Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 44 to 29 computations (34.1% saved)

sample1.4s (18.2%)

Symmetry

(sort alpha beta)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify211.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1227×	`associate-/l*_binary64`
689×	`distribute-rgt-in_binary64`
661×	`distribute-lft-in_binary64`
481×	`associate-/l/_binary64`
450×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	36	38
2	114	38
3	468	37
4	2359	37
5	2330	37
6	2458	37
7	2717	37
8	3067	37
9	3038	37
10	3136	37
11	3263	37
12	3406	37
13	3706	37
14	4273	37
15	4084	37
16	4107	37
17	4114	37
18	4121	37
19	4128	37
20	4135	37
21	4142	37
22	4149	37
23	4156	37
24	5226	37

prune4.0ms (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

1.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
▶	2.2b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))

Status

Error

Program

3.1b

(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (*.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))

▶

2.2b

(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 190 to 123 computations (35.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
✓	0.1b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
✓	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
✓	18.5b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series158.0ms (2.1%)

Counts

4 → 96

Calls

4 calls:

75.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
42.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
33.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
7.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

rewrite83.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

233×	`prod-diff_binary64`
198×	`add-sqr-sqrt_binary64`
194×	`log1p-expm1-u_binary64`
194×	`expm1-log1p-u_binary64`
190×	`add-log-exp_binary64`

Counts

4 → 119

Calls

4 calls:

80.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
80.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
80.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
80.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	79
1	394	79
2	4840	79
3	5273	79

simplify191.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

824×	`times-frac_binary64`
352×	`+-commutative_binary64`
290×	`associate-+r+_binary64`
263×	`fma-def_binary64`
209×	`*-commutative_binary64`

Counts

215 → 226

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	856	9844
1	3106	9844
2	4969	9844

prune453.0ms (5.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	219	7	226
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	221	7	228

Error

0.0b

Counts

228 → 7

Alt Table

Status	Error	Program
	2.5b	(/.f64 (/.f64 (fma.f64 alpha alpha -1) (*.f64 (/.f64 (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2) (+.f64 beta 1)) (-.f64 alpha 1))) (+.f64 alpha (+.f64 beta 3)))
	3.2b	(.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 1 alpha) (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) 1) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 1 alpha) (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (+.f64 alpha (+.f64 beta 3))))
▶	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
	33.9b	(-.f64 (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 1 (.f64 beta beta))) (fma.f64 9 (/.f64 alpha (pow.f64 beta 3)) (fma.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3)) (/.f64 6 (pow.f64 beta 3)))))
	2.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha))) 2) 1) (/.f64 (cbrt.f64 (*.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha))) (+.f64 alpha (+.f64 beta 3))))
	2.9b	(*.f64 (/.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 alpha) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
	30.5b	(/.f64 (/.f64 (+.f64 1 alpha) beta) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 15576 to 11209 computations (28% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
✓	0.0b	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
✓	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))

series166.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

77.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
42.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))
31.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
15.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

rewrite87.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

207×	`add-sqr-sqrt_binary64`
201×	`log1p-expm1-u_binary64`
201×	`expm1-log1p-u_binary64`
197×	`add-log-exp_binary64`
196×	`add-exp-log_binary64`

Counts

4 → 131

Calls

4 calls:

84.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
84.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
84.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
84.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	100
1	415	82
2	4949	82
3	5268	82

simplify155.0ms (2%)

Algorithm

1×	egg-herbie

Rules

862×	`times-frac_binary64`
373×	`+-commutative_binary64`
303×	`associate-+r+_binary64`
270×	`fma-def_binary64`
219×	`*-commutative_binary64`

Counts

227 → 241

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	912	10607
1	3319	10607
2	4980	10607

prune497.0ms (6.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	239	2	241
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	242	6	248

Error

0.0b

Counts

248 → 6

Alt Table

Status	Error	Program
	33.9b	(-.f64 (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 1 (.f64 beta beta))) (fma.f64 9 (/.f64 alpha (pow.f64 beta 3)) (fma.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3)) (/.f64 6 (pow.f64 beta 3)))))
	0.9b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
	2.5b	(/.f64 (/.f64 (fma.f64 alpha alpha -1) (*.f64 (/.f64 (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2) (+.f64 beta 1)) (-.f64 alpha 1))) (+.f64 alpha (+.f64 beta 3)))
	2.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha))) 2) 1) (/.f64 (cbrt.f64 (*.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha))) (+.f64 alpha (+.f64 beta 3))))
▶	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
	30.5b	(/.f64 (/.f64 (+.f64 1 alpha) beta) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 16868 to 12086 computations (28.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2)))))
✓	0.1b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))
✓	0.2b	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2)))

series190.0ms (2.5%)

Counts

4 → 88

Calls

4 calls:

79.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
44.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2)))))
35.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2)))
31.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))

rewrite76.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

235×	`add-sqr-sqrt_binary64`
228×	`log1p-expm1-u_binary64`
228×	`expm1-log1p-u_binary64`
223×	`add-log-exp_binary64`
222×	`add-exp-log_binary64`

Counts

4 → 77

Calls

4 calls:

74.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
74.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2)))))
74.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))
74.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	93
1	479	93
2	4887	93
3	5014	93

simplify179.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

935×	`fma-def_binary64`
858×	`times-frac_binary64`
323×	`+-commutative_binary64`
260×	`associate-+r+_binary64`
217×	`*-commutative_binary64`

Counts

165 → 188

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	856	9588
1	3083	9558
2	5067	9558

prune403.0ms (5.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	187	7	194

Error

Counts

194 → 7

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
	33.9b	(-.f64 (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 1 (.f64 beta beta))) (fma.f64 9 (/.f64 alpha (pow.f64 beta 3)) (fma.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3)) (/.f64 6 (pow.f64 beta 3)))))
	0.9b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
	2.5b	(/.f64 (/.f64 (fma.f64 alpha alpha -1) (*.f64 (/.f64 (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2) (+.f64 beta 1)) (-.f64 alpha 1))) (+.f64 alpha (+.f64 beta 3)))
	2.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha))) 2) 1) (/.f64 (cbrt.f64 (*.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha))) (+.f64 alpha (+.f64 beta 3))))
✓	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
	30.5b	(/.f64 (/.f64 (+.f64 1 alpha) beta) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 14754 to 10610 computations (28.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 alpha (+.f64 beta 3)))
✓	0.0b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2))
✓	0.1b	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2)))
✓	0.1b	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))

series217.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

85.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
82.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2)))
37.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2))
12.0ms	(/.f64 1 (+.f64 alpha (+.f64 beta 3)))

rewrite84.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

232×	`prod-diff_binary64`
205×	`add-sqr-sqrt_binary64`
199×	`log1p-expm1-u_binary64`
199×	`expm1-log1p-u_binary64`
195×	`add-log-exp_binary64`

Counts

4 → 114

Calls

4 calls:

79.0ms	(/.f64 1 (+.f64 alpha (+.f64 beta 3)))
79.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2))
79.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2)))
79.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	97
1	413	79
2	4991	79
3	5386	79

simplify153.0ms (2%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
365×	`+-commutative_binary64`
293×	`associate-+r+_binary64`
271×	`fma-def_binary64`
215×	`*-commutative_binary64`

Counts

210 → 223

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	895	10260
1	3240	10260
2	5027	10260

prune459.0ms (6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	223	7	230

Error

Counts

230 → 7

Alt Table

Status	Error	Program
	2.2b	(/.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 (+.f64 alpha beta) 2)))
	0.9b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
✓	0.2b	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 beta alpha) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
	2.5b	(/.f64 (/.f64 (fma.f64 alpha alpha -1) (*.f64 (/.f64 (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2) (+.f64 beta 1)) (-.f64 alpha 1))) (+.f64 alpha (+.f64 beta 3)))
	2.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha))) 2) 1) (/.f64 (cbrt.f64 (*.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha))) (+.f64 alpha (+.f64 beta 3))))
✓	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
	30.5b	(/.f64 (/.f64 (+.f64 1 alpha) beta) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 16047 to 11541 computations (28.1% saved)

regimes2.1s (27.2%)

Accuracy

Total 0.1b remaining (79.4%)

Threshold costs 0.1b (79.4%)

Counts

331 → 1

Compiler

Compiled 32879 to 24611 computations (25.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	27	41
2	26	41

end359.0ms (4.7%)

Compiler: Compiled 332 to 235 computations (29.2% saved)

Details

analyze3.0ms (0%)

sample1.4s (18.2%)

simplify211.0ms (2.8%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

series158.0ms (2.1%)

rewrite83.0ms (1.1%)

simplify191.0ms (2.5%)

prune453.0ms (5.9%)

localize13.0ms (0.2%)

series166.0ms (2.2%)

rewrite87.0ms (1.1%)

simplify155.0ms (2%)

prune497.0ms (6.5%)

localize18.0ms (0.2%)

series190.0ms (2.5%)

rewrite76.0ms (1%)

simplify179.0ms (2.3%)

prune403.0ms (5.3%)

localize14.0ms (0.2%)

series217.0ms (2.8%)

rewrite84.0ms (1.1%)

simplify153.0ms (2%)

prune459.0ms (6%)

regimes2.1s (27.2%)

simplify2.0ms (0%)

end359.0ms (4.7%)

Profiling