Details

analyze1.4s (8.7%)

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)

sample421.0ms (2.6%)

Algorithm

1×

intervals

Results

87.0ms	118×	body	1024	valid
78.0ms	122×	body	1024	nan
36.0ms	53×	body	512	nan
32.0ms	67×	body	512	valid
23.0ms	16×	body	2048	valid
11.0ms	37×	body	256	nan
9.0ms	27×	body	256	valid
5.0ms	28×	body	128	valid

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

61.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.2b	(.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

▶

61.2b

(*.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 (/.f64 (PI.f64) 4) f)
✓	0.3b	(*.f64 (PI.f64) f)
✓	1.7b	(/.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)))

series52.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

35.0ms	(/.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))))
10.0ms	(-.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)

rewrite41.0ms (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)
4.0ms	(*.f64 (PI.f64) f)

simplify369.0ms (2.3%)

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

prune368.0ms (2.3%)

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

2.1b

Counts

350 → 4

Alt Table

Status	Error	Program
	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 (fma.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (neg.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))))) (/.f64 -4 (PI.f64)))
	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	61.2b	(.f64 (log.f64 (/.f64 (-.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 (-.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)))
▶	2.2b	(.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 16222 to 10516 computations (35.2% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
✓	1.0b	(pow.f64 (PI.f64) 5)
✓	1.6b	(pow.f64 (PI.f64) 7)
✓	1.7b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))

series454.0ms (2.8%)

Counts

4 → 24

Calls

4 calls:

243.0ms	(.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
210.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))
0.0ms	(pow.f64 (PI.f64) 7)
0.0ms	(pow.f64 (PI.f64) 5)

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
22×	`times-frac_binary64`
16×	`log-prod_binary64`

Counts

4 → 102

Calls

4 calls:

7.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))
5.0ms	(.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
1.0ms	(pow.f64 (PI.f64) 7)
1.0ms	(pow.f64 (PI.f64) 5)

simplify248.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

336×	`associate-/r*_binary64`
317×	`fma-def_binary64`
282×	`associate-r_binary64`
282×	`times-frac_binary64`
225×	`associate-l_binary64`

Counts

126 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	482	13755
1	1396	12909
2	4965	12909

prune594.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	188	6	194
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	190	8	198

Error

1.7b

Counts

198 → 8

Alt Table

Status	Error	Program
	2.5b	(.f64 (.f64 (sqrt.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))) (sqrt.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))))) (/.f64 -4 (PI.f64)))
	2.2b	(.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 (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.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 (fma.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (neg.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))))) (/.f64 -4 (PI.f64)))
	2.6b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))))
	2.3b	(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (*.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7)))))))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
▶	2.2b	(.f64 (.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	3.1b	(.f64 (.f64 (cbrt.f64 (.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))) (cbrt.f64 (.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64))))) (cbrt.f64 (.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))))

Compiler

Compiled 19487 to 13112 computations (32.7% saved)

localize131.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(pow.f64 (PI.f64) 5)
✓	1.0b	(sqrt.f64 (PI.f64))
	1.6b	(pow.f64 (PI.f64) 7)
	1.7b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))

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))

simplify131.0ms (0.8%)

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

prune425.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	144	8	152

Error

1.7b

Counts

152 → 8

Alt Table

Status	Error	Program
	2.5b	(.f64 (.f64 (sqrt.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))) (sqrt.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))))) (/.f64 -4 (PI.f64)))
▶	2.2b	(.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 (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.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 (fma.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (neg.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))))) (/.f64 -4 (PI.f64)))
	2.6b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))))
	2.3b	(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (*.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7)))))))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
✓	2.2b	(.f64 (.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	3.1b	(.f64 (.f64 (cbrt.f64 (.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))) (cbrt.f64 (.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64))))) (cbrt.f64 (.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))))

Compiler

Compiled 13707 to 9101 computations (33.6% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.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 (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
	1.0b	(pow.f64 (PI.f64) 5)
	1.6b	(pow.f64 (PI.f64) 7)
✓	1.7b	(log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))

series435.0ms (2.7%)

Counts

2 → 24

Calls

2 calls:

377.0ms

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

58.0ms

(*.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 (fma.f64 1/192 (pow.f64 (*.f64 f (PI.f64)) 3) (fma.f64 1/61440 (*.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (*.f64 f (PI.f64)) (*.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
11×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`

Counts

2 → 60

Calls

2 calls:

9.0ms

(*.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 (fma.f64 1/192 (pow.f64 (*.f64 f (PI.f64)) 3) (fma.f64 1/61440 (*.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (*.f64 f (PI.f64)) (*.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))

6.0ms

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

simplify173.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
342×	`fma-neg_binary64`
305×	`distribute-rgt-in_binary64`
260×	`cancel-sign-sub-inv_binary64`
188×	`sub-neg_binary64`

Counts

84 → 129

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	6471
1	724	5921
2	2387	5899
3	4739	5891
4	4950	5891

prune389.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	173	8	181

Error

1.7b

Counts

181 → 8

Alt Table

Status	Error	Program
	2.5b	(.f64 (.f64 (sqrt.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))) (sqrt.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))))) (/.f64 -4 (PI.f64)))
✓	2.2b	(.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 (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.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 (fma.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (neg.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (cbrt.f64 (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))))) (/.f64 -4 (PI.f64)))
	2.6b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (.f64 f f)))))
	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.5b	(-.f64 (fma.f64 4 (+.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (.f64 (PI.f64) 1/2)) (PI.f64))) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3)))) (fma.f64 1/12 (.f64 f (.f64 f (PI.f64))) (fma.f64 4 (/.f64 (log.f64 2) (PI.f64)) (.f64 31/1451520 (*.f64 (pow.f64 f 6) (pow.f64 (PI.f64) 5))))))
✓	2.2b	(.f64 (.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 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.3b	(/.f64 (.f64 (-.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 (log.f64 (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))) (log.f64 (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))) -4) (.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 (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (PI.f64)))

Compiler

Compiled 12031 to 8317 computations (30.9% saved)

regimes1.0s (6.4%)

Accuracy

Total 0.6b remaining (28.1%)

Threshold costs 0.6b (28.1%)

Counts

97 → 1

Compiler

Compiled 34392 to 24794 computations (27.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	80
1	42	80
2	42	80

end1.0ms (0%)

Compiler: Compiled 50 to 36 computations (28% saved)

sample9.3s (57.6%)

Algorithm

1×

intervals

Results

2.7s	3974×	body	1024	valid
2.4s	3976×	body	1024	nan
1.0s	1945×	body	512	valid
960.0ms	1992×	body	512	nan
613.0ms	477×	body	2048	valid
345.0ms	990×	body	256	valid
308.0ms	1014×	body	256	nan
106.0ms	614×	body	128	valid
2.0ms	2×	body	2048	nan
0.0ms	3×	body	128	overflowed
0.0ms	1×	body	128	nan

Compiler

Compiled 632 to 454 computations (28.2% saved)

Details

analyze1.4s (8.7%)

sample421.0ms (2.6%)

simplify47.0ms (0.3%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series52.0ms (0.3%)

rewrite41.0ms (0.2%)

simplify369.0ms (2.3%)

prune368.0ms (2.3%)

localize34.0ms (0.2%)

series454.0ms (2.8%)

rewrite27.0ms (0.2%)

simplify248.0ms (1.5%)

prune594.0ms (3.7%)

localize131.0ms (0.8%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify131.0ms (0.8%)

prune425.0ms (2.6%)

localize39.0ms (0.2%)

series435.0ms (2.7%)

rewrite28.0ms (0.2%)

simplify173.0ms (1.1%)

prune389.0ms (2.4%)

regimes1.0s (6.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample9.3s (57.6%)

Profiling