Details

analyze1.9s (26.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0%	99.7%	0.3%	13
0%	99.7%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample3.4s (48.1%)

Results

1.6s	2062×	body	8192	exit
1.4s	8256×	body	128	valid
325.0ms	1945×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
19×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	66	15
3	122	13
4	157	13
5	164	13
6	167	13
7	167	13

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	1.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	1.5b	(fma.f64 a (fma.f64 z b t) x)

series42.0ms (0.6%)

Counts

2 → 132

Calls

2 calls:

24.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
17.0ms	(fma.f64 a (fma.f64 z b t) x)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
0.0ms	(fma.f64 a (fma.f64 z b t) x)

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

739×	`associate-+l+_binary64`
732×	`associate-+r+_binary64`
701×	`fma-def_binary64`
559×	`associate-l_binary64`
480×	`associate-r_binary64`

Counts

152 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	1737
1	97	1579
2	249	1579
3	1063	1579
4	5721	1579

prune43.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Error

0.0b

Counts

68 → 4

Alt Table

Status	Error	Program
▶	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	3.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	34.0b	(*.f64 (sqrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x))) (sqrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x))))
✓	1.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

Compiler

Compiled 1001 to 233 computations (76.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	5.4b	(.f64 (.f64 a z) b)

series56.0ms (0.8%)

Counts

4 → 204

Calls

4 calls:

25.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
14.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
11.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-log-exp_binary64`
10×	`sum-log_binary64`
9×	`fma-def_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 73

Calls

4 calls:

8.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
4.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
4.0ms	(.f64 (.f64 a z) b)
2.0ms	(+.f64 x (*.f64 y z))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
720×	`distribute-rgt-in_binary64`
683×	`distribute-lft-in_binary64`
194×	`cancel-sign-sub-inv_binary64`
192×	`fma-neg_binary64`

Counts

277 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2855
1	406	2550
2	1474	2538
3	5045	2538

prune84.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	133	5	138

Error

0.0b

Counts

138 → 5

Alt Table

Status	Error	Program
	37.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
▶	3.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	34.0b	(*.f64 (sqrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x))) (sqrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x))))
✓	1.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

Compiler

Compiled 2795 to 538 computations (80.8% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	3.1b	(fma.f64 z (fma.f64 a b y) x)

series47.0ms (0.7%)

Counts

2 → 132

Calls

2 calls:

28.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
18.0ms	(fma.f64 z (fma.f64 a b y) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 z (fma.f64 a b y) x)
0.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

simplify121.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
520×	`associate-+r+_binary64`
505×	`associate-l_binary64`
470×	`associate-+l+_binary64`
444×	`associate-r_binary64`

Counts

152 → 52

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	1796
1	103	1579
2	236	1579
3	906	1579
4	3548	1579
5	3771	1579
6	4661	1579
7	4888	1579
8	4888	1579

prune34.0ms (0.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	52	5	57

Error

0.0b

Counts

57 → 5

Alt Table

Status	Error	Program
	37.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	3.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	33.6b	(fma.f64 a t (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x))))
✓	1.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

Compiler

Compiled 783 to 199 computations (74.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x))))
✓	0.0b	(sqrt.f64 (fma.f64 z (fma.f64 a b y) x))
✓	0.2b	(*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)))
	3.1b	(fma.f64 z (fma.f64 a b y) x)

series300.0ms (4.2%)

Counts

3 → 152

Calls

3 calls:

258.0ms

(sqrt.f64 (fma.f64 z (fma.f64 a b y) x))

26.0ms

(fma.f64 a t (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x))))

16.0ms

(*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms

(*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)))

1.0ms

(sqrt.f64 (fma.f64 z (fma.f64 a b y) x))

0.0ms

(fma.f64 a t (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x))))

simplify94.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

472×	`distribute-rgt-in_binary64`
465×	`distribute-lft-in_binary64`
349×	`cancel-sign-sub-inv_binary64`
276×	`associate-r_binary64`
265×	`associate-l_binary64`

Counts

230 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	237	3960
1	610	3555
2	2162	3396
3	5070	3396

prune140.0ms (2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	252	5	257

Error

0.0b

Counts

257 → 5

Alt Table

Status	Error	Program
	37.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	3.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	33.6b	(fma.f64 a t (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x))))
✓	1.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

Compiler

Compiled 7755 to 2054 computations (73.5% saved)

regimes447.0ms (6.3%)

Accuracy

Total 1.6b remaining (99.5%)

Threshold costs 0b (0%)

Counts

50 → 3

Compiler

Compiled 5376 to 3353 computations (37.6% saved)

bsearch83.0ms (1.2%)

Steps

Iters	Range		Point
2	4.8191050986679773e+117	6.57555517743568e+117	6.080354734126125e+117
8	-2.838789218222595e+66	-1.4312663259250223e+63	-7.958751954996774e+64

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	60
1	34	60
2	34	60

end83.0ms (1.2%)

Compiler: Compiled 202 to 107 computations (47% saved)

Details

analyze1.9s (26.4%)

sample3.4s (48.1%)

simplify11.0ms (0.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series42.0ms (0.6%)

rewrite2.0ms (0%)

simplify55.0ms (0.8%)

prune43.0ms (0.6%)

localize12.0ms (0.2%)

series56.0ms (0.8%)

rewrite21.0ms (0.3%)

simplify77.0ms (1.1%)

prune84.0ms (1.2%)

localize12.0ms (0.2%)

series47.0ms (0.7%)

rewrite1.0ms (0%)

simplify121.0ms (1.7%)

prune34.0ms (0.5%)

localize12.0ms (0.2%)

series300.0ms (4.2%)

rewrite14.0ms (0.2%)

simplify94.0ms (1.3%)

prune140.0ms (2%)

regimes447.0ms (6.3%)

bsearch83.0ms (1.2%)

simplify3.0ms (0%)

end83.0ms (1.2%)

Profiling