Details

analyze360.0ms (7.8%)

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)

sample29.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 49 to 37 computations (24.5% saved)

simplify52.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

693×	`div-sub_binary64`
599×	`times-frac_binary64`
519×	`associate-/l*_binary64`
508×	`sub-neg_binary64`
357×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	36	29
2	93	29
3	336	29
4	1152	29
5	3231	29
6	4534	29
7	5241	29

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

12.0b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	12.0b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	12.0b	(.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

▶

12.0b

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

12.0b

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

Compiler

Compiled 109 to 79 computations (27.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.9b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.6b	(-.f64 (.f64 b b) (.f64 a a))
7.6b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite358.0ms (7.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

224×	`times-frac_binary64`
144×	`add-sqr-sqrt_binary64`
127×	`*-un-lft-identity_binary64`
111×	`add-cube-cbrt_binary64`
58×	`associate-l_binary64`

Counts

3 → 229

Calls

3 calls:

36.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
7.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.0ms	(-.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 7406 to 3509 computations (52.6% saved)

series84.0ms (1.8%)

Error

7.9b

Counts

3 → 33

Calls

3 calls:

34.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
22.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
17.0ms	(-.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 1324 to 1044 computations (21.1% saved)

simplify288.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

291×	`associate-*l/_binary64`
230×	`*-commutative_binary64`
219×	`associate-*r/_binary64`
208×	`associate-/l/_binary64`
194×	`associate-/r*_binary64`

Counts

262 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	384	8315
1	1057	7838
2	3725	7824
3	4787	7824
4	4994	7824
5	4959	7824

prune148.0ms (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	198	9	207
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	200	9	209

Error

0.0b

Counts

209 → 9

Alt Table

Status	Error	Program
	12.0b	(.f64 (.f64 PI.f64 (/.f64 1/2 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	0.3b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
	0.3b	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
	12.0b	(+.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a))) a) (/.f64 (/.f64 (neg.f64 (/.f64 PI.f64 2)) b) (-.f64 (.f64 b b) (.f64 a a))))
	12.0b	(.f64 (/.f64 PI.f64 2) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 (.f64 b b) (*.f64 a a))))
	7.6b	(.f64 (.f64 (/.f64 PI.f64 (+.f64 a b)) (/.f64 1/2 (-.f64 b a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
▶	0.2b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))
	0.5b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 (sqrt.f64 2)) (-.f64 b a))))
	0.6b	(.f64 (/.f64 (/.f64 (sqrt.f64 PI.f64) 1) (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 (sqrt.f64 PI.f64) 2) (-.f64 b a))))

Compiler

Compiled 4770 to 2348 computations (50.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))
0.2b	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))

rewrite190.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

98×	`times-frac_binary64`
79×	`*-un-lft-identity_binary64`
60×	`add-exp-log_binary64`
51×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`

Counts

2 → 122

Calls

2 calls:

10.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))
7.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))

Compiler

Compiled 2567 to 1250 computations (51.3% saved)

series49.0ms (1.1%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

22.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))
20.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))

Compiler

Compiled 992 to 738 computations (25.6% saved)

simplify150.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

457×	`associate-/r/_binary64`
432×	`associate-r_binary64`
329×	`*-commutative_binary64`
320×	`unswap-sqr_binary64`
216×	`times-frac_binary64`

Counts

146 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	3501
1	599	3099
2	1859	3071
3	3662	3071
4	4821	3071
5	4957	3071

prune103.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	137	7	144

Error

Counts

144 → 7

Alt Table

Status	Error	Program
	2.7b	(/.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) a) b)
	7.6b	(.f64 (.f64 (/.f64 PI.f64 (+.f64 a b)) (/.f64 1/2 (-.f64 b a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	3.1b	(/.f64 1 (/.f64 b (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) a)))
	12.0b	(.f64 (/.f64 PI.f64 2) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 (.f64 b b) (*.f64 a a))))
	0.7b	(/.f64 (.f64 (/.f64 PI.f64 2) 1) (.f64 (+.f64 b a) (*.f64 b a)))
	0.3b	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
▶	0.2b	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (/.f64 1 (*.f64 b a)))

Compiler

Compiled 1965 to 1000 computations (49.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (/.f64 1 (*.f64 b a)))
0.2b	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))
0.6b	(/.f64 1 (*.f64 b a))

rewrite255.0ms (5.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

215×	`add-exp-log_binary64`
115×	`prod-exp_binary64`
103×	`times-frac_binary64`
84×	`*-un-lft-identity_binary64`
77×	`div-exp_binary64`

Counts

3 → 197

Calls

3 calls:

15.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (/.f64 1 (*.f64 b a)))
6.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))
6.0ms	(/.f64 1 (*.f64 b a))

Compiler

Compiled 4298 to 2307 computations (46.3% saved)

series67.0ms (1.4%)

Error

Counts

3 → 30

Calls

3 calls:

24.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (/.f64 1 (*.f64 b a)))
24.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))
12.0ms	(/.f64 1 (*.f64 b a))

Compiler

Compiled 1255 to 948 computations (24.5% saved)

simplify194.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

397×	`*-commutative_binary64`
317×	`distribute-rgt-in_binary64`
296×	`associate-/r/_binary64`
255×	`unswap-sqr_binary64`
186×	`associate-/l/_binary64`

Counts

227 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	286	4774
1	634	4196
2	1892	4168
3	2983	4138
4	4706	4138
5	4953	4138

prune67.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	165	7	172

Error

Counts

172 → 7

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 a b)) (+.f64 a b))
	12.0b	(.f64 (/.f64 PI.f64 2) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 (.f64 b b) (*.f64 a a))))
	2.7b	(/.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) a) b)
	7.6b	(.f64 (.f64 (/.f64 PI.f64 (+.f64 a b)) (/.f64 1/2 (-.f64 b a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	3.1b	(/.f64 1 (/.f64 b (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) a)))
	0.3b	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
✓	0.2b	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (/.f64 1 (*.f64 b a)))

Compiler

Compiled 1411 to 777 computations (44.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 a b)) (+.f64 a b))
0.6b	(/.f64 (/.f64 PI.f64 2) (*.f64 a b))

rewrite211.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

209×	`times-frac_binary64`
110×	`*-un-lft-identity_binary64`
74×	`add-sqr-sqrt_binary64`
74×	`add-cube-cbrt_binary64`
32×	`add-cbrt-cube_binary64`

Counts

2 → 158

Calls

2 calls:

11.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 a b)) (+.f64 a b))
6.0ms	(/.f64 (/.f64 PI.f64 2) (*.f64 a b))

Compiler

Compiled 2980 to 1379 computations (53.7% saved)

series40.0ms (0.9%)

Error

Counts

2 → 18

Calls

2 calls:

24.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 a b)) (+.f64 a b))
13.0ms	(/.f64 (/.f64 PI.f64 2) (*.f64 a b))

Compiler

Compiled 621 to 463 computations (25.4% saved)

simplify152.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

645×	`associate-l_binary64`
529×	`associate-*l/_binary64`
478×	`associate-r_binary64`
404×	`associate-/l/_binary64`
389×	`associate-/r/_binary64`

Counts

176 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	282	4546
1	691	4212
2	2116	4196
3	4992	4196
4	4977	4196

prune77.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	120	7	127

Error

Counts

127 → 7

Alt Table

Status	Error	Program
	0.2b	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 a b)) (+.f64 a b))
	12.0b	(.f64 (/.f64 PI.f64 2) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 (.f64 b b) (*.f64 a a))))
	3.1b	(/.f64 1 (/.f64 b (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) a)))
	2.7b	(/.f64 (/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) a) b)
	0.3b	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
	0.3b	(/.f64 (*.f64 (/.f64 PI.f64 a) (/.f64 1/2 b)) (+.f64 a b))
	0.2b	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (/.f64 1 (*.f64 b a)))

Compiler

Compiled 1509 to 674 computations (55.3% saved)

regimes799.0ms (17.2%)

Accuracy

Total 0.2b remaining (89.1%)

Threshold costs 0.2b (89.1%)

Compiler

Compiled 15226 to 10704 computations (29.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	16	20
2	15	20

end0.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample940.0ms (20.2%)

Algorithm

1×

intervals

Results

588.0ms	8000×	body	128	valid
24.0ms	357×	body	128	invalid

Compiler

Compiled 150 to 110 computations (26.7% saved)

Details

analyze360.0ms (7.8%)

sample29.0ms (0.6%)

simplify52.0ms (1.1%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite358.0ms (7.7%)

series84.0ms (1.8%)

simplify288.0ms (6.2%)

prune148.0ms (3.2%)

localize7.0ms (0.2%)

rewrite190.0ms (4.1%)

series49.0ms (1.1%)

simplify150.0ms (3.2%)

prune103.0ms (2.2%)

localize9.0ms (0.2%)

rewrite255.0ms (5.5%)

series67.0ms (1.4%)

simplify194.0ms (4.2%)

prune67.0ms (1.4%)

localize6.0ms (0.1%)

rewrite211.0ms (4.5%)

series40.0ms (0.9%)

simplify152.0ms (3.3%)

prune77.0ms (1.6%)

regimes799.0ms (17.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample940.0ms (20.2%)

Profiling