Details

analyze48.0ms (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)

sample87.0ms (0.9%)

Algorithm

1×

intervals

Symmetry

(sort alpha beta)

Results

25.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 126 to 65 computations (48.4% saved)

simplify38.0ms (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

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

53.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	53.3b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Status

Error

Program

▶

53.3b

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

Compiler

Compiled 203 to 89 computations (56.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
✓	0.1b	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
✓	35.3b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	45.7b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))

series3.5s (36.4%)

Counts

4 → 144

Calls

4 calls:

3.2s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
254.0ms	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
47.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
15.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite52.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-cbrt-cube_binary64`
61×	`add-exp-log_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`
21×	`add-sqr-sqrt_binary64`

Counts

4 → 132

Calls

4 calls:

11.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
9.0ms	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
8.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
3.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

simplify431.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
507×	`associate-/l*_binary64`
344×	`times-frac_binary64`
54×	`sqr-pow_binary64`
54×	`sub-neg_binary64`

Counts

276 → 296

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2566	48816
1	5158	48816

prune1.2s (12.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	287	9	296
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	288	9	297

Error

10.4b

Counts

297 → 9

Alt Table

Status	Error	Program
	53.2b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (+.f64 (.f64 (.f64 i 2) (fma.f64 i 2 (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	51.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	53.7b	(/.f64 (.f64 i (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i))) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (.f64 beta i)))) 1)))
	27.0b	(-.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)))))
▶	21.2b	1/16
	39.4b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	57.1b	(-.f64 (+.f64 (/.f64 (.f64 i i) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (fma.f64 50 (/.f64 (.f64 (pow.f64 i 3) alpha) (pow.f64 beta 4)) (fma.f64 31 (/.f64 (.f64 (.f64 i i) (.f64 alpha alpha)) (pow.f64 beta 4)) (fma.f64 6 (/.f64 (.f64 i (pow.f64 alpha 3)) (pow.f64 beta 4)) (fma.f64 25 (/.f64 (pow.f64 i 4) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i alpha) (.f64 beta beta)) (/.f64 (.f64 i alpha) (pow.f64 beta 4))))))))) (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))))))
	39.5b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
	58.5b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 63641 to 36761 computations (42.2% saved)

localize0.0ms (0%)

prune14.0ms (0.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

10.4b

Counts

9 → 9

Alt Table

Status	Error	Program
	53.2b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (+.f64 (.f64 (.f64 i 2) (fma.f64 i 2 (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	51.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	53.7b	(/.f64 (.f64 i (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i))) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (.f64 beta i)))) 1)))
▶	27.0b	(-.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)))))
✓	21.2b	1/16
	39.4b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	57.1b	(-.f64 (+.f64 (/.f64 (.f64 i i) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (fma.f64 50 (/.f64 (.f64 (pow.f64 i 3) alpha) (pow.f64 beta 4)) (fma.f64 31 (/.f64 (.f64 (.f64 i i) (.f64 alpha alpha)) (pow.f64 beta 4)) (fma.f64 6 (/.f64 (.f64 i (pow.f64 alpha 3)) (pow.f64 beta 4)) (fma.f64 25 (/.f64 (pow.f64 i 4) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i alpha) (.f64 beta beta)) (/.f64 (.f64 i alpha) (pow.f64 beta 4))))))))) (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))))))
	39.5b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
	58.5b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 808 to 428 computations (47% saved)

localize14.0ms (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)))
✓	0.3b	(/.f64 1 (*.f64 i i))
✓	2.9b	(/.f64 (.f64 alpha alpha) (.f64 i i))
✓	17.3b	(/.f64 (.f64 beta beta) (.f64 i i))

series136.0ms (1.4%)

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))
30.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
2.0ms	(/.f64 1 (*.f64 i i))

rewrite25.0ms (0.3%)

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:

8.0ms	(+.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))

simplify103.0ms (1.1%)

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

prune122.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	135	9	144

Error

10.2b

Counts

144 → 9

Alt Table

Status	Error	Program
	53.2b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (+.f64 (.f64 (.f64 i 2) (fma.f64 i 2 (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	51.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	53.7b	(/.f64 (.f64 i (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i))) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (.f64 beta i)))) 1)))
✓	21.2b	1/16
	39.4b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	57.1b	(-.f64 (+.f64 (/.f64 (.f64 i i) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (fma.f64 50 (/.f64 (.f64 (pow.f64 i 3) alpha) (pow.f64 beta 4)) (fma.f64 31 (/.f64 (.f64 (.f64 i i) (.f64 alpha alpha)) (pow.f64 beta 4)) (fma.f64 6 (/.f64 (.f64 i (pow.f64 alpha 3)) (pow.f64 beta 4)) (fma.f64 25 (/.f64 (pow.f64 i 4) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i alpha) (.f64 beta beta)) (/.f64 (.f64 i alpha) (pow.f64 beta 4))))))))) (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))))))
	39.5b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
▶	21.6b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)) (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))))
	58.5b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 5160 to 2092 computations (59.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/64 (/.f64 1 (.f64 i i)))
✓	0.0b	(hypot.f64 (/.f64 beta i) (/.f64 alpha i))
	0.3b	(/.f64 1 (*.f64 i i))
✓	0.3b	(*.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)) (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))

series147.0ms (1.5%)

Counts

3 → 84

Calls

3 calls:

103.0ms	(*.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)) (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))
41.0ms	(hypot.f64 (/.f64 beta i) (/.f64 alpha i))
2.0ms	(.f64 1/64 (/.f64 1 (.f64 i i)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
17×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
12×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`

Counts

3 → 75

Calls

3 calls:

7.0ms	(.f64 1/64 (/.f64 1 (.f64 i i)))
3.0ms	(*.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)) (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))
0.0ms	(hypot.f64 (/.f64 beta i) (/.f64 alpha i))

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Rules

628×	`times-frac_binary64`
587×	`fma-neg_binary64`
357×	`associate-l_binary64`
345×	`associate-/l*_binary64`
339×	`associate-/r*_binary64`

Counts

159 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	2909
1	398	2413
2	1133	2271
3	4702	2271
4	5150	2271

prune252.0ms (2.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	229	10	239

Error

10.2b

Counts

239 → 10

Alt Table

Status	Error	Program
	53.2b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (+.f64 (.f64 (.f64 i 2) (fma.f64 i 2 (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	51.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	53.7b	(/.f64 (.f64 i (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i))) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (.f64 beta i)))) 1)))
	21.1b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)) (/.f64 alpha i))))
✓	21.2b	1/16
	39.4b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	57.1b	(-.f64 (+.f64 (/.f64 (.f64 i i) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (fma.f64 50 (/.f64 (.f64 (pow.f64 i 3) alpha) (pow.f64 beta 4)) (fma.f64 31 (/.f64 (.f64 (.f64 i i) (.f64 alpha alpha)) (pow.f64 beta 4)) (fma.f64 6 (/.f64 (.f64 i (pow.f64 alpha 3)) (pow.f64 beta 4)) (fma.f64 25 (/.f64 (pow.f64 i 4) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i alpha) (.f64 beta beta)) (/.f64 (.f64 i alpha) (pow.f64 beta 4))))))))) (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))))))
	39.5b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
✓	21.6b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)) (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))))
	58.5b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 8259 to 3551 computations (57% saved)

regimes1.4s (15.1%)

Accuracy

Total 1.5b remaining (12.3%)

Threshold costs 0b (0%)

Counts

142 → 3

Compiler

Compiled 30716 to 17141 computations (44.2% saved)

bsearch62.0ms (0.6%)

Steps

Iters	Range		Point
9	2.9301124621348808e+144	5.672361571903956e+151	2.188249741327851e+149
5	1.7463623866102175e+90	4.477928012656038e+90	2.909911752051985e+90

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	108
1	34	108
2	34	108

end7.0ms (0.1%)

Remove: (sort alpha beta)
Compiler: Compiled 237 to 120 computations (49.4% saved)

sample1.8s (18.7%)

Algorithm

1×

intervals

Results

942.0ms	8000×	body	128	valid
240.0ms	8000×	pre	128	true

Compiler

Compiled 581 to 310 computations (46.6% saved)

Details

analyze48.0ms (0.5%)

sample87.0ms (0.9%)

simplify38.0ms (0.4%)

prune4.0ms (0%)

localize14.0ms (0.2%)

series3.5s (36.4%)

rewrite52.0ms (0.5%)

simplify431.0ms (4.5%)

prune1.2s (12.2%)

localize0.0ms (0%)

prune14.0ms (0.1%)

localize14.0ms (0.1%)

series136.0ms (1.4%)

rewrite25.0ms (0.3%)

simplify103.0ms (1.1%)

prune122.0ms (1.3%)

localize12.0ms (0.1%)

series147.0ms (1.5%)

rewrite15.0ms (0.2%)

simplify92.0ms (1%)

prune252.0ms (2.6%)

regimes1.4s (15.1%)

bsearch62.0ms (0.6%)

simplify3.0ms (0%)

end7.0ms (0.1%)

sample1.8s (18.7%)

Profiling