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)

sample1.5s (14.2%)

Symmetry

(sort alpha beta)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify219.0ms (2.1%)

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%)

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

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.9b	(/.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))
▶	2.6b	(/.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

3.9b

(/.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))

▶

2.6b

(/.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)

localize15.0ms (0.1%)

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)))
✓	18.2b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series285.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

153.0ms	(/.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)))
73.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
50.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
8.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

rewrite76.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
34×	`distribute-lft-out_binary64`
34×	`add-cbrt-cube_binary64`
34×	`add-exp-log_binary64`
24×	`flip-+_binary64`

Counts

4 → 166

Calls

4 calls:

21.0ms	(/.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)))
20.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
12.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
10.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify232.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

363×	`+-commutative_binary64`
342×	`distribute-rgt-in_binary64`
291×	`associate-+r+_binary64`
266×	`fma-def_binary64`
257×	`*-commutative_binary64`

Counts

262 → 350

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1061	15235
1	3719	14320
2	5141	14320

prune681.0ms (6.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	343	7	350
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	345	7	352

Error

0.0b

Counts

352 → 7

Alt Table

Status	Error	Program
	0.2b	(/.f64 (.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	26.1b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 3) 3))) (+.f64 (.f64 alpha alpha) (-.f64 (.f64 (+.f64 beta 3) (+.f64 beta 3)) (.f64 alpha (+.f64 beta 3)))))
	2.8b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (/.f64 (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 beta 1))))) (+.f64 alpha (+.f64 beta 3)))
	30.1b	(/.f64 (+.f64 1 alpha) (pow.f64 beta 2))
	2.6b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 (.f64 alpha alpha) (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
	8.9b	(/.f64 (+.f64 beta 1) (*.f64 (pow.f64 (+.f64 beta 2) 2) (+.f64 beta 3)))
▶	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 21253 to 14414 computations (32.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series263.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

149.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
73.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
21.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
20.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))

rewrite86.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`*-un-lft-identity_binary64`
89×	`times-frac_binary64`
82×	`distribute-lft-out_binary64`
60×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64`

Counts

4 → 210

Calls

4 calls:

25.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
23.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
9.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
7.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))

simplify227.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-def_binary64`
340×	`+-commutative_binary64`
271×	`associate-+r+_binary64`
244×	`*-commutative_binary64`
216×	`sub-neg_binary64`

Counts

306 → 393

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1073	16270
1	3699	15449
2	4984	15449

prune723.0ms (7.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	391	2	393
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	394	6	400

Error

Counts

400 → 6

Alt Table

Status	Error	Program
	0.2b	(/.f64 (.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	26.1b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 3) 3))) (+.f64 (.f64 alpha alpha) (-.f64 (.f64 (+.f64 beta 3) (+.f64 beta 3)) (.f64 alpha (+.f64 beta 3)))))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))) (cbrt.f64 (/.f64 (.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3))))) (cbrt.f64 (/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))))
	30.1b	(/.f64 (+.f64 1 alpha) (pow.f64 beta 2))
	2.6b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 (.f64 alpha alpha) (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
▶	0.1b	(/.f64 (*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 22603 to 15290 computations (32.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))))
	0.0b	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))
✓	0.1b	(/.f64 (*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

series245.0ms (2.4%)

Counts

3 → 72

Calls

3 calls:

152.0ms

(/.f64 (*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

70.0ms

(*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))

23.0ms

(expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
26×	`associate-r_binary64`
26×	`times-frac_binary64`
23×	`distribute-lft-out_binary64`
21×	`add-sqr-sqrt_binary64`

Counts

3 → 90

Calls

3 calls:

14.0ms

(/.f64 (*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

13.0ms

(*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))

0.0ms

(expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))))

simplify169.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

896×	`times-frac_binary64`
865×	`fma-def_binary64`
310×	`+-commutative_binary64`
250×	`associate-+r+_binary64`
215×	`*-commutative_binary64`

Counts

162 → 214

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	923	11780
1	3201	11268
2	5167	11268

prune595.0ms (5.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	299	2	301
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	302	5	307

Error

Counts

307 → 5

Alt Table

Status	Error	Program
	2.6b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 (.f64 alpha alpha) (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
	0.6b	(/.f64 (/.f64 (*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
▶	0.2b	(/.f64 (.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.7b	(/.f64 (.f64 (.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))) (cbrt.f64 (/.f64 (.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3))))) (cbrt.f64 (/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))))

Compiler

Compiled 19454 to 13440 computations (30.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series368.0ms (3.6%)

Counts

4 → 80

Calls

4 calls:

159.0ms	(/.f64 (.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
89.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
73.0ms	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
46.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

rewrite126.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

217×	`*-un-lft-identity_binary64`
112×	`times-frac_binary64`
89×	`distribute-lft-out_binary64`
82×	`associate-r_binary64`
71×	`add-sqr-sqrt_binary64`

Counts

4 → 260

Calls

4 calls:

41.0ms	(/.f64 (.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
25.0ms	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
18.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

simplify279.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

347×	`+-commutative_binary64`
296×	`*-commutative_binary64`
296×	`distribute-rgt-in_binary64`
271×	`associate-+r+_binary64`
250×	`fma-def_binary64`

Counts

340 → 437

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1120	18960
1	3879	17510
2	5323	17510

prune1.5s (14.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	534	0	534
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	534	5	539

Error

Counts

539 → 5

Alt Table

Status	Error	Program
	2.6b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 (.f64 alpha alpha) (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
	0.6b	(/.f64 (/.f64 (*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
✓	0.2b	(/.f64 (.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.7b	(/.f64 (.f64 (.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))) (cbrt.f64 (/.f64 (.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3))))) (cbrt.f64 (/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))))

Compiler

Compiled 31307 to 21706 computations (30.7% saved)

regimes2.3s (22.4%)

Accuracy

Total 0.1b remaining (71.4%)

Threshold costs 0.1b (71.4%)

Counts

449 → 1

Compiler

Compiled 56654 to 40376 computations (28.7% saved)

simplify3.0ms (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	21	45
1	29	45
2	28	45

end290.0ms (2.8%)

Compiler: Compiled 353 to 243 computations (31.2% saved)

Details

analyze3.0ms (0%)

sample1.5s (14.2%)

simplify219.0ms (2.1%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series285.0ms (2.8%)

rewrite76.0ms (0.7%)

simplify232.0ms (2.3%)

prune681.0ms (6.6%)

localize14.0ms (0.1%)

series263.0ms (2.6%)

rewrite86.0ms (0.8%)

simplify227.0ms (2.2%)

prune723.0ms (7.1%)

localize17.0ms (0.2%)

series245.0ms (2.4%)

rewrite36.0ms (0.4%)

simplify169.0ms (1.7%)

prune595.0ms (5.8%)

localize15.0ms (0.1%)

series368.0ms (3.6%)

rewrite126.0ms (1.2%)

simplify279.0ms (2.7%)

prune1.5s (14.9%)

regimes2.3s (22.4%)

simplify3.0ms (0%)

end290.0ms (2.8%)

Profiling