Details

analyze110.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Compiler

Compiled 66 to 34 computations (48.5% saved)

sample49.0ms (0.4%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 125 to 64 computations (48.8% saved)

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-+l+_binary64`
492×	`associate-l_binary64`
422×	`associate-r_binary64`
369×	`times-frac_binary64`
336×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	79
1	65	79
2	280	79
3	1518	79
4	4862	79
5	5395	79

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

53.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	53.5b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))

Status

Error

Program

▶

53.5b

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

Compiler

Compiled 168 to 81 computations (51.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
35.3b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
45.9b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite701.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

35.4b

Rules

86×	`times-frac_binary64`
66×	`flip3-+_binary64` `flip-+_binary64` `associate-/r/_binary64`
61×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
46×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64` `frac-times_binary64`

Counts

4 → 228

Calls

4 calls:

42.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
25.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
14.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))

Compiler

Compiled 17676 to 6571 computations (62.8% saved)

series1.9s (15.6%)

Error

11.7b

Counts

4 → 88

Calls

4 calls:

1.4s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
144.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
137.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
75.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 21562 to 14450 computations (33% saved)

simplify401.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

502×	`distribute-rgt-in_binary64`
473×	`distribute-lft-in_binary64`
210×	`*-commutative_binary64`
165×	`+-commutative_binary64`
123×	`associate-/l*_binary64`

Counts

316 → 297

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	792	26527
1	2724	24488
2	5517	24488

prune290.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	289	8	297
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	290	8	298

Error

13.6b

Counts

298 → 8

Alt Table

Status	Error	Program
	54.8b	(/.f64 i (/.f64 (*.f64 beta beta) (+.f64 alpha i)))
	63.4b	(/.f64 i (/.f64 (*.f64 alpha alpha) (+.f64 beta i)))
▶	24.3b	(-.f64 (+.f64 1/16 (/.f64 1/64 (.f64 i i))) (.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (/.f64 (.f64 beta beta) (.f64 i i)))))
	54.2b	(/.f64 (.f64 (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i))))) (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (-.f64 (pow.f64 (+.f64 alpha beta) 2) (.f64 (.f64 i i) 4)))) (-.f64 (+.f64 alpha beta) (.f64 2 i))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
	56.5b	(/.f64 (-.f64 (.f64 i (+.f64 alpha i)) (+.f64 (.f64 3 (/.f64 (.f64 alpha (.f64 i i)) beta)) (+.f64 (/.f64 (.f64 (.f64 alpha alpha) i) beta) (.f64 2 (/.f64 (pow.f64 i 3) beta))))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
	35.5b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
	38.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (.f64 (cbrt.f64 (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) 1)) (cbrt.f64 (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) 1)))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (cbrt.f64 (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) 1))))
	37.6b	(/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (/.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))

Compiler

Compiled 16012 to 7235 computations (54.8% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.5b	(/.f64 1/64 (*.f64 i i))
3.1b	(/.f64 (.f64 alpha alpha) (.f64 i i))
18.3b	(/.f64 (.f64 beta beta) (.f64 i i))

rewrite110.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

Rules

32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`div-exp_binary64` `cbrt-undiv_binary64`
9×	`prod-exp_binary64` `cbrt-unprod_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64` `-un-lft-identity_binary64` `associate-/l_binary64`
3×	`pow1_binary64` `add-log-exp_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/r*_binary64`

Counts

3 → 63

Calls

3 calls:

6.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
6.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
4.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1948 to 675 computations (65.3% saved)

series60.0ms (0.5%)

Error

13.6b

Counts

3 → 15

Calls

3 calls:

24.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
23.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
8.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 918 to 608 computations (33.8% saved)

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

691×	`associate-/l*_binary64`
488×	`unswap-sqr_binary64`
465×	`associate-*l/_binary64`
360×	`associate-/r*_binary64`
318×	`associate-l_binary64`

Counts

78 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	1122
1	247	809
2	854	750
3	3283	704
4	4150	704
5	5097	704

prune40.0ms (0.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	55	7	62

Error

9.6b

Counts

62 → 7

Alt Table

Status	Error	Program
	54.8b	(/.f64 i (/.f64 (*.f64 beta beta) (+.f64 alpha i)))
	54.2b	(/.f64 (.f64 (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i))))) (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (-.f64 (pow.f64 (+.f64 alpha beta) 2) (.f64 (.f64 i i) 4)))) (-.f64 (+.f64 alpha beta) (.f64 2 i))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
	56.5b	(/.f64 (-.f64 (.f64 i (+.f64 alpha i)) (+.f64 (.f64 3 (/.f64 (.f64 alpha (.f64 i i)) beta)) (+.f64 (/.f64 (.f64 (.f64 alpha alpha) i) beta) (.f64 2 (/.f64 (pow.f64 i 3) beta))))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
	35.5b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
▶	20.1b	(-.f64 (+.f64 1/16 (/.f64 1/64 (.f64 i i))) (.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (cbrt.f64 (pow.f64 (/.f64 beta i) 6)))))
	38.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (.f64 (cbrt.f64 (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) 1)) (cbrt.f64 (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) 1)))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (cbrt.f64 (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) 1))))
	37.6b	(/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (/.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))

Compiler

Compiled 1259 to 647 computations (48.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 beta i) 6)
0.5b	(/.f64 1/64 (*.f64 i i))
3.1b	(/.f64 (.f64 alpha alpha) (.f64 i i))
20.2b	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))

rewrite155.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

9.6b

Rules

26×	`unpow-prod-down_binary64`
24×	`add-exp-log_binary64`
22×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64` `*-un-lft-identity_binary64`
21×	`add-cbrt-cube_binary64`
17×	`cbrt-prod_binary64`

Counts

4 → 95

Calls

4 calls:

6.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
4.0ms	(pow.f64 (/.f64 beta i) 6)
4.0ms	(/.f64 1/64 (*.f64 i i))
4.0ms	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))

Compiler

Compiled 2873 to 1404 computations (51.1% saved)

series96.0ms (0.8%)

Error

9.6b

Counts

4 → 21

Calls

4 calls:

31.0ms	(pow.f64 (/.f64 beta i) 6)
25.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
24.0ms	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))
9.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1272 to 903 computations (29% saved)

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

656×	`times-frac_binary64`
438×	`associate-/l*_binary64`
391×	`associate-*l/_binary64`
380×	`associate-l_binary64`
379×	`log-prod_binary64`

Counts

116 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	1678
1	356	1367
2	978	1285
3	4323	1285
4	5102	1285

prune53.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	74	7	81

Error

9.6b

Counts

81 → 7

Alt Table

Status	Error	Program
	54.8b	(/.f64 i (/.f64 (*.f64 beta beta) (+.f64 alpha i)))
	54.2b	(/.f64 (.f64 (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i))))) (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (-.f64 (pow.f64 (+.f64 alpha beta) 2) (.f64 (.f64 i i) 4)))) (-.f64 (+.f64 alpha beta) (.f64 2 i))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
	56.5b	(/.f64 (-.f64 (.f64 i (+.f64 alpha i)) (+.f64 (.f64 3 (/.f64 (.f64 alpha (.f64 i i)) beta)) (+.f64 (/.f64 (.f64 (.f64 alpha alpha) i) beta) (.f64 2 (/.f64 (pow.f64 i 3) beta))))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
▶	35.5b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
✓	20.1b	(-.f64 (+.f64 1/16 (/.f64 1/64 (.f64 i i))) (.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (cbrt.f64 (pow.f64 (/.f64 beta i) 6)))))
	38.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (.f64 (cbrt.f64 (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) 1)) (cbrt.f64 (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) 1)))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (cbrt.f64 (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) 1))))
	37.6b	(/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (/.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))

Compiler

Compiled 1413 to 787 computations (44.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
0.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
31.9b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
33.1b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite1.1s (9.4%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

Rules

437×	`*-un-lft-identity_binary64`
409×	`times-frac_binary64`
235×	`add-sqr-sqrt_binary64`
150×	`associate-r_binary64`
142×	`add-cube-cbrt_binary64`

Counts

4 → 394

Calls

4 calls:

164.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
20.0ms	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
12.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
10.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

Compiler

Compiled 22518 to 10899 computations (51.6% saved)

series1.8s (14.9%)

Error

8.6b

Counts

4 → 72

Calls

4 calls:

1.3s	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
176.0ms	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
105.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
68.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 21297 to 14544 computations (31.7% saved)

simplify530.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

412×	`distribute-rgt-in_binary64`
386×	`distribute-lft-in_binary64`
310×	`*-commutative_binary64`
197×	`associate-*r/_binary64`
159×	`+-commutative_binary64`

Counts

466 → 441

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	985	35833
1	3482	33572
2	5615	33572

prune546.0ms (4.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	434	7	441
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	439	9	448

Error

8.6b

Counts

448 → 9

Alt Table

Status	Error	Program
	36.1b	(.f64 (/.f64 (/.f64 i 1) 1) (.f64 (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1))) (/.f64 (/.f64 (+.f64 alpha (+.f64 i beta)) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 1 (+.f64 (+.f64 beta (.f64 i 2)) alpha)))))
	37.8b	(.f64 (.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 1 (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (-.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta (.f64 i 2)) 2))) (sqrt.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1))))) (/.f64 (-.f64 alpha (+.f64 beta (.f64 2 i))) (sqrt.f64 (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))))
	35.5b	(.f64 (/.f64 1 (/.f64 (+.f64 1 (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
	35.5b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i)))))
	54.8b	(/.f64 i (/.f64 (*.f64 beta beta) (+.f64 alpha i)))
	36.0b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (.f64 (cbrt.f64 (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (cbrt.f64 (+.f64 (+.f64 beta (.f64 i 2)) alpha)))) (/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (cbrt.f64 (+.f64 (+.f64 beta (.f64 i 2)) alpha)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
	50.2b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (+.f64 i alpha) (-.f64 (+.f64 alpha (+.f64 beta (*.f64 2 i))) 1)))
	36.0b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (cbrt.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))) (cbrt.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
	20.1b	(-.f64 (+.f64 1/16 (/.f64 1/64 (.f64 i i))) (.f64 1/32 (+.f64 (/.f64 (.f64 alpha alpha) (.f64 i i)) (cbrt.f64 (pow.f64 (/.f64 beta i) 6)))))

Compiler

Compiled 23880 to 12104 computations (49.3% saved)

regimes2.3s (19.2%)

Accuracy

Total -0.8b remaining (-7.8%)

Threshold costs -0.8b (-7.8%)

Compiler

Compiled 50008 to 29129 computations (41.8% saved)

bsearch39.0ms (0.3%)

Steps

Iters	Range		Point
7	6.457137374296923e+130	1.1703761377648405e+132	5.5059367458921626e+131

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
4×	`*-commutative_binary64`
1×	`1-exp_binary64` `sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	89
1	41	89
2	42	89
3	40	89

end9.0ms (0.1%)

Remove: (sort alpha beta)
Compiler: Compiled 189 to 111 computations (41.3% saved)

sample1.5s (12.4%)

Algorithm

1×

intervals

Results

648.0ms	8000×	body	128	valid
186.0ms	8000×	pre	128	true

Compiler

Compiled 659 to 387 computations (41.3% saved)

Details

analyze110.0ms (0.9%)

sample49.0ms (0.4%)

simplify46.0ms (0.4%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite701.0ms (5.7%)

series1.9s (15.6%)

simplify401.0ms (3.3%)

prune290.0ms (2.4%)

localize12.0ms (0.1%)

rewrite110.0ms (0.9%)

series60.0ms (0.5%)

simplify80.0ms (0.7%)

prune40.0ms (0.3%)

localize14.0ms (0.1%)

rewrite155.0ms (1.3%)

series96.0ms (0.8%)

simplify100.0ms (0.8%)

prune53.0ms (0.4%)

localize19.0ms (0.2%)

rewrite1.1s (9.4%)

series1.8s (14.9%)

simplify530.0ms (4.3%)

prune546.0ms (4.5%)

regimes2.3s (19.2%)

bsearch39.0ms (0.3%)

simplify4.0ms (0%)

end9.0ms (0.1%)

sample1.5s (12.4%)

Profiling