Details

analyze1.3s (8.2%)

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)

sample420.0ms (2.6%)

Algorithm

1×

intervals

Results

136.0ms	131×	body	1024	valid
84.0ms	117×	body	1024	nan
35.0ms	65×	body	512	nan
30.0ms	64×	body	512	valid
23.0ms	18×	body	2048	valid
10.0ms	36×	body	256	nan
9.0ms	28×	body	256	valid
2.0ms	15×	body	128	valid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify47.0ms (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

61.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.9b	(.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

▶

61.9b

(*.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 (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (PI.f64) f)
✓	0.4b	(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))))
✓	3.1b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series869.0ms (5.4%)

Counts

4 → 48

Calls

4 calls:

820.0ms	(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)))))
34.0ms	(/.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)))
6.0ms	(*.f64 (PI.f64) f)

rewrite49.0ms (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))))
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)))))
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)

simplify342.0ms (2.1%)

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

prune340.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	293	6	299
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	294	6	300

Error

2.4b

Counts

300 → 6

Alt Table

Status	Error	Program
	61.9b	(.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)))
▶	2.9b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	61.9b	(.f64 (log.f64 (.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) 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)))
	3.1b	(*.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (/.f64 -4 (PI.f64)))
	62.0b	(.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 (/.f64 (PI.f64) 4) f))) (pow.f64 (exp.f64 -1/4) (/.f64 (.f64 (PI.f64) f) 2))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (exp.f64 -1/4) (/.f64 (.f64 (PI.f64) f) 2)))))) (/.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)))

Compiler

Compiled 15332 to 9952 computations (35.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))
✓	0.2b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.3b	(*.f64 f (PI.f64))
✓	0.4b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

series38.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

21.0ms	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
8.0ms	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))
6.0ms	(/.f64 4 (*.f64 f (PI.f64)))
2.0ms	(*.f64 f (PI.f64))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 88

Calls

4 calls:

5.0ms	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
5.0ms	(/.f64 4 (*.f64 f (PI.f64)))
3.0ms	(*.f64 f (PI.f64))
0.0ms	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))

simplify184.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
336×	`fma-neg_binary64`
319×	`associate-/r*_binary64`
281×	`associate-*l/_binary64`
280×	`associate-*r/_binary64`

Counts

112 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	2580
1	546	2310
2	1707	2301
3	4281	2293
4	4990	2293
5	4930	2293

prune208.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	196	7	203
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	197	12	209

Error

2.1b

Counts

209 → 12

Alt Table

Status	Error	Program
	3.2b	(cbrt.f64 (pow.f64 (.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f)))) (/.f64 -4 (PI.f64))) 3))
	62.0b	(.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 (/.f64 (PI.f64) 4) f))) (pow.f64 (exp.f64 -1/4) (/.f64 (.f64 (PI.f64) f) 2))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (exp.f64 -1/4) (/.f64 (.f64 (PI.f64) f) 2)))))) (/.f64 -4 (PI.f64)))
	61.9b	(.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)))
	62.6b	(log1p.f64 (expm1.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))
	61.9b	(.f64 (log.f64 (.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) 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)))
	3.1b	(*.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (/.f64 -4 (PI.f64)))
	3.2b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64))))
▶	2.8b	(.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (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)))
	2.9b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (log1p.f64 (expm1.f64 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	2.9b	(fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	3.8b	(.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64))))

Compiler

Compiled 5229 to 3143 computations (39.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
✓	0.3b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64))))
	0.3b	(*.f64 f (PI.f64))
✓	1.0b	(sqrt.f64 (PI.f64))

series44.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

23.0ms

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

21.0ms

(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64))))

0.0ms

(sqrt.f64 (PI.f64))

rewrite34.0ms (0.2%)

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:

12.0ms

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

8.0ms

(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64))))

1.0ms

(sqrt.f64 (PI.f64))

simplify234.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-def_binary64`
397×	`cancel-sign-sub-inv_binary64`
396×	`fma-neg_binary64`
284×	`times-frac_binary64`
260×	`associate-l_binary64`

Counts

145 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	296	5315
1	791	4548
2	2665	4280
3	4517	4270
4	4952	4270
5	5000	4270
6	4908	4270

prune312.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	283	3	286
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	288	10	298

Error

2.1b

Counts

298 → 10

Alt Table

Status	Error	Program
	3.2b	(cbrt.f64 (pow.f64 (.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f)))) (/.f64 -4 (PI.f64))) 3))
	62.0b	(.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 (/.f64 (PI.f64) 4) f))) (pow.f64 (exp.f64 -1/4) (/.f64 (.f64 (PI.f64) f) 2))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (exp.f64 -1/4) (/.f64 (.f64 (PI.f64) f) 2)))))) (/.f64 -4 (PI.f64)))
	61.9b	(.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)))
	62.6b	(log1p.f64 (expm1.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))
▶	2.8b	(.f64 (log.f64 (pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (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)))
	2.8b	(.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (log1p.f64 (expm1.f64 (.f64 (PI.f64) f)))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.9b	(fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	2.9b	(.f64 (.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))) (/.f64 -4 (sqrt.f64 (cbrt.f64 (PI.f64)))))
	61.9b	(.f64 (log.f64 (.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) 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 9010 to 5246 computations (41.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (PI.f64) f)
✓	1.0b	(*.f64 (PI.f64) 1/12)
	1.0b	(sqrt.f64 (PI.f64))
✓	3.9b	(pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (.f64 (PI.f64) f))) (sqrt.f64 (/.f64 1 (PI.f64))))

series34.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

34.0ms	(pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (.f64 (PI.f64) f))) (sqrt.f64 (/.f64 1 (PI.f64))))
0.0ms	(*.f64 (PI.f64) 1/12)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow-unpow_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

2 → 52

Calls

2 calls:

4.0ms	(*.f64 (PI.f64) 1/12)
3.0ms	(pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (.f64 (PI.f64) f))) (sqrt.f64 (/.f64 1 (PI.f64))))

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
643×	`associate-l_binary64`
274×	`times-frac_binary64`
267×	`associate-/r*_binary64`
249×	`cancel-sign-sub-inv_binary64`

Counts

64 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	2757
1	563	2680
2	1729	2251
3	5167	2251

prune190.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	130	11	141

Error

2.1b

Counts

141 → 11

Alt Table

Status	Error	Program
	3.2b	(cbrt.f64 (pow.f64 (.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f)))) (/.f64 -4 (PI.f64))) 3))
	62.0b	(.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 (/.f64 (PI.f64) 4) f))) (pow.f64 (exp.f64 -1/4) (/.f64 (.f64 (PI.f64) f) 2))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (exp.f64 -1/4) (/.f64 (.f64 (PI.f64) f) 2)))))) (/.f64 -4 (PI.f64)))
	62.9b	(.f64 (log.f64 (pow.f64 (.f64 f (*.f64 (PI.f64) 1/12)) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	61.9b	(.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)))
	62.6b	(log1p.f64 (expm1.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))
✓	2.8b	(.f64 (log.f64 (pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (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)))
	2.8b	(.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (log1p.f64 (expm1.f64 (.f64 (PI.f64) f)))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.9b	(fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	2.9b	(.f64 (.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))) (/.f64 -4 (sqrt.f64 (cbrt.f64 (PI.f64)))))
	61.9b	(.f64 (log.f64 (.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) 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 5044 to 3460 computations (31.4% saved)

regimes1.8s (11%)

Accuracy

Total 0.7b remaining (30.8%)

Threshold costs 0.7b (30.8%)

Counts

242 → 1

Compiler

Compiled 51024 to 36590 computations (28.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	23	36
2	22	36

end1.0ms (0%)

Compiler: Compiled 22 to 17 computations (22.7% saved)

sample9.5s (58.9%)

Algorithm

1×

intervals

Results

3.0s	3993×	body	1024	nan
2.6s	3938×	body	1024	valid
915.0ms	1953×	body	512	valid
856.0ms	1951×	body	512	nan
688.0ms	499×	body	2048	valid
317.0ms	984×	body	256	valid
303.0ms	1019×	body	256	nan
104.0ms	626×	body	128	valid
2.0ms	2×	body	2048	nan
0.0ms	3×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 388 to 286 computations (26.3% saved)

Details

analyze1.3s (8.2%)

sample420.0ms (2.6%)

simplify47.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series869.0ms (5.4%)

rewrite49.0ms (0.3%)

simplify342.0ms (2.1%)

prune340.0ms (2.1%)

localize8.0ms (0.1%)

series38.0ms (0.2%)

rewrite17.0ms (0.1%)

simplify184.0ms (1.1%)

prune208.0ms (1.3%)

localize11.0ms (0.1%)

series44.0ms (0.3%)

rewrite34.0ms (0.2%)

simplify234.0ms (1.5%)

prune312.0ms (1.9%)

localize17.0ms (0.1%)

series34.0ms (0.2%)

rewrite10.0ms (0.1%)

simplify75.0ms (0.5%)

prune190.0ms (1.2%)

regimes1.8s (11%)

simplify2.0ms (0%)

end1.0ms (0%)

sample9.5s (58.9%)

Profiling