Details

analyze1.8s (33.1%)

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
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.8s (34%)

Results

1.2s	8256×	body	128	valid
585.0ms	4121×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify10.0ms (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

prune3.0ms (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
▶	1.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize7.0ms (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))
✓	1.7b	(fma.f64 a (fma.f64 z b t) x)

series35.0ms (0.7%)

Counts

2 → 132

Calls

2 calls:

22.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
13.0ms	(fma.f64 a (fma.f64 z b t) 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 a (fma.f64 z b t) x)
0.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

simplify50.0ms (0.9%)

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

prune51.0ms (0.9%)

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

Counts

68 → 4

Alt Table

Status	Error	Program
	33.2b	(*.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))))
✓	1.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.1b	(+.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))

Compiler

Compiled 1001 to 233 computations (76.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	5.5b	(.f64 (.f64 a z) b)

series34.0ms (0.6%)

Counts

2 → 108

Calls

2 calls:

26.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
8.0ms	(.f64 (.f64 a z) b)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`sum-log_binary64`

Counts

2 → 39

Calls

2 calls:

6.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
6.0ms	(.f64 (.f64 a z) b)

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

601×	`distribute-rgt-in_binary64`
586×	`distribute-lft-in_binary64`
470×	`fma-def_binary64`
440×	`fma-neg_binary64`
340×	`*-commutative_binary64`

Counts

147 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1850
1	264	1571
2	1010	1560
3	3951	1560
4	5042	1560

prune41.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	80	4	84

Error

Counts

84 → 4

Alt Table

Status	Error	Program
	33.2b	(*.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))))
✓	1.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.1b	(+.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))

Compiler

Compiled 1577 to 292 computations (81.5% saved)

localize7.0ms (0.1%)

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)

series38.0ms (0.7%)

Counts

2 → 132

Calls

2 calls:

23.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
14.0ms	(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))

simplify107.0ms (2%)

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

prune30.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	52	4	56

Error

Counts

56 → 4

Alt Table

Status	Error	Program
▶	33.2b	(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))))
✓	1.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.1b	(+.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))

Compiler

Compiled 733 to 169 computations (76.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 z (fma.f64 a b y) x))
✓	0.3b	(*.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)

series420.0ms (7.8%)

Counts

2 → 80

Calls

2 calls:

405.0ms	(sqrt.f64 (fma.f64 z (fma.f64 a b y) x))
15.0ms	(*.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 (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms	(*.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))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

404×	`distribute-rgt-in_binary64`
397×	`distribute-lft-in_binary64`
349×	`cancel-sign-sub-inv_binary64`
276×	`associate-r_binary64`
264×	`associate-l_binary64`

Counts

148 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	2790
1	558	2583
2	2053	2424
3	4727	2407
4	4979	2407

prune122.0ms (2.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	220	4	224

Error

Counts

224 → 4

Alt Table

Status	Error	Program
✓	33.2b	(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))))
✓	1.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.1b	(+.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))

Compiler

Compiled 7147 to 1981 computations (72.3% saved)

regimes506.0ms (9.4%)

Accuracy

Total 0.3b remaining (96.8%)

Threshold costs 0.3b (96.8%)

Counts

54 → 3

Compiler

Compiled 6167 to 3773 computations (38.8% saved)

bsearch30.0ms (0.6%)

Steps

Iters	Range		Point
4	3.3564390473604805e-89	4.3521608537828175e-88	3.7766997801208336e-88
4	-4.8194229455766453e+55	-8.439737848963411e+54	-1.4537501272190535e+55

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	51
1	20	51

end69.0ms (1.3%)

Compiler: Compiled 167 to 78 computations (53.3% saved)

Details

analyze1.8s (33.1%)

sample1.8s (34%)

simplify10.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series35.0ms (0.7%)

rewrite1.0ms (0%)

simplify50.0ms (0.9%)

prune51.0ms (0.9%)

localize10.0ms (0.2%)

series34.0ms (0.6%)

rewrite14.0ms (0.3%)

simplify70.0ms (1.3%)

prune41.0ms (0.8%)

localize7.0ms (0.1%)

series38.0ms (0.7%)

rewrite1.0ms (0%)

simplify107.0ms (2%)

prune30.0ms (0.6%)

localize9.0ms (0.2%)

series420.0ms (7.8%)

rewrite14.0ms (0.3%)

simplify93.0ms (1.7%)

prune122.0ms (2.3%)

regimes506.0ms (9.4%)

bsearch30.0ms (0.6%)

simplify3.0ms (0%)

end69.0ms (1.3%)

Profiling