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 (14.6%)

Symmetry

(sort alpha beta)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify212.0ms (2.3%)

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%)

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

1.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.8b	(/.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

3.8b

(/.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)

localize11.0ms (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 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
✓	21.1b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series162.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

81.0ms	(/.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))))
32.0ms	(/.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))

rewrite78.0ms (0.8%)

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)))
19.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
13.0ms	(/.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))

simplify195.0ms (2.1%)

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 → 351

Iterations

Useful iterations: 1 (0.0ms)

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

prune759.0ms (8.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	342	9	351
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	344	9	353

Error

0.0b

Counts

353 → 9

Alt Table

Status	Error	Program
	28.6b	(.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)))))
	31.4b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 8 (pow.f64 (+.f64 alpha beta) 3)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) -4))) (.f64 (+.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (-.f64 (.f64 2 2) (*.f64 (+.f64 alpha beta) 2))) (-.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	4.0b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2))) (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))))) (+.f64 alpha (+.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)))
	3.5b	(.f64 (.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
	0.3b	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	29.3b	(/.f64 (+.f64 1 alpha) (pow.f64 beta 2))
	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.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)))
	9.3b	(/.f64 (.f64 (+.f64 alpha 1) (+.f64 beta 1)) (.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))

Compiler

Compiled 21630 to 14640 computations (32.3% 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)))

series157.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

81.0ms	(/.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)))
45.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
16.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))
15.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

rewrite86.0ms (0.9%)

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:

27.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
22.0ms	(/.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)))

simplify229.0ms (2.5%)

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

prune839.0ms (9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	389	4	393
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	394	8	402

Error

Counts

402 → 8

Alt Table

Status	Error	Program
	3.5b	(.f64 (.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
▶	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3))) (+.f64 alpha (+.f64 beta 3)))
	28.6b	(.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)))))
	0.2b	(.f64 (sqrt.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)))) (sqrt.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)))))
	0.2b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 1 alpha)) (cbrt.f64 (+.f64 1 alpha))) (/.f64 (+.f64 2 (+.f64 alpha beta)) (cbrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	2.6b	(/.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 2 (+.f64 alpha beta))))
	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.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)))
	4.0b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2))) (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 22869 to 15464 computations (32.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))
✓	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3)
✓	0.4b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3))

series591.0ms (6.3%)

Counts

3 → 72

Calls

3 calls:

509.0ms

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

65.0ms

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

17.0ms

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

rewrite83.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

177×	`*-un-lft-identity_binary64`
85×	`times-frac_binary64`
74×	`distribute-lft-out_binary64`
58×	`cbrt-prod_binary64`
52×	`cube-prod_binary64`

Counts

3 → 178

Calls

3 calls:

43.0ms

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

12.0ms

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

9.0ms

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

simplify205.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary64`
275×	`+-commutative_binary64`
218×	`associate-+r+_binary64`
191×	`*-commutative_binary64`
168×	`distribute-rgt-in_binary64`

Counts

250 → 261

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	937	13366
1	3206	12771
2	5151	12771

prune840.0ms (9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	347	1	348
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	348	8	356

Error

Counts

356 → 8

Alt Table

Status	Error	Program
	3.5b	(.f64 (.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
✓	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3))) (+.f64 alpha (+.f64 beta 3)))
	4.0b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2))) (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))))) (+.f64 alpha (+.f64 beta 3)))
▶	0.1b	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (sqrt.f64 (+.f64 1 alpha)) (+.f64 2 (+.f64 beta alpha)))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3))) (+.f64 alpha (+.f64 beta 3)))
	28.6b	(.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)))))
	0.2b	(.f64 (sqrt.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)))) (sqrt.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)))))
	0.2b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 1 alpha)) (cbrt.f64 (+.f64 1 alpha))) (/.f64 (+.f64 2 (+.f64 alpha beta)) (cbrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	2.6b	(/.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 2 (+.f64 alpha beta))))

Compiler

Compiled 20978 to 14594 computations (30.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series125.0ms (1.3%)

Counts

2 → 40

Calls

2 calls:

91.0ms

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

34.0ms

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

rewrite55.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
36×	`distribute-lft-out_binary64`
24×	`sqrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`

Counts

2 → 109

Calls

2 calls:

33.0ms

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

10.0ms

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

simplify137.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

874×	`times-frac_binary64`
601×	`fma-def_binary64`
186×	`+-commutative_binary64`
176×	`distribute-rgt-in_binary64`
165×	`*-commutative_binary64`

Counts

149 → 176

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	701	9038
1	2379	8567
2	4962	8567

prune904.0ms (9.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	351	8	359

Error

Counts

359 → 8

Alt Table

Status	Error	Program
	3.5b	(.f64 (.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
✓	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3))) (+.f64 alpha (+.f64 beta 3)))
	4.0b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2))) (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (sqrt.f64 (+.f64 1 alpha)) (+.f64 2 (+.f64 beta alpha)))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3))) (+.f64 alpha (+.f64 beta 3)))
	28.6b	(.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)))))
	0.2b	(.f64 (sqrt.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)))) (sqrt.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)))))
	0.2b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 1 alpha)) (cbrt.f64 (+.f64 1 alpha))) (/.f64 (+.f64 2 (+.f64 alpha beta)) (cbrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	2.6b	(/.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 2 (+.f64 alpha beta))))

Compiler

Compiled 22717 to 16156 computations (28.9% saved)

regimes1.9s (20.2%)

Accuracy

Total 0.1b remaining (73.4%)

Threshold costs 0.1b (73.4%)

Counts

459 → 1

Compiler

Compiled 49856 to 34709 computations (30.4% 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	17	37
1	25	37
2	24	37

end355.0ms (3.8%)

Compiler: Compiled 482 to 324 computations (32.8% saved)

Details

analyze3.0ms (0%)

sample1.4s (14.6%)

simplify212.0ms (2.3%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series162.0ms (1.7%)

rewrite78.0ms (0.8%)

simplify195.0ms (2.1%)

prune759.0ms (8.1%)

localize14.0ms (0.1%)

series157.0ms (1.7%)

rewrite86.0ms (0.9%)

simplify229.0ms (2.5%)

prune839.0ms (9%)

localize16.0ms (0.2%)

series591.0ms (6.3%)

rewrite83.0ms (0.9%)

simplify205.0ms (2.2%)

prune840.0ms (9%)

localize15.0ms (0.2%)

series125.0ms (1.3%)

rewrite55.0ms (0.6%)

simplify137.0ms (1.5%)

prune904.0ms (9.7%)

regimes1.9s (20.2%)

simplify2.0ms (0%)

end355.0ms (3.8%)

Profiling