Details

analyze3.0s (5.3%)

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)

sample613.0ms (1.1%)

Algorithm

1×

intervals

Results

210.0ms	130×	body	1024	valid
179.0ms	110×	body	1024	nan
59.0ms	62×	body	512	valid
50.0ms	57×	body	512	nan
39.0ms	15×	body	2048	valid
25.0ms	42×	body	256	nan
20.0ms	32×	body	256	valid
5.0ms	17×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify67.0ms (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

prune8.0ms (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

62.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	62.2b	(.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

▶

62.2b

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

localize31.0ms (0.1%)

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))))
✓	6.4b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite68.0ms (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:

19.0ms	(/.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))))
14.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
10.0ms	(*.f64 (/.f64 PI.f64 4) f)
5.0ms	(*.f64 PI.f64 f)

series268.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

181.0ms	(/.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))))
51.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
20.0ms	(*.f64 (/.f64 PI.f64 4) f)
15.0ms	(*.f64 PI.f64 f)

simplify448.0ms (0.8%)

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

prune649.0ms (1.1%)

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

1.9b

Counts

388 → 4

Alt Table

Status	Error	Program
	62.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (fma.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
	62.2b	(.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 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
▶	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 (fma.f64 1/512 (/.f64 (.f64 f (pow.f64 PI.f64 4)) (pow.f64 (.f64 PI.f64 1/2) 3)) (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 1/8 (/.f64 (.f64 f (.f64 1/16 (pow.f64 PI.f64 3))) (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 1/32 (/.f64 (.f64 f (pow.f64 PI.f64 2)) (.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 1/2 (/.f64 (.f64 f (.f64 (pow.f64 PI.f64 2) 1/16)) (.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 1/16 (/.f64 (pow.f64 PI.f64 2) (pow.f64 (.f64 PI.f64 1/2) 2)) (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)) (.f64 5/384 (/.f64 (.f64 f (pow.f64 PI.f64 3)) (pow.f64 (*.f64 PI.f64 1/2) 2)))))))) (/.f64 -4 PI.f64))

Compiler

Compiled 15863 to 10979 computations (30.8% saved)

localize351.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
✓	1.6b	(pow.f64 PI.f64 6)
	1.6b	(pow.f64 PI.f64 4)
✓	1.6b	(pow.f64 PI.f64 4)

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow-unpow_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

3 → 57

Calls

3 calls:

5.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
3.0ms	(pow.f64 PI.f64 4)
3.0ms	(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 PI.f64 1/2) 4)
0.0ms	(pow.f64 PI.f64 6)

simplify95.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

798×	`log-prod_binary64`
727×	`exp-prod_binary64`
296×	`associate-l_binary64`
264×	`associate-r_binary64`
259×	`cube-prod_binary64`

Counts

57 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	503
1	135	452
2	290	449
3	1478	446
4	4172	446
5	5138	446

prune2.2s (3.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	124	3	127

Error

1.9b

Counts

127 → 3

Alt Table

Status	Error	Program
	62.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (fma.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
	62.2b	(.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 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
▶	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 (pow.f64 PI.f64 (.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.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))

Compiler

Compiled 41025 to 30319 computations (26.1% saved)

localize366.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.6b	(pow.f64 PI.f64 4)
	1.6b	(pow.f64 (*.f64 PI.f64 1/2) 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

simplify24.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune2.1s (3.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	465	1	466
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	466	3	469

Error

1.9b

Counts

469 → 3

Alt Table

Status	Error	Program
	62.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (fma.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
	62.2b	(.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 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
▶	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 (pow.f64 PI.f64 (.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.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 (pow.f64 PI.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.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))

Compiler

Compiled 42565 to 31628 computations (25.7% saved)

localize368.0ms (0.6%)

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 PI.f64 1/2) 4)
	1.6b	(pow.f64 PI.f64 4)
	1.6b	(pow.f64 PI.f64 4)

rewrite8.0ms (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:

6.0ms

(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))

simplify168.0ms (0.3%)

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

prune2.6s (4.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1593	1	1594
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	1594	3	1597

Error

1.9b

Counts

1597 → 3

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 (pow.f64 PI.f64 (.f64 (cbrt.f64 6) (cbrt.f64 6))) (cbrt.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 (pow.f64 (pow.f64 PI.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 2)) (cbrt.f64 (sqrt.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))
	62.2b	(.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 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))
	62.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (fma.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (/.f64 -4 PI.f64))

Compiler

Compiled 45944 to 34344 computations (25.2% saved)

regimes25.8s (45.3%)

Accuracy

Total 0.5b remaining (19.6%)

Threshold costs 0.5b (19.6%)

Compiler

Compiled 503106 to 377078 computations (25% saved)

simplify42.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

46×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	728
1	204	728
2	209	728
3	211	728
4	212	728
5	211	728

end16.0ms (0%)

Compiler: Compiled 453 to 341 computations (24.7% saved)

sample17.7s (31.1%)

Algorithm

1×

intervals

Results

4.9s	3954×	body	1024	valid
4.6s	3864×	body	1024	nan
1.7s	1896×	body	512	valid
1.7s	2017×	body	512	nan
1.2s	494×	body	2048	valid
597.0ms	998×	body	256	valid
548.0ms	1007×	body	256	nan
223.0ms	658×	body	128	valid
5.0ms	2×	body	2048	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 1032 to 777 computations (24.7% saved)

Details

analyze3.0s (5.3%)

sample613.0ms (1.1%)

simplify67.0ms (0.1%)

prune8.0ms (0%)

localize31.0ms (0.1%)

rewrite68.0ms (0.1%)

series268.0ms (0.5%)

simplify448.0ms (0.8%)

prune649.0ms (1.1%)

localize351.0ms (0.6%)

rewrite13.0ms (0%)

series0.0ms (0%)

simplify95.0ms (0.2%)

prune2.2s (3.8%)

localize366.0ms (0.6%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify24.0ms (0%)

prune2.1s (3.6%)

localize368.0ms (0.6%)

rewrite8.0ms (0%)

series0.0ms (0%)

simplify168.0ms (0.3%)

prune2.6s (4.5%)

regimes25.8s (45.3%)

simplify42.0ms (0.1%)

end16.0ms (0%)

sample17.7s (31.1%)

Profiling