Details

analyze1.2s (9%)

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)

sample229.0ms (1.7%)

Algorithm

1×

intervals

Results

61.0ms	116×	body	1024	valid
60.0ms	128×	body	1024	nan
24.0ms	23×	body	2048	valid
23.0ms	62×	body	512	valid
22.0ms	57×	body	512	nan
8.0ms	38×	body	256	nan
8.0ms	33×	body	256	valid
3.0ms	22×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify84.0ms (0.6%)

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

prune10.0ms (0.1%)

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

61.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	61.1b	(.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

▶

61.1b

(*.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)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.2b	(*.f64 (/.f64 PI.f64 4) f)
1.0b	(/.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))))
5.9b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite548.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

61.0b

Rules

75×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`

Counts

4 → 141

Calls

4 calls:

13.0ms	(/.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))))
8.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 5776 to 3852 computations (33.3% saved)

series84.0ms (0.6%)

Error

1.5b

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.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))))
23.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
11.0ms	(*.f64 (/.f64 PI.f64 4) f)
10.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1137 to 841 computations (26% saved)

simplify248.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

586×	`associate-l_binary64`
539×	`associate-r_binary64`
488×	`times-frac_binary64`
231×	`associate-*l/_binary64`
203×	`exp-prod_binary64`

Counts

153 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	5769
1	467	5390
2	1153	5388
3	3682	5376
4	4922	5376
5	4977	5376

prune153.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	5	138

Error

1.4b

Counts

138 → 5

Alt Table

Status	Error	Program
	2.4b	(.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))
	61.6b	(.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 (sqrt.f64 (pow.f64 (exp.f64 PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 f PI.f64) 2))) (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))))) (/.f64 -4 PI.f64))
▶	2.4b	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
	61.6b	(.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 PI.f64 4))) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) 3)) (+.f64 (sqrt.f64 (pow.f64 (exp.f64 PI.f64) f)) (.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))))))) (/.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 (sqrt.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64))) (-.f64 (sqrt.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))

Compiler

Compiled 4759 to 3209 computations (32.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 f (.f64 PI.f64 1/2))
0.3b	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
0.4b	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))

rewrite120.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
13×	`times-frac_binary64`
11×	`pow1_binary64`

Counts

3 → 74

Calls

3 calls:

12.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
6.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
5.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 1347 to 1018 computations (24.4% saved)

series44.0ms (0.3%)

Error

1.3b

Counts

3 → 9

Calls

3 calls:

20.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
10.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
7.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 284 to 233 computations (18% saved)

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

578×	`div-sub_binary64`
379×	`associate-/r*_binary64`
321×	`associate-*l/_binary64`
305×	`associate-/l*_binary64`
267×	`associate-/l/_binary64`

Counts

83 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	1630
1	340	1221
2	1280	1210
3	4410	1210
4	5763	1210

prune93.0ms (0.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	62	14	76

Error

1.1b

Counts

76 → 14

Alt Table

Status	Error	Program
	3.1b	(.f64 (.f64 (cbrt.f64 (log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))) (cbrt.f64 (log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2)))))) (.f64 (/.f64 -4 PI.f64) (cbrt.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))))))
	13.9b	(log.f64 (pow.f64 (/.f64 4 (*.f64 PI.f64 f)) (/.f64 -4 PI.f64)))
	2.5b	(.f64 (/.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) (sqrt.f64 PI.f64)) (/.f64 -4 (sqrt.f64 PI.f64)))
▶	2.4b	(.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))
	63.9b	(.f64 (log.f64 (log.f64 (exp.f64 (/.f64 4 (.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	61.6b	(.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 (sqrt.f64 (pow.f64 (exp.f64 PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 f PI.f64) 2))) (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))))) (/.f64 -4 PI.f64))
	2.6b	(.f64 (sqrt.f64 (log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))) (.f64 (/.f64 -4 PI.f64) (sqrt.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))))))
	2.6b	(cbrt.f64 (pow.f64 (.f64 -4 (/.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) PI.f64)) 3))
	41.6b	(.f64 (log.f64 (/.f64 2 (cbrt.f64 (.f64 1/8 (pow.f64 (*.f64 PI.f64 f) 3))))) (/.f64 -4 PI.f64))
	3.2b	(.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))))
	61.6b	(.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 PI.f64 4))) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) 3)) (+.f64 (sqrt.f64 (pow.f64 (exp.f64 PI.f64) f)) (.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))))))) (/.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 (sqrt.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64))) (-.f64 (sqrt.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	2.4b	(.f64 (log.f64 (/.f64 2 (exp.f64 (log.f64 (.f64 (*.f64 PI.f64 f) 1/2))))) (/.f64 -4 PI.f64))
	3.6b	(.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)))

Compiler

Compiled 1542 to 1112 computations (27.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.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))
1.0b	(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))))

rewrite237.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

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:

10.0ms	(/.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)))
9.0ms	(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))))
9.0ms	(.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	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 3782 to 2552 computations (32.5% saved)

series107.0ms (0.8%)

Error

1.1b

Counts

4 → 12

Calls

4 calls:

34.0ms	(.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))
30.0ms	(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))))
18.0ms	(/.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)))
9.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 835 to 637 computations (23.7% saved)

simplify131.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

125 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	248	4630
1	587	3955
2	2029	3934
3	5305	3934

prune181.0ms (1.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	101	17	118

Error

1.1b

Counts

118 → 17

Alt Table

Status	Error	Program
	3.1b	(.f64 (.f64 (cbrt.f64 (log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))) (cbrt.f64 (log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2)))))) (.f64 (/.f64 -4 PI.f64) (cbrt.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))))))
	13.9b	(log.f64 (pow.f64 (/.f64 4 (*.f64 PI.f64 f)) (/.f64 -4 PI.f64)))
	2.5b	(.f64 (/.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) (sqrt.f64 PI.f64)) (/.f64 -4 (sqrt.f64 PI.f64)))
	3.6b	(.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)))
	2.7b	(.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))
	63.9b	(.f64 (log.f64 (log.f64 (exp.f64 (/.f64 4 (.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	3.2b	(.f64 (.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))
	3.1b	(.f64 (exp.f64 (log.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))
	61.6b	(.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 (sqrt.f64 (pow.f64 (exp.f64 PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 f PI.f64) 2))) (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))))) (/.f64 -4 PI.f64))
	2.6b	(.f64 (sqrt.f64 (log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))) (.f64 (/.f64 -4 PI.f64) (sqrt.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))))))
	2.6b	(cbrt.f64 (pow.f64 (.f64 -4 (/.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) PI.f64)) 3))
	2.6b	(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)))
▶	2.3b	(.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))
	61.6b	(.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 PI.f64 4))) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) 3)) (+.f64 (sqrt.f64 (pow.f64 (exp.f64 PI.f64) f)) (.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))))))) (/.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 (sqrt.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64))) (-.f64 (sqrt.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	2.4b	(.f64 (log.f64 (/.f64 2 (exp.f64 (log.f64 (.f64 (*.f64 PI.f64 f) 1/2))))) (/.f64 -4 PI.f64))
	3.6b	(.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)))

Compiler

Compiled 3797 to 2657 computations (30% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.2b	(*.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)
2.9b	(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)))

rewrite187.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

47×	`pow1_binary64`
43×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
30×	`log-pow_binary64` `times-frac_binary64`
24×	`distribute-lft-out--_binary64`

Counts

4 → 108

Calls

4 calls:

18.0ms	(/.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)
8.0ms	(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)
4.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 2937 to 1723 computations (41.3% saved)

series89.0ms (0.7%)

Error

1.1b

Counts

4 → 12

Calls

4 calls:

35.0ms	(/.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)
27.0ms	(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)))
11.0ms	(*.f64 PI.f64 f)
8.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 780 to 588 computations (24.6% saved)

simplify185.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

611×	`sub-neg_binary64`
362×	`div-sub_binary64`
315×	`associate-/l*_binary64`
299×	`times-frac_binary64`
273×	`associate-*l/_binary64`

Counts

120 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	4320
1	305	4035
2	819	4005
3	1879	4005
4	4202	4005
5	5316	4005

prune65.0ms (0.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	3	13	16
Picked	0	1	1
Done	0	0	0
Total	38	16	54

Error

1.1b

Counts

54 → 16

Alt Table

Status	Error	Program
	3.1b	(.f64 (.f64 (cbrt.f64 (log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))) (cbrt.f64 (log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2)))))) (.f64 (/.f64 -4 PI.f64) (cbrt.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))))))
	13.9b	(log.f64 (pow.f64 (/.f64 4 (*.f64 PI.f64 f)) (/.f64 -4 PI.f64)))
	2.5b	(.f64 (/.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) (sqrt.f64 PI.f64)) (/.f64 -4 (sqrt.f64 PI.f64)))
	3.6b	(.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)))
	2.7b	(.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))
	63.9b	(.f64 (log.f64 (log.f64 (exp.f64 (/.f64 4 (.f64 PI.f64 f))))) (/.f64 -4 PI.f64))
	3.2b	(.f64 (.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))
	2.5b	(.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)))))))
	2.6b	(.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)))))))
	61.6b	(.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 (sqrt.f64 (pow.f64 (exp.f64 PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 f PI.f64) 2))) (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))))) (/.f64 -4 PI.f64))
	2.6b	(.f64 (sqrt.f64 (log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))) (.f64 (/.f64 -4 PI.f64) (sqrt.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))))))
	2.6b	(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)))
	2.3b	(.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))
	61.6b	(.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 PI.f64 4))) 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) 3)) (+.f64 (sqrt.f64 (pow.f64 (exp.f64 PI.f64) f)) (.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (+.f64 (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))))))) (/.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 (sqrt.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64))) (-.f64 (sqrt.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4)))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	3.6b	(.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)))

Compiler

Compiled 1381 to 919 computations (33.5% saved)

regimes1.7s (13.1%)

Accuracy

Total 1.2b remaining (43.1%)

Threshold costs 0b (0%)

Compiler

Compiled 35208 to 26660 computations (24.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	12	17
2	12	17

end1.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

sample7.3s (55.4%)

Algorithm

1×

intervals

Results

2.0s	3841×	body	1024	valid
1.9s	3870×	body	1024	nan
723.0ms	1985×	body	512	valid
651.0ms	1911×	body	512	nan
512.0ms	479×	body	2048	valid
261.0ms	1019×	body	256	valid
213.0ms	943×	body	256	nan
89.0ms	676×	body	128	valid
1.0ms	1×	body	2048	nan
0.0ms	2×	body	128	nan

Compiler

Compiled 664 to 489 computations (26.4% saved)

Details

analyze1.2s (9%)

sample229.0ms (1.7%)

simplify84.0ms (0.6%)

prune10.0ms (0.1%)

localize25.0ms (0.2%)

rewrite548.0ms (4.2%)

series84.0ms (0.6%)

simplify248.0ms (1.9%)

prune153.0ms (1.2%)

localize10.0ms (0.1%)

rewrite120.0ms (0.9%)

series44.0ms (0.3%)

simplify88.0ms (0.7%)

prune93.0ms (0.7%)

localize19.0ms (0.1%)

rewrite237.0ms (1.8%)

series107.0ms (0.8%)

simplify131.0ms (1%)

prune181.0ms (1.4%)

localize20.0ms (0.2%)

rewrite187.0ms (1.4%)

series89.0ms (0.7%)

simplify185.0ms (1.4%)

prune65.0ms (0.5%)

regimes1.7s (13.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample7.3s (55.4%)

Profiling