Details

analyze57.0ms (0.5%)

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 67 to 35 computations (47.8% saved)

sample121.0ms (1.1%)

Algorithm

1×

intervals

Symmetry

(sort alpha beta)

Results

53.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 126 to 65 computations (48.4% saved)

simplify39.0ms (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 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	75
1	67	67
2	293	67
3	1612	67
4	4979	67
5	5035	67

prune14.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

56.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	56.5b	(/.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

▶

56.5b

(/.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 215 to 99 computations (54% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))))
✓	37.1b	(/.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))
✓	48.3b	(/.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))))

series3.5s (32.2%)

Counts

4 → 144

Calls

4 calls:

2.8s	(/.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))
594.0ms	(/.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))))
46.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
17.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite137.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64`
66×	`associate-/r/_binary64`
66×	`flip-+_binary64`
66×	`flip3-+_binary64`
61×	`add-cbrt-cube_binary64`

Counts

4 → 236

Calls

4 calls:

35.0ms	(/.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))
22.0ms	(/.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))))
12.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
11.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))

simplify562.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

743×	`fma-def_binary64`
533×	`associate-/l*_binary64`
352×	`times-frac_binary64`
64×	`sub-neg_binary64`
59×	`associate-/l/_binary64`

Counts

380 → 516

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2697	59448
1	5660	59448

prune1.4s (13.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	579	7	586
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	579	8	587

Error

8.3b

Counts

587 → 8

Alt Table

Status	Error	Program
	25.6b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (*.f64 i i)))))
▶	21.1b	1/16
	57.9b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (fma.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)) -1) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
✓	56.5b	(/.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))
	55.2b	(-.f64 (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (/.f64 (.f64 i alpha) (.f64 beta beta))) (fma.f64 3 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
	51.4b	(/.f64 (.f64 (+.f64 i alpha) i) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
	37.5b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 1)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 1)))
	58.6b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 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 88731 to 46940 computations (47.1% saved)

localize0.0ms (0%)

prune10.0ms (0.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	1	1
Total	8	8

Error

8.3b

Counts

8 → 8

Alt Table

Status	Error	Program
▶	25.6b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (*.f64 i i)))))
✓	21.1b	1/16
	57.9b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (fma.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)) -1) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
✓	56.5b	(/.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))
	55.2b	(-.f64 (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (/.f64 (.f64 i alpha) (.f64 beta beta))) (fma.f64 3 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
	51.4b	(/.f64 (.f64 (+.f64 i alpha) i) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
	37.5b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 1)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 1)))
	58.6b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 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 590 to 323 computations (45.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))
✓	1.2b	(/.f64 1 (*.f64 i i))
✓	3.2b	(/.f64 (.f64 alpha alpha) (.f64 i i))
✓	18.8b	(/.f64 (.f64 beta beta) (.f64 i i))

series138.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

73.0ms	(+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))
31.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
31.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
2.0ms	(/.f64 1 (*.f64 i i))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-exp-log_binary64`
33×	`add-cbrt-cube_binary64`
12×	`div-exp_binary64`
12×	`pow1_binary64`
11×	`prod-exp_binary64`

Counts

4 → 101

Calls

4 calls:

9.0ms	(+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))
5.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
5.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
3.0ms	(/.f64 1 (*.f64 i i))

simplify109.0ms (1%)

Algorithm

1×	egg-herbie

Rules

650×	`associate-l_binary64`
616×	`associate-*r/_binary64`
473×	`associate-/r*_binary64`
399×	`associate-/r/_binary64`
313×	`associate-/l/_binary64`

Counts

197 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	2596
1	340	2301
2	1279	2170
3	4552	2124
4	4982	2124
5	4959	2124

prune128.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	135	8	143

Error

8.2b

Counts

143 → 8

Alt Table

Status	Error	Program
	55.2b	(-.f64 (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (/.f64 (.f64 i alpha) (.f64 beta beta))) (fma.f64 3 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
▶	21.5b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (fma.f64 (/.f64 beta i) (/.f64 beta i) (/.f64 (.f64 alpha alpha) (*.f64 i i)))))
✓	21.1b	1/16
	57.9b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (fma.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)) -1) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
✓	56.5b	(/.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))
	51.4b	(/.f64 (.f64 (+.f64 i alpha) i) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
	37.5b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 1)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 1)))
	58.6b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 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 4940 to 1987 computations (59.8% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 (/.f64 beta i) (/.f64 beta i) (/.f64 (.f64 alpha alpha) (.f64 i i)))
	1.2b	(/.f64 1 (*.f64 i i))
	3.2b	(/.f64 (.f64 alpha alpha) (.f64 i i))

series65.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

65.0ms

(fma.f64 (/.f64 beta i) (/.f64 beta i) (/.f64 (*.f64 alpha alpha) (*.f64 i i)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 beta i) (/.f64 beta i) (/.f64 (*.f64 alpha alpha) (*.f64 i i)))

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

913×	`fma-def_binary64`
726×	`distribute-rgt-in_binary64`
594×	`unswap-sqr_binary64`
204×	`associate-*l/_binary64`
183×	`associate-*r/_binary64`

Counts

46 → 26

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	922
1	50	797
2	95	797
3	319	797
4	1971	797
5	5717	797

prune94.0ms (0.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	96	8	104

Error

8.2b

Counts

104 → 8

Alt Table

Status	Error	Program
	55.2b	(-.f64 (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (/.f64 (.f64 i alpha) (.f64 beta beta))) (fma.f64 3 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
✓	21.5b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (fma.f64 (/.f64 beta i) (/.f64 beta i) (/.f64 (.f64 alpha alpha) (*.f64 i i)))))
✓	21.1b	1/16
	57.9b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (fma.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)) -1) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
✓	56.5b	(/.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))
	51.4b	(/.f64 (.f64 (+.f64 i alpha) i) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
	37.5b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 1)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 1)))
	58.6b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 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 3207 to 1340 computations (58.2% saved)

regimes1.1s (10.3%)

Accuracy

Total 2.0b remaining (18.8%)

Threshold costs 0b (0%)

Counts

107 → 2

Compiler

Compiled 24432 to 14041 computations (42.5% saved)

bsearch36.0ms (0.3%)

Steps

Iters	Range		Point
7	2.7754739940315827e+116	9.375350388496499e+117	9.274916335475843e+117

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	89
1	39	89
2	40	89
3	38	89

end7.0ms (0.1%)

Remove: (sort alpha beta)
Compiler: Compiled 189 to 99 computations (47.6% saved)

sample3.2s (29.4%)

Algorithm

1×

intervals

Results

1.9s	8000×	body	128	valid
420.0ms	8000×	pre	128	true

Compiler

Compiled 457 to 247 computations (46% saved)

Details

analyze57.0ms (0.5%)

sample121.0ms (1.1%)

simplify39.0ms (0.4%)

prune14.0ms (0.1%)

localize15.0ms (0.1%)

series3.5s (32.2%)

rewrite137.0ms (1.3%)

simplify562.0ms (5.2%)

prune1.4s (13.1%)

localize0.0ms (0%)

prune10.0ms (0.1%)

localize15.0ms (0.1%)

series138.0ms (1.3%)

rewrite26.0ms (0.2%)

simplify109.0ms (1%)

prune128.0ms (1.2%)

localize15.0ms (0.1%)

series65.0ms (0.6%)

rewrite1.0ms (0%)

simplify49.0ms (0.5%)

prune94.0ms (0.9%)

regimes1.1s (10.3%)

bsearch36.0ms (0.3%)

simplify4.0ms (0%)

end7.0ms (0.1%)

sample3.2s (29.4%)

Profiling