Details

analyze1.4s (8.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample271.0ms (1.7%)

Algorithm

1×

intervals

Results

77.0ms	120×	body	1024	valid
69.0ms	113×	body	1024	nan
33.0ms	67×	body	512	nan
28.0ms	60×	body	512	valid
18.0ms	16×	body	2048	valid
11.0ms	37×	body	256	valid
10.0ms	36×	body	256	nan
8.0ms	23×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

520×	`sub-neg_binary64`
373×	`div-sub_binary64`
267×	`log-prod_binary64`
240×	`associate-/r*_binary64`
225×	`sqr-pow_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	117	59
3	292	55
4	689	55
5	1392	55
6	3381	55
7	4578	55
8	4212	55
9	4795	55

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

61.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))

Status

Error

Program

▶

61.2b

(*.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))

Compiler

Compiled 99 to 72 computations (27.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.5b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
6.3b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite585.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

61.1b

Rules

66×	`add-sqr-sqrt_binary64`
57×	`*-un-lft-identity_binary64`
38×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`

Counts

4 → 127

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
5.0ms	(*.f64 (/.f64 PI.f64 4) f)
5.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
3.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 5197 to 3460 computations (33.4% saved)

series50.0ms (0.3%)

Error

1.0b

Counts

4 → 12

Calls

4 calls:

20.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
10.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(*.f64 PI.f64 f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1067 to 805 computations (24.6% saved)

simplify339.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

444×	`times-frac_binary64`
381×	`unswap-sqr_binary64`
331×	`*-commutative_binary64`
255×	`associate-/l*_binary64`
238×	`associate-*l/_binary64`

Counts

139 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	5537
1	492	5180
2	1284	5169
3	2815	5156
4	4879	5156

prune135.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	5	125

Error

1.0b

Counts

125 → 5

Alt Table

Status	Error	Program
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (.f64 (neg.f64 (pow.f64 (.f64 (cbrt.f64 (exp.f64 -1/4)) (cbrt.f64 (exp.f64 -1/4))) (.f64 f PI.f64))) (pow.f64 (cbrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	61.2b	(.f64 (log.f64 (/.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f PI.f64))) (+.f64 (pow.f64 (exp.f64 (.f64 f PI.f64)) -1/2) (exp.f64 (+.f64 (.f64 f (.f64 1/4 PI.f64)) (.f64 f (.f64 PI.f64 -1/4))))))))) (/.f64 -4 PI.f64))
	1.4b	(*.f64 (log.f64 (/.f64 (/.f64 4 f) PI.f64)) (/.f64 -4 PI.f64))
▶	1.4b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))

Compiler

Compiled 4421 to 2967 computations (32.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))
0.4b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
0.5b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))

rewrite186.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

34×	`add-sqr-sqrt_binary64`
33×	`add-exp-log_binary64`
30×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 113

Calls

4 calls:

9.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))
8.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
7.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))
5.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 3782 to 2552 computations (32.5% saved)

series149.0ms (0.9%)

Error

0.8b

Counts

4 → 12

Calls

4 calls:

99.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
22.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))
12.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))
6.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 809 to 620 computations (23.4% saved)

simplify135.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

641×	`associate-/l*_binary64`
402×	`distribute-rgt-in_binary64`
382×	`distribute-lft-in_binary64`
245×	`associate-/l/_binary64`
202×	`associate-l_binary64`

Counts

125 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4630
1	581	3955
2	2028	3934
3	5294	3934

prune183.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	95	9	104
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	96	13	109

Error

0.6b

Counts

109 → 13

Alt Table

Status	Error	Program
	1.6b	(.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))) 3)) (/.f64 -4 PI.f64))
	1.4b	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (log.f64 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (.f64 (neg.f64 (pow.f64 (.f64 (cbrt.f64 (exp.f64 -1/4)) (cbrt.f64 (exp.f64 -1/4))) (.f64 f PI.f64))) (pow.f64 (cbrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	2.2b	(.f64 (.f64 (cbrt.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))) (cbrt.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64)))) (cbrt.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))))
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f PI.f64))) (+.f64 (pow.f64 (exp.f64 (.f64 f PI.f64)) -1/2) (exp.f64 (+.f64 (.f64 f (.f64 1/4 PI.f64)) (.f64 f (.f64 PI.f64 -1/4))))))))) (/.f64 -4 PI.f64))
▶	1.3b	(.f64 -4 (/.f64 (-.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) PI.f64))) (log.f64 f)) PI.f64))
	1.4b	(*.f64 (log.f64 (/.f64 (/.f64 4 f) PI.f64)) (/.f64 -4 PI.f64))
	1.4b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (log.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	2.6b	(.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))) (*.f64 (cbrt.f64 (/.f64 -4 PI.f64)) (cbrt.f64 (/.f64 -4 PI.f64)))) (cbrt.f64 (/.f64 -4 PI.f64)))
	1.6b	(cbrt.f64 (/.f64 -64 (pow.f64 (/.f64 PI.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))) 3)))
	1.6b	(.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))) (/.f64 -4 PI.f64)))
	61.2b	(.f64 (log.f64 (/.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	11.8b	(log.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))) (/.f64 -4 PI.f64)))

Compiler

Compiled 3787 to 2629 computations (30.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(*.f64 PI.f64 f)
0.3b	(/.f64 (-.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) (log.f64 f)) PI.f64)
2.5b	(log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64)))

rewrite141.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

47×	`pow1_binary64`
43×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
30×	`log-pow_binary64`

Counts

4 → 108

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) (log.f64 f)) PI.f64)
6.0ms	(log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64)))
4.0ms	(*.f64 PI.f64 f)
3.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 2937 to 1723 computations (41.3% saved)

series65.0ms (0.4%)

Error

0.6b

Counts

4 → 12

Calls

4 calls:

28.0ms	(/.f64 (-.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) (log.f64 f)) PI.f64)
19.0ms	(log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64)))
7.0ms	(*.f64 PI.f64 f)
6.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 778 to 598 computations (23.1% saved)

simplify159.0ms (1%)

Algorithm

1×	egg-herbie

Rules

595×	`sub-neg_binary64`
365×	`div-sub_binary64`
311×	`associate-/l*_binary64`
299×	`times-frac_binary64`
273×	`associate-*l/_binary64`

Counts

120 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	4320
1	303	4035
2	814	4005
3	1869	4005
4	4168	4005
5	5269	4005

prune61.0ms (0.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	41	15	56

Error

0.6b

Counts

56 → 15

Alt Table

Status	Error	Program
	1.6b	(.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))) 3)) (/.f64 -4 PI.f64))
	1.4b	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (log.f64 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	2.6b	(.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))) (*.f64 (cbrt.f64 (/.f64 -4 PI.f64)) (cbrt.f64 (/.f64 -4 PI.f64)))) (cbrt.f64 (/.f64 -4 PI.f64)))
	1.6b	(.f64 -4 (cbrt.f64 (pow.f64 (/.f64 (-.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) PI.f64))) (log.f64 f)) PI.f64) 3)))
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (.f64 (neg.f64 (pow.f64 (.f64 (cbrt.f64 (exp.f64 -1/4)) (cbrt.f64 (exp.f64 -1/4))) (.f64 f PI.f64))) (pow.f64 (cbrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	2.2b	(.f64 (.f64 (cbrt.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))) (cbrt.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64)))) (cbrt.f64 (.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))))
	1.5b	(.f64 -4 (/.f64 (-.f64 (pow.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) 3) (pow.f64 (log.f64 f) 3)) (.f64 PI.f64 (+.f64 (.f64 (log.f64 f) (log.f64 f)) (.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) (+.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) (log.f64 f)))))))
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f PI.f64))) (+.f64 (pow.f64 (exp.f64 (.f64 f PI.f64)) -1/2) (exp.f64 (+.f64 (.f64 f (.f64 1/4 PI.f64)) (.f64 f (.f64 PI.f64 -1/4))))))))) (/.f64 -4 PI.f64))
✓	1.3b	(.f64 -4 (/.f64 (-.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) PI.f64))) (log.f64 f)) PI.f64))
▶	1.4b	(*.f64 (log.f64 (/.f64 (/.f64 4 f) PI.f64)) (/.f64 -4 PI.f64))
	1.4b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (log.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2)))))) (/.f64 -4 PI.f64))
	1.5b	(.f64 -4 (/.f64 (-.f64 (.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64)))) (.f64 (log.f64 f) (log.f64 f))) (.f64 PI.f64 (+.f64 (log.f64 f) (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64)))))))
	1.6b	(.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))) (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))))) (/.f64 -4 PI.f64)))
	61.2b	(.f64 (log.f64 (/.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	11.8b	(log.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (.f64 f (.f64 PI.f64 1/2))) (/.f64 -4 PI.f64)))

Compiler

Compiled 2072 to 1412 computations (31.9% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (/.f64 (/.f64 4 f) PI.f64))
0.3b	(/.f64 (/.f64 4 f) PI.f64)
0.4b	(*.f64 (log.f64 (/.f64 (/.f64 4 f) PI.f64)) (/.f64 -4 PI.f64))

rewrite295.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

151×	`times-frac_binary64`
93×	`add-sqr-sqrt_binary64`
88×	`*-un-lft-identity_binary64`
88×	`add-cube-cbrt_binary64`
43×	`log-prod_binary64`

Counts

3 → 158

Calls

3 calls:

6.0ms	(*.f64 (log.f64 (/.f64 (/.f64 4 f) PI.f64)) (/.f64 -4 PI.f64))
4.0ms	(/.f64 (/.f64 4 f) PI.f64)
4.0ms	(log.f64 (/.f64 (/.f64 4 f) PI.f64))

Compiler

Compiled 3035 to 2022 computations (33.4% saved)

series36.0ms (0.2%)

Error

0.6b

Counts

3 → 9

Calls

3 calls:

14.0ms	(*.f64 (log.f64 (/.f64 (/.f64 4 f) PI.f64)) (/.f64 -4 PI.f64))
11.0ms	(log.f64 (/.f64 (/.f64 4 f) PI.f64))
5.0ms	(/.f64 (/.f64 4 f) PI.f64)

Compiler

Compiled 311 to 254 computations (18.3% saved)

simplify161.0ms (1%)

Algorithm

1×	egg-herbie

Rules

486×	`log-div_binary64`
343×	`associate-/l/_binary64`
331×	`distribute-rgt-in_binary64`
325×	`times-frac_binary64`
320×	`distribute-lft-in_binary64`

Counts

167 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	297	3562
1	632	3335
2	1704	3277
3	4608	3277
4	4970	3277
5	4967	3277

prune142.0ms (0.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	7	6	13
Picked	1	0	1
Done	1	0	1
Total	126	15	141

Error

0.6b

Counts

141 → 15

Alt Table

Status	Error	Program
	1.4b	(*.f64 (+.f64 (log.f64 (/.f64 4 f)) (neg.f64 (log.f64 PI.f64))) (/.f64 -4 PI.f64))
	1.4b	(.f64 (-.f64 (log.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)) (exp.f64 (.f64 f (/.f64 PI.f64 4))))) (log.f64 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	1.3b	(.f64 -4 (/.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) PI.f64))
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (.f64 (neg.f64 (pow.f64 (.f64 (cbrt.f64 (exp.f64 -1/4)) (cbrt.f64 (exp.f64 -1/4))) (.f64 f PI.f64))) (pow.f64 (cbrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	1.5b	(.f64 -4 (/.f64 (-.f64 (pow.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) 3) (pow.f64 (log.f64 f) 3)) (.f64 PI.f64 (+.f64 (.f64 (log.f64 f) (log.f64 f)) (.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) (+.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) (log.f64 f)))))))
	2.6b	(.f64 (.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) (.f64 (cbrt.f64 (/.f64 -4 PI.f64)) (cbrt.f64 (/.f64 -4 PI.f64)))) (cbrt.f64 (/.f64 -4 PI.f64)))
	61.2b	(.f64 (log.f64 (/.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64))) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 f (.f64 1/4 PI.f64))) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f PI.f64))) (+.f64 (pow.f64 (exp.f64 (.f64 f PI.f64)) -1/2) (exp.f64 (+.f64 (.f64 f (.f64 1/4 PI.f64)) (.f64 f (.f64 PI.f64 -1/4))))))))) (/.f64 -4 PI.f64))
	1.7b	(.f64 (sqrt.f64 (log.f64 (/.f64 (/.f64 4 f) PI.f64))) (.f64 (/.f64 -4 PI.f64) (sqrt.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))))))
	1.5b	(.f64 (+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 4 f)))) (log.f64 (sqrt.f64 PI.f64))) (log.f64 (/.f64 (cbrt.f64 (/.f64 4 f)) (sqrt.f64 PI.f64)))) (/.f64 -4 PI.f64))
	1.5b	(.f64 -4 (/.f64 (-.f64 (.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64))) (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64)))) (.f64 (log.f64 f) (log.f64 f))) (.f64 PI.f64 (+.f64 (log.f64 f) (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64)))))))
	3.2b	(.f64 (.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) (/.f64 (.f64 (cbrt.f64 -4) (cbrt.f64 -4)) (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))) (/.f64 (cbrt.f64 -4) (cbrt.f64 PI.f64)))
	2.3b	(.f64 (.f64 (cbrt.f64 (log.f64 (/.f64 (/.f64 4 f) PI.f64))) (cbrt.f64 (log.f64 (/.f64 (/.f64 4 f) PI.f64)))) (.f64 (/.f64 -4 PI.f64) (cbrt.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))))))
	2.2b	(.f64 (.f64 (cbrt.f64 (.f64 -4 (/.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) PI.f64))) (cbrt.f64 (.f64 -4 (/.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) PI.f64)))) (cbrt.f64 (.f64 -4 (/.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) PI.f64))))
	11.8b	(log.f64 (pow.f64 (/.f64 4 (*.f64 PI.f64 f)) (/.f64 -4 PI.f64)))

Compiler

Compiled 2457 to 1593 computations (35.2% saved)

regimes2.6s (16%)

Accuracy

Total 1.0b remaining (38.4%)

Threshold costs 0b (0%)

Compiler

Compiled 61512 to 45956 computations (25.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	41
1	26	41
2	26	41

end4.0ms (0%)

Compiler: Compiled 25 to 19 computations (24% saved)

sample9.0s (55.4%)

Algorithm

1×

intervals

Results

2.6s	3890×	body	1024	valid
2.4s	3826×	body	1024	nan
872.0ms	1922×	body	512	valid
869.0ms	1918×	body	512	nan
700.0ms	558×	body	2048	valid
317.0ms	997×	body	256	valid
285.0ms	977×	body	256	nan
105.0ms	633×	body	128	valid
3.0ms	3×	body	2048	nan
0.0ms	2×	body	128	nan

Compiler

Compiled 590 to 434 computations (26.4% saved)

Details

analyze1.4s (8.6%)

sample271.0ms (1.7%)

simplify80.0ms (0.5%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite585.0ms (3.6%)

series50.0ms (0.3%)

simplify339.0ms (2.1%)

prune135.0ms (0.8%)

localize18.0ms (0.1%)

rewrite186.0ms (1.1%)

series149.0ms (0.9%)

simplify135.0ms (0.8%)

prune183.0ms (1.1%)

localize19.0ms (0.1%)

rewrite141.0ms (0.9%)

series65.0ms (0.4%)

simplify159.0ms (1%)

prune61.0ms (0.4%)

localize7.0ms (0%)

rewrite295.0ms (1.8%)

series36.0ms (0.2%)

simplify161.0ms (1%)

prune142.0ms (0.9%)

regimes2.6s (16%)

simplify3.0ms (0%)

end4.0ms (0%)

sample9.0s (55.4%)

Profiling