Details

analyze1.3s (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)

sample11.3s (69%)

Results

3.5s	4009×	body	1024	valid
3.3s	3930×	body	1024	invalid
1.3s	1962×	body	512	invalid
1.3s	2016×	body	512	valid
786.0ms	494×	body	2048	valid
466.0ms	1029×	body	256	valid
447.0ms	961×	body	256	invalid
165.0ms	708×	body	128	valid
8.0ms	5×	body	2048	invalid
1.0ms	6×	body	128	invalid

Compiler

Compiled 116 to 92 computations (20.7% saved)

simplify52.0ms (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

60.8b

Counts

3 → 1

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))) (-.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

▶

60.8b

(*.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
✓	0.3b	(*.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)))))
✓	0.5b	(/.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))))
✓	6.5b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series611.0ms (3.7%)

Counts

4 → 48

Calls

4 calls:

566.0ms	(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)))
2.0ms	(*.f64 (PI.f64) f)

rewrite115.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

155× egg-rr

Counts

4 → 155

Calls

2 calls:

108.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	121
1	328	121
2	4187	121
3	5316	121
0	0	0
1	0	0

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

580×	`distribute-rgt-neg-in_binary64`
561×	`distribute-lft-neg-in_binary64`
551×	`fma-neg_binary64`
475×	`associate-r_binary64`
469×	`associate-l_binary64`

Counts

203 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	1344
1	241	1338
2	718	1334
3	2998	1334
4	5212	1334

prune202.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	192	7	199
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	193	7	200

Error

1.1b

Counts

200 → 7

Alt Table

Status	Error	Program
	60.8b	(.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)))
▶	1.7b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	60.8b	(.f64 (pow.f64 (cbrt.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)))))) 3) (/.f64 -4 (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))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 3) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 (PI.f64) f) 3))) (+.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 2) (+.f64 (pow.f64 (exp.f64 -1/2) (.f64 (PI.f64) f)) (pow.f64 (*.f64 (exp.f64 (/.f64 (PI.f64) 4)) (pow.f64 (exp.f64 -1/4) (PI.f64))) f)))))) (/.f64 -4 (PI.f64)))
	2.1b	(*.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (/.f64 -4 (PI.f64)))
	1.8b	(.f64 (log.f64 (fma.f64 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
	60.8b	(.f64 (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.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 9988 to 6768 computations (32.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (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)))

series42.0ms (0.3%)

Counts

4 → 24

Calls

4 calls:

19.0ms	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
13.0ms	(log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))
8.0ms	(/.f64 4 (*.f64 f (PI.f64)))
2.0ms	(*.f64 f (PI.f64))

rewrite68.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

97× egg-rr

Counts

4 → 97

Calls

2 calls:

66.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	56
1	254	56
2	2936	56
3	5148	56
0	0	0
1	0	0

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

445×	`times-frac_binary64`
390×	`fma-def_binary64`
343×	`associate-r_binary64`
342×	`associate-l_binary64`
279×	`associate-/r*_binary64`

Counts

121 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1004
1	404	987
2	1324	978
3	4558	978
4	5088	978

prune206.0ms (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	151	10	161
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	153	15	168

Error

0.8b

Counts

168 → 15

Alt Table

Status	Error	Program
	2.6b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))) 3) (/.f64 -4 (PI.f64)))
	1.8b	(/.f64 1 (/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4)))
	1.8b	(.f64 (log.f64 (fma.f64 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
	38.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (pow.f64 (pow.f64 (*.f64 f (PI.f64)) 3) 1/3)))) (/.f64 -4 (PI.f64)))
	13.6b	(+.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64)))) (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64)))))) (log.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))))))
	60.8b	(.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)))
	1.7b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (expm1.f64 (log1p.f64 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	1.7b	(.f64 (-.f64 (fma.f64 1/48 (.f64 (*.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (log.f64 f)) (/.f64 -4 (PI.f64)))
	60.8b	(.f64 (pow.f64 (cbrt.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)))))) 3) (/.f64 -4 (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))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 3) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 (PI.f64) f) 3))) (+.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 2) (+.f64 (pow.f64 (exp.f64 -1/2) (.f64 (PI.f64) f)) (pow.f64 (*.f64 (exp.f64 (/.f64 (PI.f64) 4)) (pow.f64 (exp.f64 -1/4) (PI.f64))) f)))))) (/.f64 -4 (PI.f64)))
	2.4b	(.f64 (expm1.f64 (log1p.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
▶	1.6b	(/.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 (PI.f64) -4))
	63.0b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))
	60.8b	(.f64 (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	1.7b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))

Compiler

Compiled 4497 to 2943 computations (34.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series21.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

21.0ms

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

rewrite59.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

43× egg-rr

Counts

1 → 43

Calls

2 calls:

58.0ms	((/.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 (PI.f64) -4)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	261	25
2	3163	25
3	5632	25
0	0	0
1	0	0

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
308×	`sub-neg_binary64`
300×	`unswap-sqr_binary64`
264×	`times-frac_binary64`
211×	`fma-def_binary64`

Counts

55 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	564
1	273	555
2	831	546
3	2512	513
4	4758	513
5	4967	513

prune194.0ms (1.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	177	15	192

Error

0.8b

Counts

192 → 15

Alt Table

Status	Error	Program
	2.6b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))) 3) (/.f64 -4 (PI.f64)))
	1.8b	(/.f64 1 (/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4)))
	1.8b	(.f64 (log.f64 (fma.f64 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
	38.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (pow.f64 (pow.f64 (*.f64 f (PI.f64)) 3) 1/3)))) (/.f64 -4 (PI.f64)))
	13.6b	(+.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64)))) (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64)))))) (log.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))))))
	60.8b	(.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)))
	1.7b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (expm1.f64 (log1p.f64 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
▶	1.7b	(.f64 (-.f64 (fma.f64 1/48 (.f64 (*.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (log.f64 f)) (/.f64 -4 (PI.f64)))
	60.8b	(.f64 (pow.f64 (cbrt.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)))))) 3) (/.f64 -4 (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))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 3) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 (PI.f64) f) 3))) (+.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 2) (+.f64 (pow.f64 (exp.f64 -1/2) (.f64 (PI.f64) f)) (pow.f64 (*.f64 (exp.f64 (/.f64 (PI.f64) 4)) (pow.f64 (exp.f64 -1/4) (PI.f64))) f)))))) (/.f64 -4 (PI.f64)))
	2.4b	(.f64 (expm1.f64 (log1p.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
✓	1.6b	(/.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 (PI.f64) -4))
	63.0b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))
	60.8b	(.f64 (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	1.7b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))

Compiler

Compiled 4932 to 3211 computations (34.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series145.0ms (0.9%)

Counts

4 → 36

Calls

4 calls:

75.0ms	(.f64 (-.f64 (fma.f64 1/48 (.f64 (*.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (log.f64 f)) (/.f64 -4 (PI.f64)))
63.0ms	(-.f64 (fma.f64 1/48 (.f64 (.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (log.f64 f))
6.0ms	(.f64 (.f64 f f) (pow.f64 (PI.f64) 2))
0.0ms	(log.f64 (/.f64 4 (PI.f64)))

rewrite93.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

156× egg-rr

Counts

4 → 156

Calls

2 calls:

89.0ms

((log.f64 (/.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)))) (log.f64 f)) (/.f64 -4 (PI.f64))) (*.f64 (*.f64 f f) (pow.f64 (PI.f64) 2)) (-.f64 (fma.f64 1/48 (*.f64 (*.f64 f f) (pow.f64 (PI.f64) 2)) (log.f64 (/.f64 4 (PI.f64)))) (log.f64 f)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	77
1	360	68
2	3847	68
3	5077	68
0	0	0
1	0	0

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

462×	`associate-l_binary64`
423×	`times-frac_binary64`
391×	`fma-neg_binary64`
353×	`associate-r_binary64`
346×	`cancel-sign-sub-inv_binary64`

Counts

192 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	804
1	137	804
2	393	759
3	1244	741
4	4285	741
5	5038	741

prune208.0ms (1.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	173	15	188

Error

0.8b

Counts

188 → 15

Alt Table

Status	Error	Program
	1.8b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 1/48 (pow.f64 (.f64 (PI.f64) f) 2) (log.f64 (/.f64 4 (PI.f64)))) 2) (pow.f64 (log.f64 f) 2)) -4) (.f64 (+.f64 (fma.f64 1/48 (pow.f64 (.f64 (PI.f64) f) 2) (log.f64 (/.f64 4 (PI.f64)))) (log.f64 f)) (PI.f64)))
	1.8b	(/.f64 1 (/.f64 (PI.f64) (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) -4)))
	1.8b	(.f64 (log.f64 (fma.f64 (.f64 (pow.f64 f 3) (pow.f64 (PI.f64) 3)) -1/2880 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64)))
	38.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (pow.f64 (pow.f64 (*.f64 f (PI.f64)) 3) 1/3)))) (/.f64 -4 (PI.f64)))
	13.6b	(+.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64)))) (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64)))))) (log.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))) (/.f64 -4 (PI.f64))))))
	60.8b	(.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)))
	1.7b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (expm1.f64 (log1p.f64 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	60.8b	(.f64 (pow.f64 (cbrt.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)))))) 3) (/.f64 -4 (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))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 3) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 (PI.f64) f) 3))) (+.f64 (pow.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) 2) (+.f64 (pow.f64 (exp.f64 -1/2) (.f64 (PI.f64) f)) (pow.f64 (*.f64 (exp.f64 (/.f64 (PI.f64) 4)) (pow.f64 (exp.f64 -1/4) (PI.f64))) f)))))) (/.f64 -4 (PI.f64)))
	2.4b	(.f64 (expm1.f64 (log1p.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
✓	1.6b	(/.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (/.f64 (PI.f64) -4))
	1.9b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 1/48 (pow.f64 (.f64 (PI.f64) f) 2) (log.f64 (/.f64 4 (PI.f64)))) 3) (pow.f64 (log.f64 f) 3)) -4) (.f64 (+.f64 (pow.f64 (fma.f64 1/48 (pow.f64 (.f64 (PI.f64) f) 2) (log.f64 (/.f64 4 (PI.f64)))) 2) (.f64 (log.f64 f) (+.f64 (fma.f64 1/48 (pow.f64 (.f64 (PI.f64) f) 2) (log.f64 (/.f64 4 (PI.f64)))) (log.f64 f)))) (PI.f64)))
	63.0b	(.f64 -4 (/.f64 (+.f64 (log.f64 f) (log.f64 (.f64 (PI.f64) 1/12))) (PI.f64)))
	60.8b	(.f64 (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	1.7b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))))

Compiler

Compiled 5534 to 3414 computations (38.3% saved)

regimes1.1s (6.8%)

Accuracy

Total 0.7b remaining (30.8%)

Threshold costs 0.7b (30.8%)

Counts

181 → 1

Compiler

Compiled 29376 to 21800 computations (25.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	83
1	45	83
2	45	83

end335.0ms (2%)

Compiler: Compiled 568 to 414 computations (27.1% saved)

Details

analyze1.3s (8%)

sample11.3s (69%)

simplify52.0ms (0.3%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series611.0ms (3.7%)

rewrite115.0ms (0.7%)

simplify60.0ms (0.4%)

prune202.0ms (1.2%)

localize9.0ms (0.1%)

series42.0ms (0.3%)

rewrite68.0ms (0.4%)

simplify63.0ms (0.4%)

prune206.0ms (1.3%)

localize9.0ms (0.1%)

series21.0ms (0.1%)

rewrite59.0ms (0.4%)

simplify60.0ms (0.4%)

prune194.0ms (1.2%)

localize15.0ms (0.1%)

series145.0ms (0.9%)

rewrite93.0ms (0.6%)

simplify62.0ms (0.4%)

prune208.0ms (1.3%)

regimes1.1s (6.8%)

simplify3.0ms (0%)

end335.0ms (2%)

Profiling