2.4s	8000×	body	128	valid
216.0ms	11803×	pre	128	true
25.0ms	79×	body	128	invalid

Compiler

Compiled 1205 to 999 computations (17.1% saved)

Details

analyze1.8s (3.4%)

sample1.2s (2.2%)

simplify52.0ms (0.1%)

prune14.0ms (0%)

localize71.0ms (0.1%)

rewrite504.0ms (0.9%)

series101.0ms (0.2%)

simplify104.0ms (0.2%)

prune227.0ms (0.4%)

localize56.0ms (0.1%)

rewrite440.0ms (0.8%)

series178.0ms (0.3%)

simplify166.0ms (0.3%)

prune245.0ms (0.5%)

localize37.0ms (0.1%)

rewrite193.0ms (0.4%)

series121.0ms (0.2%)

simplify108.0ms (0.2%)

prune135.0ms (0.3%)

localize42.0ms (0.1%)

rewrite244.0ms (0.5%)

series113.0ms (0.2%)

simplify129.0ms (0.2%)

prune155.0ms (0.3%)

regimes1.6s (3.1%)

simplify8.0ms (0%)

end3.0ms (0%)

sample45.2s (84.8%)

Profiling