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)

sample1.3s (18.6%)

Symmetry

(sort alpha beta)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify212.0ms (3.1%)

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

prune5.0ms (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

2.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.1b	(/.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))
▶	2.8b	(/.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

5.1b

(/.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))

▶

2.8b

(/.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)

localize14.0ms (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)))
✓	17.9b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series170.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

92.0ms	(/.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)))
41.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
30.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
6.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

rewrite79.0ms (1.1%)

Algorithm

2×	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:

76.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
76.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
76.0ms	(/.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)))
76.0ms	(/.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
0	0	0
1	0	0

simplify133.0ms (1.9%)

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

prune502.0ms (7.3%)

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
	5.2b	(.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))))
	36.1b	(-.f64 (+.f64 (/.f64 beta (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (+.f64 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (+.f64 (/.f64 1 (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (/.f64 alpha (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3)))))) (fma.f64 16 (/.f64 beta (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (fma.f64 17 (/.f64 (.f64 beta (.f64 alpha alpha)) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (fma.f64 3 (/.f64 (.f64 beta (pow.f64 alpha 3)) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (.f64 30 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))))))))
	3.4b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
	2.3b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) -2))) (+.f64 alpha (+.f64 beta 3)))
	3.2b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 4 (+.f64 (.f64 beta beta) (fma.f64 2 (.f64 alpha beta) (.f64 alpha 4))))))) (+.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)))
	2.8b	(*.f64 (/.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) 1) (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 beta 3))))

Compiler

Compiled 15744 to 11345 computations (27.9% 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 alpha 1) (.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)))

series165.0ms (2.4%)

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)))
40.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))
32.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
14.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

rewrite89.0ms (1.3%)

Algorithm

2×	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:

85.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
85.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
85.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))
85.0ms	(/.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)))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify146.0ms (2.1%)

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 → 240

Iterations

Useful iterations: 0 (0.0ms)

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

prune480.0ms (7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	241	6	247

Error

Counts

247 → 6

Alt Table

Status	Error	Program
	3.4b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
	2.3b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) -2))) (+.f64 alpha (+.f64 beta 3)))
▶	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)))) (+.f64 alpha (+.f64 beta 3)))
	0.2b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3))))
	2.8b	(*.f64 (/.f64 (+.f64 alpha 1) 1) (/.f64 (/.f64 (+.f64 1 beta) (pow.f64 (+.f64 (+.f64 alpha beta) 2) 2)) (+.f64 alpha (+.f64 beta 3))))
	5.2b	(.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))))

Compiler

Compiled 16831 to 12066 computations (28.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)
✓	0.1b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3))))
✓	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)))) (+.f64 alpha (+.f64 beta 3)))
✓	0.4b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3))

series184.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

80.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)))) (+.f64 alpha (+.f64 beta 3)))
48.0ms	(pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)
40.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3))))
15.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3))

rewrite78.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

223×	`add-sqr-sqrt_binary64`
221×	`log1p-expm1-u_binary64`
221×	`expm1-log1p-u_binary64`
213×	`add-log-exp_binary64`
212×	`add-exp-log_binary64`

Counts

4 → 95

Calls

4 calls:

76.0ms	(pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)
76.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3))))
76.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)))) (+.f64 alpha (+.f64 beta 3)))
76.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	94
1	456	82
2	4905	82
3	4992	82
0	0	0
1	0	0

simplify144.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

752×	`associate-/l*_binary64`
377×	`+-commutative_binary64`
309×	`associate-+r+_binary64`
276×	`fma-def_binary64`
241×	`*-commutative_binary64`

Counts

191 → 213

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	968	10835
1	3478	10835
2	5464	10835

prune438.0ms (6.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	213	6	219

Error

Counts

219 → 6

Alt Table

Status	Error	Program
	3.4b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
	2.3b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) -2))) (+.f64 alpha (+.f64 beta 3)))
✓	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)))) (+.f64 alpha (+.f64 beta 3)))
▶	0.2b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3))))
	2.8b	(*.f64 (/.f64 (+.f64 alpha 1) 1) (/.f64 (/.f64 (+.f64 1 beta) (pow.f64 (+.f64 (+.f64 alpha beta) 2) 2)) (+.f64 alpha (+.f64 beta 3))))
	5.2b	(.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))))

Compiler

Compiled 16385 to 11844 computations (27.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
✓	0.0b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(*.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
✓	0.2b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3))))

series141.0ms (2%)

Counts

4 → 96

Calls

4 calls:

74.0ms	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3))))
36.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
15.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
15.0ms	(*.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))

rewrite91.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

209×	`add-sqr-sqrt_binary64`
204×	`log1p-expm1-u_binary64`
204×	`expm1-log1p-u_binary64`
199×	`add-log-exp_binary64`
198×	`add-exp-log_binary64`

Counts

4 → 157

Calls

4 calls:

87.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
87.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
87.0ms	(*.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
87.0ms	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	85
1	425	79
2	4939	79
3	5132	79
0	0	0
1	0	0

simplify134.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-def_binary64`
763×	`associate-/l*_binary64`
298×	`+-commutative_binary64`
236×	`associate-+r+_binary64`
189×	`*-commutative_binary64`

Counts

253 → 267

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	806	9648
1	2975	9618
2	5509	9618

prune599.0ms (8.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	266	1	267
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	267	6	273

Error

Counts

273 → 6

Alt Table

Status	Error	Program
	3.4b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (.f64 (/.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) 2)) (+.f64 1 alpha)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
	2.3b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (+.f64 beta 1) (pow.f64 (+.f64 (+.f64 beta alpha) 2) -2))) (+.f64 alpha (+.f64 beta 3)))
✓	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)))) (+.f64 alpha (+.f64 beta 3)))
✓	0.2b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3))))
	5.2b	(.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 alpha beta) 2)) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))

Compiler

Compiled 17155 to 12284 computations (28.4% saved)

regimes1.6s (23.5%)

Accuracy

Total 0.1b remaining (76.3%)

Threshold costs 0.1b (76.3%)

Counts

247 → 1

Compiler

Compiled 23957 to 17660 computations (26.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
12×	`*-commutative_binary64`
10×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	42
1	35	41
2	51	39
3	70	39
4	92	37
5	104	37
6	108	37
7	109	37
8	106	37

end145.0ms (2.1%)

Remove: (sort alpha beta)
Compiler: Compiled 293 to 206 computations (29.7% saved)

Details

analyze3.0ms (0%)

sample1.3s (18.6%)

simplify212.0ms (3.1%)

prune5.0ms (0.1%)

localize14.0ms (0.2%)

series170.0ms (2.5%)

rewrite79.0ms (1.1%)

simplify133.0ms (1.9%)

prune502.0ms (7.3%)

localize13.0ms (0.2%)

series165.0ms (2.4%)

rewrite89.0ms (1.3%)

simplify146.0ms (2.1%)

prune480.0ms (7%)

localize16.0ms (0.2%)

series184.0ms (2.7%)

rewrite78.0ms (1.1%)

simplify144.0ms (2.1%)

prune438.0ms (6.4%)

localize13.0ms (0.2%)

series141.0ms (2%)

rewrite91.0ms (1.3%)

simplify134.0ms (1.9%)

prune599.0ms (8.7%)

regimes1.6s (23.5%)

simplify4.0ms (0.1%)

end145.0ms (2.1%)

Profiling