Details

analyze1.4s (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)

sample11.7s (62.6%)

Results

3.6s	4036×	body	1024	invalid
3.5s	3973×	body	1024	valid
1.4s	1999×	body	512	valid
1.2s	1935×	body	512	invalid
851.0ms	538×	body	2048	valid
452.0ms	1031×	body	256	valid
436.0ms	1049×	body	256	invalid
171.0ms	715×	body	128	valid
3.0ms	3×	body	2048	invalid
1.0ms	6×	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

61.9b

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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 (PI.f64) 4) f)
✓	0.3b	(*.f64 (PI.f64) f)
✓	2.2b	(/.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))))
✓	5.0b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series45.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

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)
2.0ms	(*.f64 (PI.f64) f)

rewrite37.0ms (0.2%)

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:

10.0ms	(/.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))))
5.0ms	(-.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)
3.0ms	(*.f64 (PI.f64) f)

simplify198.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
588×	`times-frac_binary64`
366×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
196×	`exp-prod_binary64`

Counts

207 → 258

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	312	8603
1	652	7401
2	1996	6651
3	4169	6609
4	4840	6609

prune337.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	345	4	349
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	346	4	350

Error

3.2b

Counts

350 → 4

Alt Table

Status	Error	Program
▶	3.5b	(.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 (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)))
	61.8b	(.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 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	3.6b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 16014 to 10376 computations (35.2% saved)

localize8.0ms (0%)

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))))
✓	0.3b	(*.f64 f (PI.f64))
✓	0.3b	(/.f64 4 (*.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)))

series35.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

20.0ms	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
6.0ms	(/.f64 4 (*.f64 f (PI.f64)))
6.0ms	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.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:

7.0ms	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
3.0ms	(/.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))))

simplify109.0ms (0.6%)

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

prune281.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	194	9	203
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	195	12	207

Error

2.9b

Counts

207 → 12

Alt Table

Status	Error	Program
	4.7b	(.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (*.f64 (cbrt.f64 (/.f64 -4 (PI.f64))) (cbrt.f64 (/.f64 -4 (PI.f64))))) (cbrt.f64 (/.f64 -4 (PI.f64))))
	3.6b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
	3.8b	(.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))))
	62.9b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))
	62.9b	(.f64 -4 (/.f64 (-.f64 (log.f64 (.f64 1/12 (PI.f64))) (log.f64 (/.f64 1 f))) (PI.f64)))
▶	3.4b	(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))
	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))) (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)))
	3.8b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	13.7b	(log.f64 (pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (.f64 (PI.f64) f))) (/.f64 -4 (PI.f64))))
	61.8b	(.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 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	62.4b	(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)))))
	3.5b	(.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))))

Compiler

Compiled 5089 to 3059 computations (39.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (PI.f64) (.f64 f f))
✓	0.3b	(/.f64 (log.f64 f) (PI.f64))
✓	0.4b	(-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
✓	2.0b	(log.f64 (/.f64 4 (PI.f64)))

series308.0ms (1.6%)

Counts

4 → 28

Calls

4 calls:

278.0ms	(-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
26.0ms	(/.f64 (log.f64 f) (PI.f64))
3.0ms	(.f64 (PI.f64) (.f64 f f))
0.0ms	(log.f64 (/.f64 4 (PI.f64)))

rewrite95.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

457×	`times-frac_binary64`
315×	`*-un-lft-identity_binary64`
314×	`add-sqr-sqrt_binary64`
301×	`add-cube-cbrt_binary64`
256×	`prod-diff_binary64`

Counts

4 → 402

Calls

4 calls:

21.0ms	(-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
4.0ms	(.f64 (PI.f64) (.f64 f f))
3.0ms	(/.f64 (log.f64 f) (PI.f64))
2.0ms	(log.f64 (/.f64 4 (PI.f64)))

simplify342.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

505×	`associate-*l/_binary64`
422×	`associate-/l*_binary64`
344×	`fma-neg_binary64`
193×	`associate-/l/_binary64`
156×	`fma-udef_binary64`

Counts

430 → 344

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	419	13465
1	892	10844
2	1789	9724
3	4549	9723
4	4835	9723

prune408.0ms (2.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	339	5	344
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	343	13	356

Error

2.9b

Counts

356 → 13

Alt Table

Status	Error	Program
▶	3.4b	(fma.f64 4 (-.f64 (log.f64 (pow.f64 f (/.f64 1 (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	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))) (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)))
	4.7b	(.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (*.f64 (cbrt.f64 (/.f64 -4 (PI.f64))) (cbrt.f64 (/.f64 -4 (PI.f64))))) (cbrt.f64 (/.f64 -4 (PI.f64))))
	3.6b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
	62.9b	(.f64 -4 (/.f64 (-.f64 (log.f64 (.f64 1/12 (PI.f64))) (log.f64 (/.f64 1 f))) (PI.f64)))
	3.5b	(fma.f64 4 (+.f64 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 4) (PI.f64))) (/.f64 (log.f64 (PI.f64)) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	3.7b	(fma.f64 4 (/.f64 (-.f64 (.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 f) (PI.f64))) (pow.f64 (sqrt.f64 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) 4)) (+.f64 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (/.f64 (log.f64 f) (PI.f64)))) (.f64 (.f64 (PI.f64) (.f64 f f)) -1/12))
	61.8b	(.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 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	3.5b	(fma.f64 4 (/.f64 (.f64 (PI.f64) (-.f64 (log.f64 f) (log.f64 (/.f64 4 (PI.f64))))) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	62.4b	(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)))))
	3.5b	(fma.f64 4 (fma.f64 (log.f64 f) (/.f64 1 (PI.f64)) (neg.f64 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	3.5b	(.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))))
	62.9b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))

Compiler

Compiled 17952 to 10039 computations (44.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (PI.f64) (.f64 f f))
✓	0.4b	(-.f64 (log.f64 (pow.f64 f (/.f64 1 (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
	2.0b	(log.f64 (/.f64 4 (PI.f64)))
✓	4.9b	(pow.f64 f (/.f64 1 (PI.f64)))

series644.0ms (3.4%)

Counts

2 → 24

Calls

2 calls:

613.0ms	(-.f64 (log.f64 (pow.f64 f (/.f64 1 (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
31.0ms	(pow.f64 f (/.f64 1 (PI.f64)))

rewrite47.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
70×	`times-frac_binary64`
69×	`add-cube-cbrt_binary64`
64×	`prod-diff_binary64`

Counts

2 → 137

Calls

2 calls:

10.0ms	(-.f64 (log.f64 (pow.f64 f (/.f64 1 (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
3.0ms	(pow.f64 f (/.f64 1 (PI.f64)))

simplify164.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
448×	`associate-*l/_binary64`
343×	`associate-/l*_binary64`
238×	`fma-neg_binary64`
179×	`exp-prod_binary64`

Counts

161 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	250	5261
1	587	4065
2	1360	2941
3	4435	2929
4	4983	2929
5	4760	2929

prune304.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	222	11	233

Error

2.9b

Counts

233 → 11

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 4 (-.f64 (log.f64 (pow.f64 f (/.f64 1 (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	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))) (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)))
	3.6b	(fma.f64 4 (-.f64 (log.f64 (pow.f64 (pow.f64 f (sqrt.f64 (/.f64 1 (PI.f64)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	62.4b	(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)))))
	4.7b	(.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (*.f64 (cbrt.f64 (/.f64 -4 (PI.f64))) (cbrt.f64 (/.f64 -4 (PI.f64))))) (cbrt.f64 (/.f64 -4 (PI.f64))))
	3.6b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
	62.9b	(.f64 -4 (/.f64 (-.f64 (log.f64 (.f64 1/12 (PI.f64))) (log.f64 (/.f64 1 f))) (PI.f64)))
	61.8b	(.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 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	3.5b	(fma.f64 4 (fma.f64 (log.f64 f) (/.f64 1 (PI.f64)) (neg.f64 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	3.5b	(.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))))
	62.9b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))

Compiler

Compiled 9004 to 5757 computations (36.1% saved)

regimes2.0s (10.5%)

Accuracy

Total 0.8b remaining (34.8%)

Threshold costs 0.8b (34.8%)

Counts

305 → 1

Compiler

Compiled 55794 to 40796 computations (26.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-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	16	34
1	20	34
2	25	34
3	27	34
4	28	34
5	28	34

end198.0ms (1.1%)

Compiler: Compiled 324 to 239 computations (26.2% saved)

Details

analyze1.4s (7.2%)

sample11.7s (62.6%)

simplify49.0ms (0.3%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series45.0ms (0.2%)

rewrite37.0ms (0.2%)

simplify198.0ms (1.1%)

prune337.0ms (1.8%)

localize8.0ms (0%)

series35.0ms (0.2%)

rewrite17.0ms (0.1%)

simplify109.0ms (0.6%)

prune281.0ms (1.5%)

localize13.0ms (0.1%)

series308.0ms (1.6%)

rewrite95.0ms (0.5%)

simplify342.0ms (1.8%)

prune408.0ms (2.2%)

localize15.0ms (0.1%)

series644.0ms (3.4%)

rewrite47.0ms (0.3%)

simplify164.0ms (0.9%)

prune304.0ms (1.6%)

regimes2.0s (10.5%)

simplify2.0ms (0%)

end198.0ms (1.1%)

Profiling