Details

analyze1.3s (6.8%)

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)

sample11.4s (60.1%)

Results

3.5s	3961×	body	1024	valid
3.4s	4008×	body	1024	invalid
1.3s	2077×	body	512	valid
1.2s	2077×	body	512	invalid
741.0ms	502×	body	2048	valid
522.0ms	955×	body	256	invalid
506.0ms	1040×	body	256	valid
187.0ms	676×	body	128	valid
2.0ms	2×	body	2048	invalid
0.0ms	2×	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

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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 (PI.f64) 4) 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))))
✓	5.1b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series614.0ms (3.2%)

Counts

4 → 48

Calls

4 calls:

570.0ms	(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)))))
32.0ms	(/.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)))
3.0ms	(*.f64 (/.f64 (PI.f64) 4) f)

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64`
103×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
53×	`add-cube-cbrt_binary64`
34×	`log-prod_binary64`

Counts

4 → 186

Calls

4 calls:

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 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) 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))))
9.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
5.0ms	(*.f64 (/.f64 (PI.f64) 4) f)

simplify380.0ms (2%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-def_binary64`
491×	`times-frac_binary64`
415×	`fma-neg_binary64`
279×	`cancel-sign-sub-inv_binary64`
197×	`unswap-sqr_binary64`

Counts

234 → 298

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	373	13558
1	804	11600
2	2324	10673
3	4091	10644
4	4869	10644
5	4842	10644

prune362.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	351	5	356
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	352	5	357

Error

1.7b

Counts

357 → 5

Alt Table

Status	Error	Program
	62.2b	(.f64 (exp.f64 (log.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)))
	2.6b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	62.2b	(.f64 (+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 (PI.f64) f))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
▶	2.5b	(.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)))
	62.2b	(.f64 (+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (cbrt.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 17802 to 11928 computations (33% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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)))

series41.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

34.0ms	(.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)

rewrite25.0ms (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)

simplify91.0ms (0.5%)

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

prune286.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	172	8	180
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	173	12	185

Error

1.5b

Counts

185 → 12

Alt Table

Status	Error	Program
	62.2b	(.f64 (exp.f64 (log.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)))
	2.6b	(.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))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	62.2b	(.f64 (+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 (PI.f64) f))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
	2.7b	(/.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)) (/.f64 -4 (PI.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))))))
	2.6b	(.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))))
	2.5b	(-.f64 (+.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3)))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
	2.6b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.8b	(.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))))
	3.3b	(.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))))
▶	2.4b	(/.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))) -4) (PI.f64))
	62.2b	(.f64 (+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	2.7b	(/.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)))

Compiler

Compiled 8571 to 5808 computations (32.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (.f64 f f) (pow.f64 (PI.f64) 2))
✓	0.3b	(/.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))) -4) (PI.f64))
	1.6b	(pow.f64 (PI.f64) 4)
	2.0b	(log.f64 (/.f64 4 (PI.f64)))

series35.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

35.0ms

(/.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))) -4) (PI.f64))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
3×	`associate-/r*_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`

Counts

1 → 25

Calls

1 calls:

7.0ms

(/.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))) -4) (PI.f64))

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

422×	`fma-neg_binary64`
415×	`times-frac_binary64`
363×	`associate-/l*_binary64`
309×	`associate-l_binary64`
287×	`associate-r_binary64`

Counts

37 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	2005
1	308	1716
2	1024	1685
3	4676	1681
4	4953	1681

prune260.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	151	12	163

Error

1.4b

Counts

163 → 12

Alt Table

Status	Error	Program
	62.2b	(.f64 (exp.f64 (log.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)))
	2.6b	(.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))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	62.2b	(.f64 (+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 (PI.f64) f))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
	2.7b	(/.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)) (/.f64 -4 (PI.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))))))
▶	2.5b	(/.f64 1 (/.f64 (PI.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))) -4)))
	2.7b	(/.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)))
	2.6b	(.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))))
	2.5b	(-.f64 (+.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3)))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
	2.6b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.8b	(.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))))
	3.3b	(.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))))
	62.2b	(.f64 (+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (cbrt.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 6908 to 4680 computations (32.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (.f64 f f) (pow.f64 (PI.f64) 2))
✓	0.3b	(/.f64 (PI.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))) -4))
	1.6b	(pow.f64 (PI.f64) 4)
	2.0b	(log.f64 (/.f64 4 (PI.f64)))

series47.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

47.0ms

(/.f64 (PI.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))) -4))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
3×	`associate-/l*_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`

Counts

1 → 25

Calls

1 calls:

5.0ms

(/.f64 (PI.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))) -4))

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

699×	`associate-/l*_binary64`
511×	`fma-def_binary64`
229×	`distribute-rgt-in_binary64`
213×	`distribute-lft-in_binary64`
164×	`associate-/l/_binary64`

Counts

37 → 51

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2606
1	545	2310
2	2033	2268
3	5470	2268

prune326.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	152	12	164

Error

1.4b

Counts

164 → 12

Alt Table

Status	Error	Program
	62.2b	(.f64 (exp.f64 (log.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)))
	2.6b	(.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))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.4b	(/.f64 1 (-.f64 (+.f64 (.f64 7/2211840 (/.f64 (.f64 (pow.f64 f 6) (pow.f64 (PI.f64) 7)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 3))) (+.f64 (.f64 1/192 (/.f64 (.f64 (pow.f64 f 2) (pow.f64 (PI.f64) 3)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 2))) (.f64 1/442368 (/.f64 (.f64 (pow.f64 f 6) (pow.f64 (PI.f64) 7)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 4))))) (+.f64 (.f64 1/9216 (/.f64 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 5)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 3))) (+.f64 (.f64 7/92160 (/.f64 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 5)) (pow.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) 2))) (*.f64 1/4 (/.f64 (PI.f64) (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))))))))
	62.2b	(.f64 (+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 (PI.f64) f))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
	2.6b	(.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))))
	2.5b	(-.f64 (+.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3)))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))
	2.6b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.8b	(.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))))
	3.3b	(.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))))
	2.5b	(/.f64 1 (.f64 (PI.f64) (/.f64 -1/4 (-.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))))))
	62.2b	(.f64 (+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (cbrt.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	2.7b	(/.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)))

Compiler

Compiled 7182 to 5040 computations (29.8% saved)

regimes3.0s (15.8%)

Accuracy

Total 0.7b remaining (31.7%)

Threshold costs 0.7b (31.7%)

Counts

376 → 1

Compiler

Compiled 90300 to 68228 computations (24.4% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
7×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	62
1	47	62
2	54	62
3	64	62
4	71	62
5	76	62
6	78	62
7	76	62

end463.0ms (2.4%)

Compiler: Compiled 786 to 577 computations (26.6% saved)

Details

analyze1.3s (6.8%)

sample11.4s (60.1%)

simplify49.0ms (0.3%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series614.0ms (3.2%)

rewrite56.0ms (0.3%)

simplify380.0ms (2%)

prune362.0ms (1.9%)

localize17.0ms (0.1%)

series41.0ms (0.2%)

rewrite25.0ms (0.1%)

simplify91.0ms (0.5%)

prune286.0ms (1.5%)

localize18.0ms (0.1%)

series35.0ms (0.2%)

rewrite9.0ms (0%)

simplify75.0ms (0.4%)

prune260.0ms (1.4%)

localize19.0ms (0.1%)

series47.0ms (0.2%)

rewrite7.0ms (0%)

simplify68.0ms (0.4%)

prune326.0ms (1.7%)

regimes3.0s (15.8%)

simplify5.0ms (0%)

end463.0ms (2.4%)

Profiling