Details

analyze305.0ms (1.5%)

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)

sample40.0ms (0.2%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 83 to 55 computations (33.7% saved)

simplify238.0ms (1.2%)

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 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	36	40
2	110	40
3	444	37
4	2164	37
5	2127	37
6	2255	37
7	2514	37
8	2864	37
9	2835	37
10	2933	37
11	3060	37
12	3203	37
13	3503	37
14	4070	37
15	3881	37
16	3904	37
17	3911	37
18	3918	37
19	3925	37
20	3932	37
21	3939	37
22	3946	37
23	3953	37
24	5023	37

prune6.0ms (0%)

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

1.1b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	2.1b	(/.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)))
	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))

Status

Error

Program

▶

2.1b

(/.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)))

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))

Compiler

Compiled 155 to 102 computations (34.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.0b	(.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)))
20.1b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite397.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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 → 158

Calls

4 calls:

28.0ms	(/.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)))
24.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
20.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
14.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 5264 to 3194 computations (39.3% saved)

series740.0ms (3.7%)

Error

0.0b

Counts

4 → 72

Calls

4 calls:

274.0ms	(/.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)))
137.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
102.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
37.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 13973 to 11013 computations (21.2% saved)

simplify228.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

352×	`distribute-rgt-in_binary64`
331×	`distribute-lft-in_binary64`
327×	`+-commutative_binary64`
260×	`associate-+r+_binary64`
228×	`*-commutative_binary64`

Counts

230 → 210

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	958	14678
1	3200	13205
2	5133	13205

prune417.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	202	8	210
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	204	8	212

Error

Counts

212 → 8

Alt Table

Status	Error	Program
	31.0b	(/.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 (+.f64 1 beta) 3) (pow.f64 (.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta))) 3)) (pow.f64 (+.f64 1 alpha) 3))) (+.f64 alpha (+.f64 beta 3)))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (+.f64 4 (+.f64 (.f64 beta (+.f64 (.f64 2 alpha) beta)) (+.f64 (.f64 alpha (+.f64 4 alpha)) (*.f64 beta 4)))))) (+.f64 alpha (+.f64 beta 3)))
	33.5b	(/.f64 (+.f64 1 alpha) (*.f64 (pow.f64 (+.f64 alpha 2) 2) (+.f64 alpha 3)))
	27.4b	(-.f64 (+.f64 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 alpha (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 beta (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (/.f64 1 (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3)))))) (+.f64 (.f64 17 (/.f64 (.f64 alpha (.f64 beta beta)) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (+.f64 (.f64 30 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (+.f64 (.f64 3 (/.f64 (.f64 alpha (pow.f64 beta 3)) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (.f64 16 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))))))))
	29.7b	(/.f64 (+.f64 1 alpha) (*.f64 beta beta))
	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
▶	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.2b	(/.f64 (.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 9652 to 6654 computations (31.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))
0.0b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
0.0b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

rewrite925.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

826×	`*-un-lft-identity_binary64`
508×	`times-frac_binary64`
374×	`distribute-lft-out_binary64`
191×	`add-sqr-sqrt_binary64`
182×	`add-cube-cbrt_binary64`

Counts

4 → 422

Calls

4 calls:

239.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
60.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
22.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
10.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 9138 to 6131 computations (32.9% saved)

series762.0ms (3.8%)

Error

Counts

4 → 72

Calls

4 calls:

277.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
140.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
104.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
43.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 14534 to 11415 computations (21.5% saved)

simplify391.0ms (2%)

Algorithm

1×	egg-herbie

Rules

489×	`distribute-rgt-in_binary64`
333×	`+-commutative_binary64`
258×	`associate-+r+_binary64`
257×	`*-commutative_binary64`
207×	`associate-*r/_binary64`

Counts

494 → 477

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1117	24103
1	3594	22380
2	5226	22380

prune691.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	474	3	477
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	478	7	485

Error

Counts

485 → 7

Alt Table

Status	Error	Program
	0.2b	(/.f64 (.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))) (.f64 (+.f64 (+.f64 beta 2) alpha) (+.f64 (+.f64 beta 3) alpha)))
	33.5b	(/.f64 (+.f64 1 alpha) (*.f64 (pow.f64 (+.f64 alpha 2) 2) (+.f64 alpha 3)))
	27.4b	(-.f64 (+.f64 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 alpha (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 beta (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (/.f64 1 (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3)))))) (+.f64 (.f64 17 (/.f64 (.f64 alpha (.f64 beta beta)) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (+.f64 (.f64 30 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (+.f64 (.f64 3 (/.f64 (.f64 alpha (pow.f64 beta 3)) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (.f64 16 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))))))))
▶	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	7.0b	(/.f64 (*.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)) 3))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 14029 to 9823 computations (30% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
0.0b	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
0.0b	(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))
0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

rewrite520.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

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 → 202

Calls

4 calls:

34.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
31.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
10.0ms	(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 5582 to 3723 computations (33.3% saved)

series709.0ms (3.6%)

Error

Counts

4 → 72

Calls

4 calls:

276.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
138.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
52.0ms	(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))
44.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 13512 to 10510 computations (22.2% saved)

simplify254.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

366×	`distribute-rgt-in_binary64`
343×	`distribute-lft-in_binary64`
306×	`+-commutative_binary64`
234×	`associate-+r+_binary64`
220×	`*-commutative_binary64`

Counts

274 → 256

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	980	15393
1	3256	14138
2	5185	14138

prune531.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	256	7	263

Error

Counts

263 → 7

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))) (.f64 (+.f64 (+.f64 beta 2) alpha) (+.f64 (+.f64 beta 3) alpha)))
	33.5b	(/.f64 (+.f64 1 alpha) (*.f64 (pow.f64 (+.f64 alpha 2) 2) (+.f64 alpha 3)))
	27.4b	(-.f64 (+.f64 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 alpha (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 beta (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (/.f64 1 (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3)))))) (+.f64 (.f64 17 (/.f64 (.f64 alpha (.f64 beta beta)) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (+.f64 (.f64 30 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (+.f64 (.f64 3 (/.f64 (.f64 alpha (pow.f64 beta 3)) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (.f64 16 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))))))))
✓	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	4.5b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha))) 3)) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 10417 to 7285 computations (30.1% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta 2) alpha))
0.2b	(/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
0.3b	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
0.4b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta))))

rewrite2.0s (10.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

2438×	`*-un-lft-identity_binary64`
2035×	`times-frac_binary64`
1864×	`sqrt-prod_binary64`
931×	`distribute-lft-out_binary64`
841×	`add-sqr-sqrt_binary64`

Counts

4 → 1279

Calls

4 calls:

130.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
45.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
14.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta))))
12.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta 2) alpha))

Compiler

Compiled 30306 to 21743 computations (28.3% saved)

series511.0ms (2.6%)

Error

Counts

4 → 60

Calls

4 calls:

154.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
109.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta))))
44.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta 2) alpha))
40.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))

Compiler

Compiled 10106 to 7839 computations (22.4% saved)

simplify1.6s (7.9%)

Algorithm

1×	egg-herbie

Rules

484×	`times-frac_binary64`
303×	`*-commutative_binary64`
219×	`distribute-rgt-in_binary64`
203×	`distribute-lft-in_binary64`
165×	`+-commutative_binary64`

Counts

1339 → 1288

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1077	61655
1	3051	58938
2	4915	58415
3	4998	58415
4	4918	58415

prune1.0s (5.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1287	1	1288
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	1289	6	1295

Error

Counts

1295 → 6

Alt Table

Status	Error	Program
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))) (.f64 (+.f64 (+.f64 beta 2) alpha) (+.f64 (+.f64 beta 3) alpha)))
	33.5b	(/.f64 (+.f64 1 alpha) (*.f64 (pow.f64 (+.f64 alpha 2) 2) (+.f64 alpha 3)))
	27.4b	(-.f64 (+.f64 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 alpha (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (+.f64 (/.f64 beta (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3))) (/.f64 1 (.f64 (pow.f64 (+.f64 2 beta) 2) (+.f64 beta 3)))))) (+.f64 (.f64 17 (/.f64 (.f64 alpha (.f64 beta beta)) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (+.f64 (.f64 30 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (+.f64 (.f64 3 (/.f64 (.f64 alpha (pow.f64 beta 3)) (.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2)))) (.f64 16 (/.f64 alpha (*.f64 (pow.f64 (+.f64 2 beta) 4) (pow.f64 (+.f64 beta 3) 2))))))))
	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.2b	(/.f64 (.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta 2) alpha))) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 beta))) (/.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 beta))) (sqrt.f64 (+.f64 alpha (+.f64 2 beta))))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 19968 to 14499 computations (27.4% saved)

regimes6.1s (30.6%)

Accuracy

Total 0.1b remaining (71.8%)

Threshold costs 0.1b (71.8%)

Compiler

Compiled 118544 to 86363 computations (27.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	30	40
2	29	40

end7.0ms (0%)

Compiler: Compiled 87 to 63 computations (27.6% saved)

sample1.5s (7.4%)

Algorithm

1×

intervals

Results

557.0ms	8000×	body	128	valid
142.0ms	8000×	pre	128	true

Compiler

Compiled 344 to 253 computations (26.5% saved)

Details

analyze305.0ms (1.5%)

sample40.0ms (0.2%)

simplify238.0ms (1.2%)

prune6.0ms (0%)

localize14.0ms (0.1%)

rewrite397.0ms (2%)

series740.0ms (3.7%)

simplify228.0ms (1.1%)

prune417.0ms (2.1%)

localize15.0ms (0.1%)

rewrite925.0ms (4.6%)

series762.0ms (3.8%)

simplify391.0ms (2%)

prune691.0ms (3.5%)

localize16.0ms (0.1%)

rewrite520.0ms (2.6%)

series709.0ms (3.6%)

simplify254.0ms (1.3%)

prune531.0ms (2.7%)

localize28.0ms (0.1%)

rewrite2.0s (10.2%)

series511.0ms (2.6%)

simplify1.6s (7.9%)

prune1.0s (5.1%)

regimes6.1s (30.6%)

simplify3.0ms (0%)

end7.0ms (0%)

sample1.5s (7.4%)

Profiling