Details

analyze1.3s (7.2%)

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)

sample11.6s (62.6%)

Results

3.6s	4135×	body	1024	valid
3.5s	4080×	body	1024	invalid
1.3s	1940×	body	512	valid
1.3s	2045×	body	512	invalid
902.0ms	548×	body	2048	valid
436.0ms	1009×	body	256	valid
382.0ms	974×	body	256	invalid
143.0ms	624×	body	128	valid
3.0ms	3×	body	2048	invalid
1.0ms	4×	body	128	invalid

Compiler

Compiled 116 to 92 computations (20.7% saved)

simplify49.0ms (0.3%)

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

61.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.8b	(.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

▶

61.8b

(*.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)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (PI.f64) f)
✓	0.3b	(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)))))
✓	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))))
✓	6.2b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series648.0ms (3.5%)

Counts

4 → 48

Calls

4 calls:

601.0ms	(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)))))
35.0ms	(/.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))))
9.0ms	(-.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)

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
56×	`times-frac_binary64`
47×	`add-cube-cbrt_binary64`
34×	`log-prod_binary64`

Counts

4 → 172

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))))
10.0ms	(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)))))
6.0ms	(-.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)

simplify285.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

759×	`times-frac_binary64`
446×	`fma-neg_binary64`
309×	`cancel-sign-sub-inv_binary64`
196×	`unswap-sqr_binary64`
193×	`exp-prod_binary64`

Counts

220 → 269

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	339	12804
1	728	11342
2	2171	10169
3	4156	10095
4	5101	10095

prune305.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	294	5	299
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	295	5	300

Error

1.5b

Counts

300 → 5

Alt Table

Status	Error	Program
	2.1b	(.f64 (log.f64 (-.f64 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (.f64 (pow.f64 (.f64 f (PI.f64)) 3) 1/2880))) (/.f64 -4 (PI.f64)))
	61.8b	(.f64 (+.f64 (log.f64 (sqrt.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)))))) (log.f64 (sqrt.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)))
	2.3b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	61.8b	(.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 (PI.f64)))) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2)) (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4)))))) (/.f64 -4 (PI.f64)))
▶	2.0b	(.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 15308 to 9928 computations (35.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 f f) (pow.f64 (PI.f64) 2))
✓	0.4b	(.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 -4 (PI.f64)))
✓	1.6b	(pow.f64 (PI.f64) 4)
✓	2.0b	(log.f64 (/.f64 4 (PI.f64)))

series45.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

39.0ms	(.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 -4 (PI.f64)))
7.0ms	(.f64 (.f64 f f) (pow.f64 (PI.f64) 2))
0.0ms	(log.f64 (/.f64 4 (PI.f64)))
0.0ms	(pow.f64 (PI.f64) 4)

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
26×	`add-exp-log_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

4 → 117

Calls

4 calls:

7.0ms	(.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 -4 (PI.f64)))
6.0ms	(.f64 (.f64 f f) (pow.f64 (PI.f64) 2))
2.0ms	(log.f64 (/.f64 4 (PI.f64)))
1.0ms	(pow.f64 (PI.f64) 4)

simplify107.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

449×	`distribute-rgt-in_binary64`
423×	`distribute-lft-in_binary64`
353×	`fma-def_binary64`
347×	`times-frac_binary64`
182×	`associate-l_binary64`

Counts

141 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	4144
1	571	3732
2	1915	3677
3	5238	3677

prune300.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	173	7	180
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	174	11	185

Error

1.3b

Counts

185 → 11

Alt Table

Status	Error	Program
▶	1.9b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (*.f64 4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))))
	2.0b	(.f64 (.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (*.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.1b	(.f64 (log.f64 (-.f64 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (.f64 (pow.f64 (.f64 f (PI.f64)) 3) 1/2880))) (/.f64 -4 (PI.f64)))
	61.8b	(.f64 (+.f64 (log.f64 (sqrt.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)))))) (log.f64 (sqrt.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)))
	2.3b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	61.8b	(.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 (PI.f64)))) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2)) (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4)))))) (/.f64 -4 (PI.f64)))
	2.2b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) 3) (pow.f64 (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f)) 3)) -4) (.f64 (+.f64 (.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64))))) (+.f64 (.f64 (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f)) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (*.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))))) (PI.f64)))
	2.3b	(cbrt.f64 (pow.f64 (.f64 (-.f64 (fma.f64 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) 1/48 (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 -4 (PI.f64))) 3))
	2.3b	(.f64 (sqrt.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f)))) (.f64 (sqrt.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f)))) (/.f64 -4 (PI.f64))))
	2.9b	(.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f)))) (cbrt.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))))) (.f64 (cbrt.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f)))) (/.f64 -4 (PI.f64))))
	2.2b	(/.f64 (.f64 (-.f64 (.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64))))) (.f64 (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f)) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f)))) (/.f64 -4 (PI.f64))) (+.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))))

Compiler

Compiled 8351 to 5638 computations (32.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))
✓	0.3b	(/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64))
✓	1.0b	(pow.f64 (PI.f64) 3)
	2.0b	(log.f64 (/.f64 4 (PI.f64)))

series538.0ms (2.9%)

Counts

3 → 16

Calls

3 calls:

276.0ms	(/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64))
262.0ms	(-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))
0.0ms	(pow.f64 (PI.f64) 3)

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
34×	`pow1_binary64`
33×	`times-frac_binary64`

Counts

3 → 136

Calls

3 calls:

8.0ms	(-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))
8.0ms	(/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64))
2.0ms	(pow.f64 (PI.f64) 3)

simplify129.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

865×	`fma-def_binary64`
577×	`fma-neg_binary64`
515×	`times-frac_binary64`
279×	`exp-prod_binary64`
245×	`unswap-sqr_binary64`

Counts

152 → 129

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	2795
1	397	2629
2	1529	2523
3	3662	2521
4	4972	2521
5	4900	2521

prune301.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	158	6	164
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	163	12	175

Error

1.2b

Counts

175 → 12

Alt Table

Status	Error	Program
	2.1b	(.f64 (log.f64 (-.f64 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (.f64 (pow.f64 (.f64 f (PI.f64)) 3) 1/2880))) (/.f64 -4 (PI.f64)))
	61.8b	(.f64 (+.f64 (log.f64 (sqrt.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)))))) (log.f64 (sqrt.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)))
	2.0b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (*.f64 4 (/.f64 (-.f64 (log.f64 4) (+.f64 (log.f64 (PI.f64)) (log.f64 f))) (PI.f64)))))
	61.8b	(.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 (PI.f64)))) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2)) (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4)))))) (/.f64 -4 (PI.f64)))
	2.3b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
▶	2.0b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (.f64 4 (.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (/.f64 1 (PI.f64))))))
	2.2b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (.f64 4 (cbrt.f64 (.f64 (*.f64 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)) (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64))) (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))))))
	2.0b	(.f64 (.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (*.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.2b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (*.f64 4 (/.f64 (log.f64 (/.f64 (/.f64 4 (PI.f64)) f)) (PI.f64)))))
	2.7b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (*.f64 4 (/.f64 (expm1.f64 (log1p.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)))) (PI.f64)))))
	2.9b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (.f64 4 (.f64 (*.f64 (cbrt.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))) (cbrt.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)))) (/.f64 (cbrt.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))) (PI.f64))))))
	2.2b	(/.f64 (.f64 (-.f64 (.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64))))) (.f64 (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f)) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f)))) (/.f64 -4 (PI.f64))) (+.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))))

Compiler

Compiled 6987 to 4539 computations (35% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))
✓	0.4b	(*.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (/.f64 1 (PI.f64)))
	1.0b	(pow.f64 (PI.f64) 3)
	2.0b	(log.f64 (/.f64 4 (PI.f64)))

series265.0ms (1.4%)

Counts

1 → 12

Calls

1 calls:

265.0ms

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

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 47

Calls

1 calls:

9.0ms

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

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

757×	`div-sub_binary64`
622×	`fma-def_binary64`
384×	`fma-neg_binary64`
266×	`associate-*l/_binary64`
248×	`distribute-lft-in_binary64`

Counts

59 → 69

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	1313
1	209	1193
2	623	1186
3	1837	1186
4	4174	1178
5	5519	1178

prune328.0ms (1.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	188	12	200

Error

1.2b

Counts

200 → 12

Alt Table

Status	Error	Program
	2.1b	(.f64 (log.f64 (-.f64 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (.f64 (pow.f64 (.f64 f (PI.f64)) 3) 1/2880))) (/.f64 -4 (PI.f64)))
	61.8b	(.f64 (+.f64 (log.f64 (sqrt.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)))))) (log.f64 (sqrt.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)))
	2.0b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (*.f64 4 (/.f64 (-.f64 (log.f64 4) (+.f64 (log.f64 (PI.f64)) (log.f64 f))) (PI.f64)))))
	61.8b	(.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 (PI.f64)))) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2)) (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4)))))) (/.f64 -4 (PI.f64)))
	2.3b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
✓	2.0b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (.f64 4 (.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (/.f64 1 (PI.f64))))))
	2.0b	(.f64 (.f64 (-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (fma.f64 7/23040 (*.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 4)) (log.f64 f))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.2b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (.f64 4 (/.f64 (.f64 (-.f64 (.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 (/.f64 4 (PI.f64)))) (.f64 (log.f64 f) (log.f64 f))) (/.f64 1 (PI.f64))) (+.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))))))
	2.2b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (*.f64 4 (/.f64 (log.f64 (/.f64 (/.f64 4 (PI.f64)) f)) (PI.f64)))))
	2.7b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (*.f64 4 (/.f64 (expm1.f64 (log1p.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)))) (PI.f64)))))
	2.9b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (.f64 4 (.f64 (*.f64 (cbrt.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))) (cbrt.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)))) (/.f64 (cbrt.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))) (PI.f64))))))
	2.3b	(-.f64 (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))) (fma.f64 (PI.f64) (.f64 1/12 (.f64 f f)) (*.f64 4 (log.f64 (pow.f64 (/.f64 (/.f64 4 (PI.f64)) f) (/.f64 1 (PI.f64)))))))

Compiler

Compiled 7637 to 5056 computations (33.8% saved)

regimes1.7s (9.3%)

Accuracy

Total 0.6b remaining (27.8%)

Threshold costs 0.6b (27.8%)

Counts

216 → 1

Compiler

Compiled 53874 to 39296 computations (27.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	46
1	34	46
2	39	46
3	42	46
4	43	46
5	43	46

end296.0ms (1.6%)

Compiler: Compiled 498 to 364 computations (26.9% saved)

Details

analyze1.3s (7.2%)

sample11.6s (62.6%)

simplify49.0ms (0.3%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series648.0ms (3.5%)

rewrite50.0ms (0.3%)

simplify285.0ms (1.5%)

prune305.0ms (1.6%)

localize19.0ms (0.1%)

series45.0ms (0.2%)

rewrite23.0ms (0.1%)

simplify107.0ms (0.6%)

prune300.0ms (1.6%)

localize18.0ms (0.1%)

series538.0ms (2.9%)

rewrite25.0ms (0.1%)

simplify129.0ms (0.7%)

prune301.0ms (1.6%)

localize21.0ms (0.1%)

series265.0ms (1.4%)

rewrite12.0ms (0.1%)

simplify75.0ms (0.4%)

prune328.0ms (1.8%)

regimes1.7s (9.3%)

simplify3.0ms (0%)

end296.0ms (1.6%)

Profiling