Details

analyze592.0ms (7.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample2.4s (31.7%)

Results

2.1s	8256×	body	128	valid
147.0ms	344×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

693×	`div-sub_binary64`
599×	`times-frac_binary64`
519×	`associate-/l*_binary64`
357×	`associate-/l/_binary64`
274×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	37	29
2	94	29
3	345	29
4	1207	28
5	3468	28
6	5020	28

prune9.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
	16.7b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Status

Error

Program

▶

0.4b

(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

16.7b

(*.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (*.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Compiler

Compiled 127 to 87 computations (31.5% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
✓	0.2b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
✓	0.3b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
✓	0.3b	(/.f64 (PI.f64) a)

series83.0ms (1.1%)

Counts

4 → 72

Calls

4 calls:

33.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
30.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
15.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
4.0ms	(/.f64 (PI.f64) a)

rewrite148.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

795×	`prod-diff_binary64`
164×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`
152×	`add-cbrt-cube_binary64`

Counts

4 → 146

Calls

4 calls:

142.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
142.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
142.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
142.0ms	(/.f64 (PI.f64) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	65
1	321	65
2	4508	65
3	6084	65
0	0	0
1	0	0

simplify123.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

634×	`cancel-sign-sub-inv_binary64`
564×	`fma-neg_binary64`
305×	`associate-/l/_binary64`
277×	`associate-/r/_binary64`
224×	`neg-mul-1_binary64`

Counts

218 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	1248
1	179	1212
2	524	1146
3	1998	1128
4	4718	1128
5	5009	1128

prune437.0ms (5.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	157	10	167
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	158	11	169

Error

0.0b

Counts

169 → 11

Alt Table

Status	Error	Program
	15.6b	(*.f64 (/.f64 1/2 (+.f64 b a)) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)) 3)))
	28.9b	(.f64 1/2 (/.f64 (PI.f64) (.f64 (pow.f64 a 2) b)))
	0.8b	(.f64 (/.f64 1/2 (+.f64 b a)) (.f64 (pow.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) 2) (*.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (/.f64 1 (-.f64 b a)))))
	0.8b	(/.f64 (/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (pow.f64 (cbrt.f64 (+.f64 a b)) 2)) (cbrt.f64 (+.f64 a b)))
	0.4b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)))
▶	0.3b	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))))
	0.9b	(/.f64 1/2 (/.f64 (+.f64 a b) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	0.9b	(/.f64 1/2 (*.f64 (+.f64 a b) (/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)))))
	0.9b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))) 3)
	34.9b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (PI.f64) (sqrt.f64 a)))) (-.f64 b a)))
	16.7b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Compiler

Compiled 4192 to 2034 computations (51.5% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
✓	0.2b	(/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)))
✓	0.2b	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))))
	0.3b	(/.f64 (PI.f64) a)

series96.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

62.0ms	(/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)))
34.0ms	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))))

rewrite142.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

309×	`log1p-udef_binary64`
171×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
159×	`add-cbrt-cube_binary64`

Counts

2 → 83

Calls

2 calls:

138.0ms	(/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)))
138.0ms	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	330	47
2	4958	47
3	5409	47
0	0	0
1	0	0

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

634×	`cancel-sign-sub-inv_binary64`
564×	`fma-neg_binary64`
299×	`associate-/l/_binary64`
275×	`associate-/r/_binary64`
225×	`neg-mul-1_binary64`

Counts

131 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	996
1	171	960
2	514	894
3	1983	876
4	4684	876
5	4974	876

prune488.0ms (6.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	161	11	172

Error

0.0b

Counts

172 → 11

Alt Table

Status	Error	Program
	0.8b	(.f64 (/.f64 1/2 (+.f64 b a)) (.f64 (pow.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) 2) (*.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (/.f64 1 (-.f64 b a)))))
	0.8b	(/.f64 (/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (pow.f64 (cbrt.f64 (+.f64 a b)) 2)) (cbrt.f64 (+.f64 a b)))
	28.7b	(*.f64 (/.f64 1/2 (sqrt.f64 (/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))))) (/.f64 (/.f64 1 (+.f64 a b)) (sqrt.f64 (/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))))))
	0.9b	(/.f64 1/2 (/.f64 (+.f64 a b) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	0.9b	(/.f64 1/2 (*.f64 (+.f64 a b) (/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)))))
	28.9b	(.f64 1/2 (/.f64 (PI.f64) (.f64 (pow.f64 a 2) b)))
	0.9b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))) 3)
	34.9b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (PI.f64) (sqrt.f64 a)))) (-.f64 b a)))
	0.3b	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))
▶	0.3b	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (*.f64 a b) (PI.f64)))
	16.7b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Compiler

Compiled 4355 to 2150 computations (50.6% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (+.f64 a b))
✓	0.2b	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (*.f64 a b) (PI.f64)))
✓	0.5b	(/.f64 (*.f64 a b) (PI.f64))

series80.0ms (1.1%)

Counts

3 → 48

Calls

3 calls:

31.0ms	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (*.f64 a b) (PI.f64)))
30.0ms	(/.f64 (*.f64 a b) (PI.f64))
19.0ms	(/.f64 1/2 (+.f64 a b))

rewrite104.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

637×	`prod-diff_binary64`
216×	`log1p-udef_binary64`
120×	`add-sqr-sqrt_binary64`
117×	`egg-rr`
114×	`log1p-expm1-u_binary64`

Counts

3 → 117

Calls

3 calls:

99.0ms	(/.f64 1/2 (+.f64 a b))
99.0ms	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (*.f64 a b) (PI.f64)))
99.0ms	(/.f64 (*.f64 a b) (PI.f64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	233	32
2	3512	32
3	5126	32
0	0	0
1	0	0

simplify131.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

338×	`times-frac_binary64`
331×	`distribute-rgt-neg-in_binary64`
327×	`distribute-lft-neg-in_binary64`
321×	`distribute-neg-frac_binary64`
286×	`fma-def_binary64`

Counts

165 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	1368
1	270	1296
2	853	1194
3	3388	1194
4	4909	1194
5	5077	1194

prune347.0ms (4.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	142	6	148
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	149	10	159

Error

Counts

159 → 10

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (/.f64 a 1) (/.f64 b (PI.f64))))
	34.9b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (PI.f64) (sqrt.f64 a)))) (-.f64 b a)))
	0.3b	(.f64 (PI.f64) (/.f64 (/.f64 1/2 (+.f64 a b)) (.f64 a b)))
	0.8b	(/.f64 (/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (pow.f64 (cbrt.f64 (+.f64 a b)) 2)) (cbrt.f64 (+.f64 a b)))
	0.3b	(/.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 a (/.f64 1 (/.f64 (PI.f64) b))))
	0.3b	(/.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (/.f64 a (PI.f64)) b))
	0.3b	(.f64 (/.f64 -1/2 (+.f64 a b)) (/.f64 1 (/.f64 (neg.f64 (.f64 a b)) (PI.f64))))
	0.3b	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))
	0.9b	(.f64 1/2 (/.f64 1 (.f64 (/.f64 (*.f64 a b) (PI.f64)) (+.f64 a b))))
	16.7b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Compiler

Compiled 2959 to 1448 computations (51.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1/2 (+.f64 a b))
✓	0.2b	(*.f64 (/.f64 a 1) (/.f64 b (PI.f64)))
✓	0.2b	(/.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (/.f64 a 1) (/.f64 b (PI.f64))))
✓	0.2b	(/.f64 b (PI.f64))

series71.0ms (1%)

Counts

3 → 48

Calls

3 calls:

30.0ms	(/.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (/.f64 a 1) (/.f64 b (PI.f64))))
29.0ms	(*.f64 (/.f64 a 1) (/.f64 b (PI.f64)))
12.0ms	(/.f64 b (PI.f64))

rewrite120.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

549×	`prod-diff_binary64`
228×	`log1p-udef_binary64`
128×	`add-sqr-sqrt_binary64`
126×	`egg-rr`
121×	`log1p-expm1-u_binary64`

Counts

3 → 126

Calls

3 calls:

115.0ms	(*.f64 (/.f64 a 1) (/.f64 b (PI.f64)))
115.0ms	(/.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (/.f64 a 1) (/.f64 b (PI.f64))))
115.0ms	(/.f64 b (PI.f64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	258	30
2	3687	30
3	5100	30
0	0	0
1	0	0

simplify117.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-neg_binary64`
695×	`cancel-sign-sub-inv_binary64`
321×	`associate-/l/_binary64`
189×	`distribute-neg-frac_binary64`
174×	`times-frac_binary64`

Counts

174 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	996
1	176	960
2	522	894
3	2029	876
4	4535	876
5	5031	876

prune377.0ms (5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	183	9	192

Error

Counts

192 → 9

Alt Table

Status	Error	Program
	0.4b	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 b (*.f64 (PI.f64) (/.f64 1 a))))
	0.3b	(.f64 (PI.f64) (/.f64 (/.f64 1/2 (+.f64 a b)) (.f64 a b)))
	5.6b	(*.f64 (/.f64 1/2 (/.f64 b (PI.f64))) (/.f64 (/.f64 1 (+.f64 b a)) a))
	0.3b	(/.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (/.f64 a (PI.f64)) b))
	0.3b	(.f64 (/.f64 -1/2 (+.f64 a b)) (/.f64 1 (/.f64 (neg.f64 (.f64 a b)) (PI.f64))))
✓	0.3b	(/.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (/.f64 a 1) (/.f64 b (PI.f64))))
	0.3b	(/.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 a (/.f64 (PI.f64) b)))
	0.9b	(.f64 1/2 (/.f64 1 (.f64 (/.f64 (*.f64 a b) (PI.f64)) (+.f64 a b))))
	16.7b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Compiler

Compiled 3339 to 1713 computations (48.7% saved)

regimes1.2s (16.1%)

Accuracy

Total 0.3b remaining (92.9%)

Threshold costs 0.3b (92.9%)

Counts

216 → 1

Compiler

Compiled 12634 to 8781 computations (30.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	11	17
2	11	17

end198.0ms (2.6%)

Compiler: Compiled 164 to 118 computations (28% saved)

Details

analyze592.0ms (7.9%)

sample2.4s (31.7%)

simplify66.0ms (0.9%)

prune9.0ms (0.1%)

localize20.0ms (0.3%)

series83.0ms (1.1%)

rewrite148.0ms (2%)

simplify123.0ms (1.6%)

prune437.0ms (5.9%)

localize21.0ms (0.3%)

series96.0ms (1.3%)

rewrite142.0ms (1.9%)

simplify102.0ms (1.4%)

prune488.0ms (6.5%)

localize12.0ms (0.2%)

series80.0ms (1.1%)

rewrite104.0ms (1.4%)

simplify131.0ms (1.8%)

prune347.0ms (4.6%)

localize15.0ms (0.2%)

series71.0ms (1%)

rewrite120.0ms (1.6%)

simplify117.0ms (1.6%)

prune377.0ms (5%)

regimes1.2s (16.1%)

simplify3.0ms (0%)

end198.0ms (2.6%)

Profiling