Details

analyze1.9s (37%)

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)

sample1.9s (37.6%)

Results

1.2s	8256×	body	128	valid
610.0ms	4040×	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

prune6.0ms (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
	2.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	1.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize10.0ms (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))
✓	5.1b	(.f64 (.f64 a z) b)

series57.0ms (1.1%)

Counts

4 → 204

Calls

4 calls:

26.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
15.0ms	(+.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 (0.4%)

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:

6.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
5.0ms	(.f64 (.f64 a z) b)
4.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
2.0ms	(+.f64 x (*.f64 y z))

simplify83.0ms (1.6%)

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

prune80.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	132	4	136

Error

Counts

136 → 4

Alt Table

Status	Error	Program
	2.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	1.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	31.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
▶	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 2753 to 525 computations (80.9% saved)

localize8.0ms (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))
✓	1.7b	(fma.f64 z (fma.f64 a b y) x)

series38.0ms (0.7%)

Counts

2 → 132

Calls

2 calls:

24.0ms	(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 (2.1%)

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

prune31.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Error

Counts

56 → 4

Alt Table

Status	Error	Program
▶	2.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	1.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	31.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 747 to 186 computations (75.1% saved)

localize8.0ms (0.2%)

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))
✓	2.1b	(fma.f64 a (fma.f64 z b t) x)

series38.0ms (0.7%)

Counts

2 → 132

Calls

2 calls:

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

simplify55.0ms (1.1%)

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

prune50.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	66	4	70

Error

Counts

70 → 4

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	1.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	31.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 956 to 219 computations (77.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
	0.0b	(+.f64 x (*.f64 y z))
✓	0.4b	(.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b))
✓	2.1b	(.f64 (.f64 a z) (sqrt.f64 b))

series72.0ms (1.4%)

Counts

3 → 100

Calls

3 calls:

31.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
23.0ms	(.f64 (.f64 a z) (sqrt.f64 b))
17.0ms	(.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
12×	`associate-r_binary64`
12×	`add-log-exp_binary64`

Counts

3 → 68

Calls

3 calls:

7.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
7.0ms	(.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b))
5.0ms	(.f64 (.f64 a z) (sqrt.f64 b))

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

626×	`distribute-rgt-in_binary64`
611×	`distribute-lft-in_binary64`
552×	`fma-neg_binary64`
502×	`fma-def_binary64`
257×	`associate-l_binary64`

Counts

168 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	2130
1	336	1824
2	1327	1813
3	4785	1813
4	5199	1813

prune62.0ms (1.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	136	4	140

Error

Counts

140 → 4

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	1.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	31.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 3143 to 520 computations (83.5% saved)

regimes352.0ms (6.9%)

Accuracy

Total 2.5b remaining (99.7%)

Threshold costs 0b (0%)

Counts

48 → 2

Compiler

Compiled 4851 to 3136 computations (35.4% saved)

bsearch18.0ms (0.4%)

Steps

Iters	Range		Point
4	-1.5378616023199831e-248	-7.085190684230602e-250	-8.639794952732343e-250

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	39
1	25	39
2	25	39

end66.0ms (1.3%)

Compiler: Compiled 146 to 82 computations (43.8% saved)

Details

analyze1.9s (37%)

sample1.9s (37.6%)

simplify10.0ms (0.2%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

series57.0ms (1.1%)

rewrite21.0ms (0.4%)

simplify83.0ms (1.6%)

prune80.0ms (1.6%)

localize8.0ms (0.2%)

series38.0ms (0.7%)

rewrite1.0ms (0%)

simplify107.0ms (2.1%)

prune31.0ms (0.6%)

localize8.0ms (0.2%)

series38.0ms (0.7%)

rewrite1.0ms (0%)

simplify55.0ms (1.1%)

prune50.0ms (1%)

localize12.0ms (0.2%)

series72.0ms (1.4%)

rewrite23.0ms (0.4%)

simplify86.0ms (1.7%)

prune62.0ms (1.2%)

regimes352.0ms (6.9%)

bsearch18.0ms (0.4%)

simplify3.0ms (0.1%)

end66.0ms (1.3%)

Profiling