Details

analyze55.0ms (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 67 to 35 computations (47.8% saved)

sample1.6s (24.5%)

Symmetry

(sort alpha beta)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify39.0ms (0.6%)

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 (0.1%)

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

55.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	55.8b	(/.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

▶

55.8b

(/.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)

localize17.0ms (0.3%)

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)))
✓	37.5b	(/.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))
✓	47.7b	(/.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))))

series1.4s (22.4%)

Counts

4 → 144

Calls

4 calls:

1.3s	(/.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))
132.0ms	(/.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))))
42.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
13.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite51.0ms (0.8%)

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:

10.0ms	(/.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))))
10.0ms	(/.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))
7.0ms	(.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)))

simplify405.0ms (6.3%)

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

prune1.1s (17.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	289	7	296
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	290	7	297

Error

10.9b

Counts

297 → 7

Alt Table

Status	Error	Program
	55.8b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	41.3b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.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))
▶	19.4b	1/16
	58.9b	(/.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))
	41.4b	(.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)))
	42.1b	(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	24.9b	(-.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)))))

Compiler

Compiled 63315 to 36577 computations (42.2% saved)

localize0.0ms (0%)

prune9.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

10.9b

Counts

7 → 7

Alt Table

Status	Error	Program
	55.8b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	41.3b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.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))
✓	19.4b	1/16
	58.9b	(/.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))
	41.4b	(.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)))
	42.1b	(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	24.9b	(-.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)))))

Compiler

Compiled 482 to 244 computations (49.4% saved)

localize14.0ms (0.2%)

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)))
✓	0.6b	(/.f64 1 (*.f64 i i))
✓	3.4b	(/.f64 (.f64 alpha alpha) (.f64 i i))
✓	19.5b	(/.f64 (.f64 beta beta) (.f64 i i))

series121.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

64.0ms	(+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))
27.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
27.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
2.0ms	(/.f64 1 (*.f64 i i))

rewrite27.0ms (0.4%)

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)))
6.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
5.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
3.0ms	(/.f64 1 (*.f64 i i))

simplify114.0ms (1.8%)

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

prune118.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	135	7	142

Error

10.8b

Counts

142 → 7

Alt Table

Status	Error	Program
	55.8b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	41.3b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.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))
✓	19.4b	1/16
▶	20.1b	(-.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)))))
	58.9b	(/.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))
	41.4b	(.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)))
	42.1b	(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 4832 to 1908 computations (60.5% saved)

localize13.0ms (0.2%)

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)))
	0.6b	(/.f64 1 (*.f64 i i))
	3.4b	(/.f64 (.f64 alpha alpha) (.f64 i i))

series51.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

51.0ms

(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 (0.8%)

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

prune518.0ms (8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	96	7	103

Error

10.8b

Counts

103 → 7

Alt Table

Status	Error	Program
	55.8b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	41.3b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.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))
✓	19.4b	1/16
✓	20.1b	(-.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)))))
	58.9b	(/.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))
	41.4b	(.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)))
	42.1b	(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 3125 to 1287 computations (58.8% saved)

regimes524.0ms (8.1%)

Accuracy

Total 3.1b remaining (23.2%)

Threshold costs 0b (0%)

Counts

59 → 2

Compiler

Compiled 10624 to 5645 computations (46.9% saved)

bsearch28.0ms (0.4%)

Steps

Iters	Range		Point
6	7.798579327757281e+132	9.47020994925423e+133	3.069023547095177e+133

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	22	74
1	27	74
2	27	74

end146.0ms (2.3%)

Remove: (sort alpha beta)
Compiler: Compiled 462 to 227 computations (50.9% saved)

Details

analyze55.0ms (0.9%)

sample1.6s (24.5%)

simplify39.0ms (0.6%)

prune4.0ms (0.1%)

localize17.0ms (0.3%)

series1.4s (22.4%)

rewrite51.0ms (0.8%)

simplify405.0ms (6.3%)

prune1.1s (17.3%)

localize0.0ms (0%)

prune9.0ms (0.1%)

localize14.0ms (0.2%)

series121.0ms (1.9%)

rewrite27.0ms (0.4%)

simplify114.0ms (1.8%)

prune118.0ms (1.8%)

localize13.0ms (0.2%)

series51.0ms (0.8%)

rewrite1.0ms (0%)

simplify49.0ms (0.8%)

prune518.0ms (8%)

regimes524.0ms (8.1%)

bsearch28.0ms (0.4%)

simplify3.0ms (0%)

end146.0ms (2.3%)

Profiling