Details

analyze2.9s (4.5%)

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)

sample2.0s (3.2%)

Algorithm

1×

intervals

Results

1.9s	133×	body	8192	exit
104.0ms	256×	body	128	valid
7.0ms	393×	pre	128	true
2.0ms	4×	body	128	invalid

Compiler

Compiled 252 to 223 computations (11.5% saved)

simplify51.0ms (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

prune11.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

1.8b

Counts

2 → 2

Alt Table

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

Status

Error

Program

▶

1.8b

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

1.8b

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

Compiler

Compiled 473 to 403 computations (14.8% saved)

localize62.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)

rewrite471.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

36×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
24×	`cancel-sign-sub-inv_binary64`
24×	`add-log-exp_binary64`
16×	`associate--l+_binary64`

Counts

4 → 100

Calls

4 calls:

8.0ms	(-.f64 (-.f64 1 z) 1)
7.0ms	(-.f64 (-.f64 1 z) 1)
6.0ms	(-.f64 (-.f64 1 z) 1)
6.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 11373 to 9694 computations (14.8% saved)

series75.0ms (0.1%)

Error

1.8b

Counts

4 → 12

Calls

4 calls:

15.0ms	(-.f64 (-.f64 1 z) 1)
15.0ms	(-.f64 (-.f64 1 z) 1)
15.0ms	(-.f64 (-.f64 1 z) 1)
15.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 3413 to 3009 computations (11.8% saved)

simplify102.0ms (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

prune209.0ms (0.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	5	102

Error

1.7b

Counts

102 → 5

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

Compiler

Compiled 7171 to 6066 computations (15.4% saved)

localize70.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(+.f64 -1 (sqrt.f64 (-.f64 1 z)))

rewrite492.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

30×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`add-log-exp_binary64`
18×	`cancel-sign-sub-inv_binary64`
12×	`associate--l+_binary64`

Counts

4 → 87

Calls

4 calls:

8.0ms	(-.f64 (-.f64 1 z) 1)
7.0ms	(-.f64 (-.f64 1 z) 1)
6.0ms	(-.f64 (-.f64 1 z) 1)
5.0ms	(+.f64 -1 (sqrt.f64 (-.f64 1 z)))

Compiler

Compiled 10590 to 9049 computations (14.6% saved)

series117.0ms (0.2%)

Error

1.7b

Counts

4 → 15

Calls

4 calls:

30.0ms	(+.f64 -1 (sqrt.f64 (-.f64 1 z)))
18.0ms	(-.f64 (-.f64 1 z) 1)
17.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 4370 to 3835 computations (12.2% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

452×	`neg-mul-1_binary64`
262×	`distribute-rgt-neg-out_binary64`
245×	`distribute-rgt-out_binary64`
238×	`distribute-lft-neg-out_binary64`
210×	`unsub-neg_binary64`

Counts

102 → 82

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	1035
1	216	807
2	505	756
3	1857	750
4	4285	738
5	5061	738

prune248.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Error

1.7b

Counts

87 → 4

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 (log.f64 (exp.f64 (neg.f64 z))) 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 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (*.f64 (+.f64 1 (sqrt.f64 (-.f64 1 z))) (+.f64 -1 (sqrt.f64 (-.f64 1 z)))) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (log.f64 (exp.f64 (neg.f64 z))) 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)))))
	1.8b	(.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 (sqrt.f64 (-.f64 1 z))) (+.f64 -1 (sqrt.f64 (-.f64 1 z)))) 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 (sqrt.f64 (-.f64 1 z))) (+.f64 -1 (sqrt.f64 (-.f64 1 z)))) 1))) (/.f64 -5537752839100187/4398046511104 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 848079078717083/1099511627776 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -6214088902520669/35184372088832 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 7041008316161153/562949953421312 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -4992549864024149/36028797018963968 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 5893731530977871/590295810358705651712 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 5688119651184367/37778931862957161709568 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))

Compiler

Compiled 6679 to 5666 computations (15.2% saved)

localize77.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(+.f64 -1 (sqrt.f64 (-.f64 1 z)))

rewrite479.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

30×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`add-log-exp_binary64`
18×	`cancel-sign-sub-inv_binary64`
12×	`associate--l+_binary64`

Counts

4 → 87

Calls

4 calls:

9.0ms	(-.f64 (-.f64 1 z) 1)
7.0ms	(-.f64 (-.f64 1 z) 1)
6.0ms	(-.f64 (-.f64 1 z) 1)
5.0ms	(+.f64 -1 (sqrt.f64 (-.f64 1 z)))

Compiler

Compiled 10513 to 8743 computations (16.8% saved)

series109.0ms (0.2%)

Error

1.7b

Counts

4 → 15

Calls

4 calls:

25.0ms	(+.f64 -1 (sqrt.f64 (-.f64 1 z)))
19.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 4337 to 3784 computations (12.8% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

452×	`neg-mul-1_binary64`
262×	`distribute-rgt-neg-out_binary64`
245×	`distribute-rgt-out_binary64`
238×	`distribute-lft-neg-out_binary64`
210×	`unsub-neg_binary64`

Counts

102 → 82

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	1035
1	216	807
2	505	756
3	1857	750
4	4285	738
5	5061	738

prune220.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	83	3	86

Error

1.7b

Counts

86 → 3

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

Compiler

Compiled 6478 to 5362 computations (17.2% saved)

localize73.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(+.f64 -1 (sqrt.f64 (-.f64 1 z)))

rewrite453.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

30×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`add-log-exp_binary64`
18×	`cancel-sign-sub-inv_binary64`
12×	`associate--l+_binary64`

Counts

4 → 87

Calls

4 calls:

8.0ms	(-.f64 (-.f64 1 z) 1)
7.0ms	(-.f64 (-.f64 1 z) 1)
6.0ms	(-.f64 (-.f64 1 z) 1)
5.0ms	(+.f64 -1 (sqrt.f64 (-.f64 1 z)))

Compiler

Compiled 10282 to 8435 computations (18% saved)

series126.0ms (0.2%)

Error

1.7b

Counts

4 → 15

Calls

4 calls:

46.0ms	(-.f64 (-.f64 1 z) 1)
20.0ms	(+.f64 -1 (sqrt.f64 (-.f64 1 z)))
16.0ms	(-.f64 (-.f64 1 z) 1)
14.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 4238 to 3652 computations (13.8% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

452×	`neg-mul-1_binary64`
262×	`distribute-rgt-neg-out_binary64`
245×	`distribute-rgt-out_binary64`
238×	`distribute-lft-neg-out_binary64`
210×	`unsub-neg_binary64`

Counts

102 → 82

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	1035
1	216	807
2	505	756
3	1857	750
4	4285	738
5	5061	738

prune199.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	82	3	85

Error

1.7b

Counts

85 → 3

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

Compiler

Compiled 5959 to 4846 computations (18.7% saved)

regimes902.0ms (1.4%)

Accuracy

Total 0.0b remaining (1.8%)

Threshold costs 0.0b (1.8%)

Compiler

Compiled 26934 to 23762 computations (11.8% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

28×	`+-commutative_binary64`
11×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`distribute-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	198
1	113	196
2	128	194
3	136	194
4	139	194
5	140	194
6	136	194

end2.0ms (0%)

Compiler: Compiled 125 to 107 computations (14.4% saved)

sample54.4s (84.8%)

Algorithm

1×

intervals

Results

49.7s	3859×	body	8192	exit
3.4s	8000×	body	128	valid
208.0ms	11965×	pre	128	true
44.0ms	106×	body	128	invalid

Compiler

Compiled 643 to 564 computations (12.3% saved)

Details

analyze2.9s (4.5%)

sample2.0s (3.2%)

simplify51.0ms (0.1%)

prune11.0ms (0%)

localize62.0ms (0.1%)

rewrite471.0ms (0.7%)

series75.0ms (0.1%)

simplify102.0ms (0.2%)

prune209.0ms (0.3%)

localize70.0ms (0.1%)

rewrite492.0ms (0.8%)

series117.0ms (0.2%)

simplify86.0ms (0.1%)

prune248.0ms (0.4%)

localize77.0ms (0.1%)

rewrite479.0ms (0.7%)

series109.0ms (0.2%)

simplify86.0ms (0.1%)

prune220.0ms (0.3%)

localize73.0ms (0.1%)

rewrite453.0ms (0.7%)

series126.0ms (0.2%)

simplify86.0ms (0.1%)

prune199.0ms (0.3%)

regimes902.0ms (1.4%)

simplify9.0ms (0%)

end2.0ms (0%)

sample54.4s (84.8%)

Profiling