Details

analyze1.4s (9.2%)

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)

sample409.0ms (2.6%)

Algorithm

1×

intervals

Results

90.0ms	128×	body	1024	valid
87.0ms	139×	body	1024	nan
81.0ms	67×	body	512	valid
22.0ms	48×	body	512	nan
17.0ms	14×	body	2048	valid
10.0ms	35×	body	256	nan
9.0ms	27×	body	256	valid
3.0ms	20×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify48.0ms (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

61.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.1b	(.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

▶

61.1b

(*.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)

localize16.0ms (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)
✓	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))))
✓	4.8b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series127.0ms (0.8%)

Counts

4 → 48

Calls

4 calls:

112.0ms	(/.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)))
4.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
2.0ms	(*.f64 (PI.f64) f)

rewrite138.0ms (0.9%)

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)
4.0ms	(*.f64 (PI.f64) f)

simplify202.0ms (1.3%)

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

prune384.0ms (2.5%)

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

1.4b

Counts

350 → 4

Alt Table

Status	Error	Program
	61.1b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	61.4b	(.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 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))
▶	1.7b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	1.8b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 16038 to 10390 computations (35.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 f (PI.f64))
✓	0.3b	(pow.f64 (*.f64 f (PI.f64)) 3)
✓	0.5b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
✓	1.0b	(pow.f64 (PI.f64) 5)

series91.0ms (0.6%)

Counts

4 → 24

Calls

4 calls:

52.0ms	(pow.f64 (*.f64 f (PI.f64)) 3)
34.0ms	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
3.0ms	(*.f64 f (PI.f64))
0.0ms	(pow.f64 (PI.f64) 5)

rewrite63.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

47.0ms	(pow.f64 (*.f64 f (PI.f64)) 3)
6.0ms	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
3.0ms	(*.f64 f (PI.f64))
2.0ms	(pow.f64 (PI.f64) 5)

simplify111.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

391×	`associate-/r*_binary64`
315×	`fma-neg_binary64`
300×	`fma-def_binary64`
259×	`times-frac_binary64`
243×	`associate-/l*_binary64`

Counts

122 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	3467
1	585	3133
2	1992	3106
3	4928	3101
4	5024	3101

prune410.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	222	7	229
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	223	10	233

Error

1.0b

Counts

233 → 10

Alt Table

Status	Error	Program
	1.6b	(fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (PI.f64) (.f64 (*.f64 f f) -1/12)))
	1.8b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	1.7b	(.f64 (/.f64 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f)))))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
▶	1.5b	(.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (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))))
	2.2b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	61.1b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	1.8b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	2.5b	(.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))))) (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	12.9b	(log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64))))
	61.4b	(.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 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 9500 to 5882 computations (38.1% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 f (PI.f64))
	0.3b	(pow.f64 (*.f64 f (PI.f64)) 3)
✓	1.0b	(sqrt.f64 (PI.f64))
	1.0b	(pow.f64 (PI.f64) 5)

series0.0ms (0%)

Counts

1 → 0

Calls

1 calls:

0.0ms

(sqrt.f64 (PI.f64))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

(sqrt.f64 (PI.f64))

simplify132.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

15 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	94
1	25	93
2	28	93
3	32	93
4	37	93
5	46	93
6	66	93
7	119	93
8	294	93
9	599	93
10	601	93
11	731	93
12	885	93
13	1053	93
14	1282	93
15	1583	93
16	1931	93
17	2406	93
18	3024	93
19	3220	93
20	3394	93
21	3508	93
22	3555	93
23	3607	93
24	4485	93
25	4789	93

prune324.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	180	10	190

Error

1.0b

Counts

190 → 10

Alt Table

Status	Error	Program
▶	1.6b	(fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (PI.f64) (.f64 (*.f64 f f) -1/12)))
	1.8b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	1.7b	(.f64 (/.f64 (log.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (*.f64 (PI.f64) f)))))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
✓	1.5b	(.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (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))))
	2.2b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	61.1b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	1.8b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	2.5b	(.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))))) (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	12.9b	(log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64))))
	61.4b	(.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 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 8169 to 4798 computations (41.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (PI.f64) (.f64 (*.f64 f f) -1/12))
✓	0.3b	(/.f64 (log.f64 f) (PI.f64))
✓	0.3b	(-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
✓	2.0b	(log.f64 (/.f64 4 (PI.f64)))

series351.0ms (2.3%)

Counts

4 → 28

Calls

4 calls:

321.0ms	(-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
25.0ms	(/.f64 (log.f64 f) (PI.f64))
4.0ms	(.f64 (PI.f64) (.f64 (*.f64 f f) -1/12))
0.0ms	(log.f64 (/.f64 4 (PI.f64)))

rewrite105.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 404

Calls

4 calls:

22.0ms	(-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
6.0ms	(.f64 (PI.f64) (.f64 (*.f64 f f) -1/12))
3.0ms	(/.f64 (log.f64 f) (PI.f64))
3.0ms	(log.f64 (/.f64 4 (PI.f64)))

simplify411.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

432 → 350

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	13614
1	929	10964
2	2002	9844
3	4816	9844
4	4821	9844

prune596.0ms (3.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	345	5	350
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	349	11	360

Error

0.9b

Counts

360 → 11

Alt Table

Status	Error	Program
	1.7b	(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 (PI.f64) (.f64 (*.f64 f f) -1/12)))
	61.4b	(.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 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))
✓	1.5b	(.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (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))))
	61.1b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	1.8b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	1.7b	(fma.f64 4 (/.f64 (.f64 (PI.f64) (-.f64 (log.f64 f) (log.f64 (/.f64 4 (PI.f64))))) (.f64 (PI.f64) (PI.f64))) (.f64 (PI.f64) (.f64 (*.f64 f f) -1/12)))
	1.9b	(fma.f64 4 (-.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 f) (PI.f64))) (/.f64 (log.f64 f) (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (PI.f64) (.f64 (*.f64 f f) -1/12)))
	12.9b	(log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64))))
	1.8b	(fma.f64 4 (/.f64 (-.f64 (.f64 (log.f64 f) (PI.f64)) (.f64 (PI.f64) (log.f64 (/.f64 4 (PI.f64))))) (.f64 (PI.f64) (PI.f64))) (.f64 (PI.f64) (.f64 (.f64 f f) -1/12)))
	1.7b	(fma.f64 4 (fma.f64 (log.f64 f) (/.f64 1 (PI.f64)) (neg.f64 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))) (.f64 (PI.f64) (.f64 (*.f64 f f) -1/12)))
	1.8b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 17830 to 10238 computations (42.6% saved)

regimes1.1s (7.2%)

Accuracy

Total 0.7b remaining (31.2%)

Threshold costs 0.7b (31.2%)

Counts

147 → 1

Compiler

Compiled 35688 to 24746 computations (30.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	61
1	32	61
2	31	61

end1.0ms (0%)

Compiler: Compiled 38 to 26 computations (31.6% saved)

sample8.9s (57.8%)

Algorithm

1×

intervals

Results

2.6s	3866×	body	1024	valid
2.4s	3841×	body	1024	nan
916.0ms	1945×	body	512	valid
902.0ms	1928×	body	512	nan
641.0ms	511×	body	2048	valid
337.0ms	1012×	body	256	valid
318.0ms	996×	body	256	nan
114.0ms	666×	body	128	valid
3.0ms	3×	body	2048	nan
0.0ms	1×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 447 to 309 computations (30.9% saved)

Details

analyze1.4s (9.2%)

sample409.0ms (2.6%)

simplify48.0ms (0.3%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series127.0ms (0.8%)

rewrite138.0ms (0.9%)

simplify202.0ms (1.3%)

prune384.0ms (2.5%)

localize18.0ms (0.1%)

series91.0ms (0.6%)

rewrite63.0ms (0.4%)

simplify111.0ms (0.7%)

prune410.0ms (2.7%)

localize27.0ms (0.2%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify132.0ms (0.9%)

prune324.0ms (2.1%)

localize14.0ms (0.1%)

series351.0ms (2.3%)

rewrite105.0ms (0.7%)

simplify411.0ms (2.7%)

prune596.0ms (3.9%)

regimes1.1s (7.2%)

simplify3.0ms (0%)

end1.0ms (0%)

sample8.9s (57.8%)

Profiling