Details

analyze1.5s (2.3%)

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)

sample283.0ms (0.4%)

Algorithm

1×

intervals

Results

108.0ms	119×	body	1024	valid
65.0ms	111×	body	1024	nan
34.0ms	72×	body	512	valid
23.0ms	55×	body	512	nan
16.0ms	10×	body	2048	valid
10.0ms	34×	body	256	valid
9.0ms	26×	body	256	nan
3.0ms	21×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify52.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-neg_binary64`
569×	`fma-def_binary64`
365×	`div-sub_binary64`
240×	`associate-/r*_binary64`
202×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	117	59
3	295	55
4	736	55
5	1625	55
6	4003	55
7	5053	55

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

61.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.5b	(.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

▶

61.5b

(*.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 136 to 100 computations (26.5% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 PI.f64 f)
✓	0.2b	(*.f64 (/.f64 PI.f64 4) f)
✓	1.2b	(/.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))))
✓	5.7b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite51.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
38×	`times-frac_binary64`
21×	`prod-diff_binary64`

Counts

4 → 159

Calls

4 calls:

21.0ms	(*.f64 (/.f64 PI.f64 4) f)
9.0ms	(/.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 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
3.0ms	(*.f64 PI.f64 f)

series133.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

102.0ms	(/.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))))
11.0ms	(*.f64 PI.f64 f)
11.0ms	(*.f64 (/.f64 PI.f64 4) f)
8.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

simplify217.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

350×	`associate-r_binary64`
341×	`fma-neg_binary64`
305×	`associate-l_binary64`
264×	`fma-def_binary64`
240×	`associate-/l*_binary64`

Counts

207 → 387

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	485	9789
1	1237	8111
2	4768	8111
3	5034	8111

prune514.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	383	4	387
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	384	4	388

Error

1.8b

Counts

388 → 4

Alt Table

Status	Error	Program
	2.2b	(.f64 (log.f64 (-.f64 (fma.f64 1/6 (/.f64 (.f64 f (.f64 f (.f64 (pow.f64 PI.f64 3) -1/64))) (.f64 PI.f64 1/2)) (fma.f64 1/512 (/.f64 (.f64 f (pow.f64 PI.f64 4)) (pow.f64 (.f64 PI.f64 1/2) 3)) (fma.f64 7/12 (/.f64 (.f64 (.f64 f f) (.f64 (pow.f64 PI.f64 5) -1/1024)) (pow.f64 (.f64 PI.f64 1/2) 3)) (fma.f64 1/8 (/.f64 (.f64 f (.f64 1/16 (pow.f64 PI.f64 3))) (pow.f64 (.f64 PI.f64 1/2) 2)) (fma.f64 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 4) 1/256)) (pow.f64 (.f64 PI.f64 1/2) 3)) (fma.f64 3/1024 (/.f64 (.f64 (.f64 f f) (.f64 1/16 (pow.f64 PI.f64 6))) (pow.f64 (.f64 PI.f64 1/2) 4)) (fma.f64 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 2) 1/16)) (.f64 PI.f64 1/2)) (fma.f64 1/384 (/.f64 (.f64 f (.f64 f (pow.f64 PI.f64 3))) (.f64 PI.f64 1/2)) (fma.f64 7/12288 (/.f64 (.f64 (.f64 f f) (pow.f64 PI.f64 5)) (pow.f64 (.f64 PI.f64 1/2) 3)) (fma.f64 1/1024 (/.f64 (.f64 -1/4 (.f64 (.f64 f f) (pow.f64 PI.f64 5))) (pow.f64 (.f64 PI.f64 1/2) 3)) (fma.f64 1/24 (/.f64 (.f64 (.f64 f f) (.f64 -1/64 (pow.f64 PI.f64 4))) (pow.f64 (.f64 PI.f64 1/2) 2)) (fma.f64 1/4 (/.f64 (.f64 (.f64 f f) (.f64 (pow.f64 PI.f64 6) 1/4096)) (pow.f64 (.f64 PI.f64 1/2) 4)) (fma.f64 1/16 (/.f64 (.f64 (.f64 f f) (.f64 1/256 (pow.f64 PI.f64 5))) (pow.f64 (.f64 PI.f64 1/2) 3)) (fma.f64 1/2 (/.f64 (.f64 f (.f64 f (.f64 (pow.f64 PI.f64 4) 1/256))) (pow.f64 (.f64 PI.f64 1/2) 2)) (fma.f64 1/4 (/.f64 PI.f64 (.f64 PI.f64 1/2)) (+.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))) (fma.f64 1/16 (/.f64 (pow.f64 PI.f64 2) (pow.f64 (.f64 PI.f64 1/2) 2)) (fma.f64 1/32 (/.f64 (.f64 f (pow.f64 PI.f64 2)) (.f64 PI.f64 1/2)) (fma.f64 5/6 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) -1/64)) (pow.f64 (.f64 PI.f64 1/2) 2)) (.f64 (/.f64 PI.f64 (.f64 PI.f64 1/2)) -1/4)))))))))))))))))))) (fma.f64 1/32 (/.f64 (.f64 f (.f64 -1/4 (pow.f64 PI.f64 3))) (pow.f64 (.f64 PI.f64 1/2) 2)) (fma.f64 1/16 (/.f64 (.f64 f (.f64 1/16 (pow.f64 PI.f64 4))) (pow.f64 (.f64 PI.f64 1/2) 3)) (fma.f64 5/384 (/.f64 (.f64 f (pow.f64 PI.f64 3)) (pow.f64 (.f64 PI.f64 1/2) 2)) (fma.f64 5/96 (/.f64 (.f64 (.f64 f f) (.f64 -1/64 (pow.f64 PI.f64 5))) (pow.f64 (.f64 PI.f64 1/2) 3)) (fma.f64 1/16 (/.f64 (pow.f64 PI.f64 2) (pow.f64 (.f64 PI.f64 1/2) 2)) (fma.f64 1/384 (/.f64 (.f64 (.f64 f f) (.f64 -1/4 (pow.f64 PI.f64 4))) (pow.f64 (.f64 PI.f64 1/2) 2)) (fma.f64 3/64 (/.f64 (.f64 (.f64 f f) (.f64 1/256 (pow.f64 PI.f64 6))) (pow.f64 (.f64 PI.f64 1/2) 4)) (fma.f64 5/384 (/.f64 (.f64 (.f64 f f) (.f64 1/16 (pow.f64 PI.f64 5))) (pow.f64 (.f64 PI.f64 1/2) 3)) (fma.f64 1/512 (/.f64 (.f64 f (.f64 f (pow.f64 PI.f64 4))) (pow.f64 (.f64 PI.f64 1/2) 2)) (.f64 1/16384 (/.f64 (.f64 (.f64 f f) (pow.f64 PI.f64 6)) (pow.f64 (*.f64 PI.f64 1/2) 4)))))))))))))) (/.f64 -4 PI.f64))
▶	2.2b	(.f64 (log.f64 (-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 1/512 (/.f64 (.f64 f (pow.f64 PI.f64 4)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 7/12 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 5))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/8 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 3/1024 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 6) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 2) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 1/384 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 3)) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 7/12288 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 5)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/1024 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 6) (pow.f64 (log.f64 (exp.f64 -1/4)) 6))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/4 (/.f64 PI.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 2 (/.f64 1 (.f64 f (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4))))))) (+.f64 (/.f64 (.f64 (pow.f64 PI.f64 2) (pow.f64 (log.f64 (exp.f64 -1/4)) 2)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2)) (+.f64 (.f64 1/32 (/.f64 (.f64 f (pow.f64 PI.f64 2)) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 5/6 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (/.f64 (.f64 PI.f64 (log.f64 (exp.f64 -1/4))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))))))))))))))))))))) (+.f64 (.f64 1/32 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/16 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 5/384 (/.f64 (.f64 f (pow.f64 PI.f64 3)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 5/96 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 PI.f64 2) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/384 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 4) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 3/64 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 6) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 5/384 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/512 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 4)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (.f64 1/16384 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 6)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (*.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4)))))))))))))) (/.f64 -4 PI.f64))
	61.5b	(.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 PI.f64 4)) (.f64 2 f)) (pow.f64 (exp.f64 -1/4) (.f64 2 (.f64 f PI.f64)))) (+.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	61.5b	(.f64 (log.f64 (/.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (sqrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))) (sqrt.f64 (-.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 16975 to 11927 computations (29.7% saved)

localize213.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4)
✓	1.6b	(pow.f64 PI.f64 6)
	1.6b	(pow.f64 PI.f64 4)
✓	1.6b	(pow.f64 PI.f64 4)

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow-unpow_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`unpow-prod-down_binary64`
9×	`add-cube-cbrt_binary64`

Counts

3 → 57

Calls

3 calls:

3.0ms	(pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4)
1.0ms	(pow.f64 PI.f64 4)
1.0ms	(pow.f64 PI.f64 6)

series0.0ms (0%)

Counts

3 → 0

Calls

3 calls:

0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4)
0.0ms	(pow.f64 PI.f64 6)

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

787×	`log-prod_binary64`
278×	`exp-prod_binary64`
266×	`distribute-rgt-in_binary64`
245×	`associate-l_binary64`
238×	`distribute-lft-in_binary64`

Counts

57 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	722
1	155	483
2	317	477
3	1399	477
4	4515	477
5	5344	477

prune2.0s (3.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	128	3	131

Error

1.8b

Counts

131 → 3

Alt Table

Status	Error	Program
▶	2.2b	(.f64 (log.f64 (-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 1/512 (/.f64 (.f64 f (pow.f64 PI.f64 4)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 7/12 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 5))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/8 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 3/1024 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 (pow.f64 PI.f64 (.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.f64 6)) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 2) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 1/384 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 3)) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 7/12288 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 5)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/1024 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 6) (pow.f64 (log.f64 (exp.f64 -1/4)) 6))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/4 (/.f64 PI.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 2 (/.f64 1 (.f64 f (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4))))))) (+.f64 (/.f64 (.f64 (pow.f64 PI.f64 2) (pow.f64 (log.f64 (exp.f64 -1/4)) 2)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2)) (+.f64 (.f64 1/32 (/.f64 (.f64 f (pow.f64 PI.f64 2)) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 5/6 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (/.f64 (.f64 PI.f64 (log.f64 (exp.f64 -1/4))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))))))))))))))))))))) (+.f64 (.f64 1/32 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/16 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 5/384 (/.f64 (.f64 f (pow.f64 PI.f64 3)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 5/96 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 PI.f64 2) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/384 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 4) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 3/64 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 6) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 5/384 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/512 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 4)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (.f64 1/16384 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 6)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4)))))))))))))) (/.f64 -4 PI.f64))
	61.5b	(.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 PI.f64 4)) (.f64 2 f)) (pow.f64 (exp.f64 -1/4) (.f64 2 (.f64 f PI.f64)))) (+.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	61.5b	(.f64 (log.f64 (/.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (sqrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))) (sqrt.f64 (-.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 72240 to 60523 computations (16.2% saved)

localize245.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.6b	(pow.f64 PI.f64 4)
	1.6b	(pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4)
	1.6b	(pow.f64 PI.f64 4)
	1.6b	(pow.f64 PI.f64 4)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune2.0s (3.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	469	1	470
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	470	3	473

Error

1.8b

Counts

473 → 3

Alt Table

Status	Error	Program
	61.5b	(.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 PI.f64 4)) (.f64 2 f)) (pow.f64 (exp.f64 -1/4) (.f64 2 (.f64 f PI.f64)))) (+.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
▶	2.2b	(.f64 (log.f64 (-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 1/512 (/.f64 (.f64 f (pow.f64 PI.f64 4)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 7/12 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 5))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/8 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 3/1024 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 (pow.f64 PI.f64 (.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.f64 6)) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 2) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 1/384 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 3)) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 7/12288 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 5)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/1024 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 (pow.f64 PI.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4)) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 6) (pow.f64 (log.f64 (exp.f64 -1/4)) 6))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/4 (/.f64 PI.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 2 (/.f64 1 (.f64 f (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4))))))) (+.f64 (/.f64 (.f64 (pow.f64 PI.f64 2) (pow.f64 (log.f64 (exp.f64 -1/4)) 2)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2)) (+.f64 (.f64 1/32 (/.f64 (.f64 f (pow.f64 PI.f64 2)) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 5/6 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (/.f64 (.f64 PI.f64 (log.f64 (exp.f64 -1/4))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))))))))))))))))))))) (+.f64 (.f64 1/32 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/16 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 5/384 (/.f64 (.f64 f (pow.f64 PI.f64 3)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 5/96 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 PI.f64 2) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/384 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 4) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 3/64 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 6) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 5/384 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/512 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 4)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (.f64 1/16384 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 6)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (*.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4)))))))))))))) (/.f64 -4 PI.f64))
	61.5b	(.f64 (log.f64 (/.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (sqrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))) (sqrt.f64 (-.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 74391 to 62439 computations (16.1% saved)

localize264.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(pow.f64 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))
	1.6b	(pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4)
	1.6b	(pow.f64 PI.f64 4)
	1.6b	(pow.f64 PI.f64 4)

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`unpow-prod-down_binary64`
6×	`pow-unpow_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

1 → 28

Calls

1 calls:

3.0ms

(pow.f64 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))

series0.0ms (0%)

Counts

1 → 0

Calls

1 calls:

0.0ms

(pow.f64 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))

simplify99.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

698×	`unswap-sqr_binary64`
548×	`log-prod_binary64`
320×	`associate-l_binary64`
248×	`associate-/l*_binary64`
240×	`associate-r_binary64`

Counts

28 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	59	625
1	118	606
2	239	606
3	554	606
4	1434	606
5	4518	606
6	4647	606
7	4983	606

prune2.2s (3.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1601	1	1602
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	1602	3	1605

Error

1.8b

Counts

1605 → 3

Alt Table

Status	Error	Program
	61.5b	(.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 PI.f64 4)) (.f64 2 f)) (pow.f64 (exp.f64 -1/4) (.f64 2 (.f64 f PI.f64)))) (+.f64 (exp.f64 (.f64 f (/.f64 PI.f64 4))) (pow.f64 (exp.f64 -1/4) (.f64 f PI.f64)))))) (/.f64 -4 PI.f64))
	2.2b	(.f64 (log.f64 (-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 1/512 (/.f64 (.f64 f (pow.f64 PI.f64 4)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 7/12 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 5))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/8 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 3/1024 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 (pow.f64 PI.f64 (.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.f64 6)) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 2) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 1/384 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 3)) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 7/12288 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 5)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/1024 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 (pow.f64 (pow.f64 PI.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 4))) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 6) (pow.f64 (log.f64 (exp.f64 -1/4)) 6))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/4 (/.f64 PI.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 2 (/.f64 1 (.f64 f (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4))))))) (+.f64 (/.f64 (.f64 (pow.f64 PI.f64 2) (pow.f64 (log.f64 (exp.f64 -1/4)) 2)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2)) (+.f64 (.f64 1/32 (/.f64 (.f64 f (pow.f64 PI.f64 2)) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))) (+.f64 (.f64 5/6 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (/.f64 (.f64 PI.f64 (log.f64 (exp.f64 -1/4))) (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))))))))))))))))))))))) (+.f64 (.f64 1/32 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 3) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/16 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 4) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 5/384 (/.f64 (.f64 f (pow.f64 PI.f64 3)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 5/96 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 3))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 PI.f64 2) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 1/384 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 4) (log.f64 (exp.f64 -1/4)))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (+.f64 (.f64 3/64 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 6) (pow.f64 (log.f64 (exp.f64 -1/4)) 4))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4))) (+.f64 (.f64 5/384 (/.f64 (.f64 (pow.f64 f 2) (.f64 (pow.f64 PI.f64 5) (pow.f64 (log.f64 (exp.f64 -1/4)) 2))) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 3))) (+.f64 (.f64 1/512 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 4)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 2))) (.f64 1/16384 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 PI.f64 6)) (pow.f64 (-.f64 (.f64 1/4 PI.f64) (*.f64 PI.f64 (log.f64 (exp.f64 -1/4)))) 4)))))))))))))) (/.f64 -4 PI.f64))
	61.5b	(.f64 (log.f64 (/.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (sqrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))) (sqrt.f64 (-.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 79490 to 66868 computations (15.9% saved)

regimes34.9s (54.3%)

Accuracy

Total 0.4b remaining (16%)

Threshold costs 0.4b (16%)

Compiler

Compiled 844188 to 707498 computations (16.2% saved)

simplify179.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

130×	`*-commutative_binary64`
87×	`+-commutative_binary64`
59×	`sub-neg_binary64`
57×	`neg-sub0_binary64`
57×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	191	1243
1	301	1243
2	317	1243
3	342	1243
4	372	1243
5	410	1243
6	458	1243
7	509	1243
8	560	1243
9	611	1243
10	659	1243
11	714	1243
12	753	1243
13	788	1243
14	802	1243
15	807	1243
16	797	1243

end27.0ms (0%)

Compiler: Compiled 734 to 619 computations (15.7% saved)

sample19.5s (30.2%)

Algorithm

1×

intervals

Results

5.1s	3891×	body	1024	valid
4.8s	3812×	body	1024	nan
1.9s	1987×	body	512	valid
1.7s	1901×	body	512	nan
1.2s	486×	body	2048	valid
617.0ms	970×	body	256	valid
565.0ms	928×	body	256	nan
214.0ms	666×	body	128	valid
1.0ms	2×	body	128	nan
1.0ms	2×	body	128	overflowed

Compiler

Compiled 1609 to 1344 computations (16.5% saved)

Details

analyze1.5s (2.3%)

sample283.0ms (0.4%)

simplify52.0ms (0.1%)

prune4.0ms (0%)

localize15.0ms (0%)

rewrite51.0ms (0.1%)

series133.0ms (0.2%)

simplify217.0ms (0.3%)

prune514.0ms (0.8%)

localize213.0ms (0.3%)

rewrite8.0ms (0%)

series0.0ms (0%)

simplify80.0ms (0.1%)

prune2.0s (3.1%)

localize245.0ms (0.4%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify13.0ms (0%)

prune2.0s (3.1%)

localize264.0ms (0.4%)

rewrite4.0ms (0%)

series0.0ms (0%)

simplify99.0ms (0.2%)

prune2.2s (3.4%)

regimes34.9s (54.3%)

simplify179.0ms (0.3%)

end27.0ms (0%)

sample19.5s (30.2%)

Profiling