Details

analyze3.0s (13.5%)

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)

sample648.0ms (2.9%)

Algorithm

1×

intervals

Results

221.0ms	133×	body	1024	nan
196.0ms	143×	body	1024	valid
63.0ms	53×	body	512	valid
59.0ms	62×	body	512	nan
41.0ms	15×	body	2048	valid
19.0ms	31×	body	256	nan
18.0ms	27×	body	256	valid
6.0ms	18×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify105.0ms (0.5%)

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

60.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.7b	(.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

▶

60.7b

(*.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)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (PI.f64) f)
✓	0.2b	(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)))))
✓	1.5b	(/.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))))
✓	3.9b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series1.4s (6.1%)

Counts

4 → 48

Calls

4 calls:

1.3s	(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)))))
72.0ms	(/.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))))
17.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
5.0ms	(*.f64 (PI.f64) f)

rewrite109.0ms (0.5%)

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:

21.0ms	(/.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))))
21.0ms	(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)))))
12.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
6.0ms	(*.f64 (PI.f64) f)

simplify598.0ms (2.7%)

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

prune588.0ms (2.6%)

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

2.3b

Counts

300 → 5

Alt Table

Status	Error	Program
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	3.6b	(*.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (/.f64 -4 (PI.f64)))
▶	2.9b	(.f64 (log.f64 (-.f64 (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)))
	3.1b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	60.7b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (expm1.f64 (log1p.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 15174 to 9842 computations (35.1% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 f (PI.f64))
✓	0.2b	(log.f64 (-.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (.f64 (pow.f64 (.f64 f (PI.f64)) 3) 1/2880)))
✓	0.3b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.5b	(.f64 (log.f64 (-.f64 (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)))

series106.0ms (0.5%)

Counts

4 → 24

Calls

4 calls:

51.0ms	(.f64 (log.f64 (-.f64 (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)))
35.0ms	(log.f64 (-.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (.f64 (pow.f64 (.f64 f (PI.f64)) 3) 1/2880)))
15.0ms	(/.f64 4 (*.f64 f (PI.f64)))
4.0ms	(*.f64 f (PI.f64))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64`
16×	`associate-r_binary64`

Counts

4 → 94

Calls

4 calls:

12.0ms	(.f64 (log.f64 (-.f64 (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)))
5.0ms	(/.f64 4 (*.f64 f (PI.f64)))
5.0ms	(log.f64 (-.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (.f64 (pow.f64 (.f64 f (PI.f64)) 3) 1/2880)))
5.0ms	(*.f64 f (PI.f64))

simplify223.0ms (1%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-def_binary64`
342×	`cancel-sign-sub-inv_binary64`
278×	`times-frac_binary64`
255×	`fma-neg_binary64`
196×	`distribute-rgt-neg-in_binary64`

Counts

118 → 200

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	294	4066
1	772	3648
2	2549	3516
3	4815	3512
4	4928	3512

prune670.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	253	9	262
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	255	12	267

Error

1.9b

Counts

267 → 12

Alt Table

Status	Error	Program
	3.5b	(.f64 (expm1.f64 (log1p.f64 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	3.5b	(.f64 (exp.f64 (log.f64 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	60.7b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (expm1.f64 (log1p.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	3.0b	(.f64 (/.f64 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
▶	2.8b	(.f64 (.f64 (log.f64 (-.f64 (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 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.9b	(fma.f64 4 (/.f64 (log.f64 f) (PI.f64)) (fma.f64 (PI.f64) (.f64 (.f64 f f) -1/12) (*.f64 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) -4)))
	2.9b	(/.f64 (.f64 -4 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f)))))) (PI.f64))
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	3.2b	(cbrt.f64 (.f64 (.f64 (.f64 (log.f64 (-.f64 (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))) (.f64 (log.f64 (-.f64 (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)))) (.f64 (log.f64 (-.f64 (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)))))
	3.0b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))))) (log.f64 (cbrt.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	3.1b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	3.1b	(.f64 (sqrt.f64 (log.f64 (-.f64 (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 (/.f64 -4 (PI.f64)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f))))))))

Compiler

Compiled 8969 to 5375 computations (40.1% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (log.f64 (-.f64 (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 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	0.3b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.3b	(.f64 (log.f64 (-.f64 (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 1 (sqrt.f64 (PI.f64))))
✓	1.0b	(sqrt.f64 (PI.f64))

series96.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

48.0ms

(*.f64 (log.f64 (-.f64 (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 1 (sqrt.f64 (PI.f64))))

48.0ms

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

0.0ms

(sqrt.f64 (PI.f64))

rewrite66.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-exp-log_binary64`
44×	`associate-r_binary64`
44×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`

Counts

3 → 121

Calls

3 calls:

20.0ms

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

15.0ms

(*.f64 (log.f64 (-.f64 (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 1 (sqrt.f64 (PI.f64))))

2.0ms

(sqrt.f64 (PI.f64))

simplify305.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

771×	`times-frac_binary64`
712×	`fma-def_binary64`
445×	`cancel-sign-sub-inv_binary64`
275×	`associate-l_binary64`
220×	`fma-neg_binary64`

Counts

145 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	310	7074
1	851	6083
2	2876	5792
3	4735	5790
4	5322	5790

prune595.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	256	3	259
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	262	9	271

Error

1.9b

Counts

271 → 9

Alt Table

Status	Error	Program
	3.1b	(.f64 (log.f64 (-.f64 (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 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64)))))
	2.9b	(/.f64 (.f64 -4 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f)))))) (PI.f64))
▶	2.7b	(.f64 (log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	3.7b	(.f64 (.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (sqrt.f64 (/.f64 1 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	3.1b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	60.7b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (expm1.f64 (log1p.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
✓	2.8b	(.f64 (.f64 (log.f64 (-.f64 (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 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	3.1b	(.f64 (sqrt.f64 (log.f64 (-.f64 (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 (/.f64 -4 (PI.f64)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f))))))))

Compiler

Compiled 10362 to 6183 computations (40.3% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64))))
✓	0.3b	(/.f64 4 (*.f64 (PI.f64) f))
	1.0b	(sqrt.f64 (PI.f64))
✓	4.0b	(pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f)))) (sqrt.f64 (/.f64 1 (PI.f64))))

series265.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

133.0ms

(*.f64 (log.f64 (pow.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (*.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64))))

115.0ms

(pow.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (*.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f)))) (sqrt.f64 (/.f64 1 (PI.f64))))

16.0ms

(/.f64 4 (*.f64 (PI.f64) f))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
23×	`sqrt-prod_binary64`

Counts

3 → 100

Calls

3 calls:

15.0ms

(*.f64 (log.f64 (pow.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (*.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64))))

6.0ms

(pow.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (*.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f)))) (sqrt.f64 (/.f64 1 (PI.f64))))

6.0ms

(/.f64 4 (*.f64 (PI.f64) f))

simplify323.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

529×	`times-frac_binary64`
459×	`fma-neg_binary64`
245×	`associate-l_binary64`
240×	`associate-r_binary64`
187×	`*-commutative_binary64`

Counts

136 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	6755
1	989	6287
2	3399	6187
3	4847	6187
4	5055	6187

prune496.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	201	9	210

Error

1.9b

Counts

210 → 9

Alt Table

Status	Error	Program
	3.1b	(.f64 (log.f64 (-.f64 (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 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64)))))
	2.9b	(/.f64 (.f64 -4 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f)))))) (PI.f64))
✓	2.7b	(.f64 (log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	3.7b	(.f64 (.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (sqrt.f64 (/.f64 1 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	3.1b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	60.7b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (expm1.f64 (log1p.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
✓	2.8b	(.f64 (.f64 (log.f64 (-.f64 (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 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	3.1b	(.f64 (sqrt.f64 (log.f64 (-.f64 (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 (/.f64 -4 (PI.f64)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f))))))))

Compiler

Compiled 9093 to 5950 computations (34.6% saved)

regimes1.7s (7.4%)

Accuracy

Total 0.8b remaining (34.8%)

Threshold costs 0.8b (34.8%)

Counts

118 → 1

Compiler

Compiled 25476 to 17576 computations (31% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	47
1	25	47
2	24	47

end2.0ms (0%)

Compiler: Compiled 29 to 20 computations (31% saved)

sample11.0s (48.8%)

Algorithm

1×

intervals

Results

3.2s	3902×	body	1024	valid
3.1s	3941×	body	1024	nan
1.1s	1922×	body	512	nan
1.1s	1961×	body	512	valid
762.0ms	489×	body	2048	valid
460.0ms	1007×	body	256	valid
376.0ms	987×	body	256	nan
132.0ms	641×	body	128	valid
2.0ms	2×	body	2048	nan
1.0ms	4×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 330 to 234 computations (29.1% saved)

Details

analyze3.0s (13.5%)

sample648.0ms (2.9%)

simplify105.0ms (0.5%)

prune8.0ms (0%)

localize35.0ms (0.2%)

series1.4s (6.1%)

rewrite109.0ms (0.5%)

simplify598.0ms (2.7%)

prune588.0ms (2.6%)

localize25.0ms (0.1%)

series106.0ms (0.5%)

rewrite39.0ms (0.2%)

simplify223.0ms (1%)

prune670.0ms (3%)

localize34.0ms (0.2%)

series96.0ms (0.4%)

rewrite66.0ms (0.3%)

simplify305.0ms (1.4%)

prune595.0ms (2.6%)

localize36.0ms (0.2%)

series265.0ms (1.2%)

rewrite46.0ms (0.2%)

simplify323.0ms (1.4%)

prune496.0ms (2.2%)

regimes1.7s (7.4%)

simplify6.0ms (0%)

end2.0ms (0%)

sample11.0s (48.8%)

Profiling