Details

analyze1.2s (35.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	98.3%	1.7%	9
0%	96.3%	3.7%	10
0.8%	94.8%	4.4%	11
0.8%	93.5%	5.7%	12
1%	92.1%	7%	13
1.9%	90.9%	7.3%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.5s (45.5%)

Symmetry

(sort d2 d3)

Results

901.0ms	8256×	body	128	valid
558.0ms	1112×	body	8192	exit
34.0ms	310×	body	128	invalid

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`distribute-lft-out_binary64`
1×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	13	7
2	18	7
3	18	7

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
	0.0b	(*.f64 d1 (+.f64 d2 d3))
▶	0.0b	(+.f64 (.f64 d1 d2) (.f64 d1 d3))

Compiler

Compiled 51 to 30 computations (41.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 d1 d2) (.f64 d1 d3))

series8.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(+.f64 (*.f64 d1 d2) (*.f64 d1 d3))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`+-commutative_binary64`
1×	`distribute-lft-out_binary64`
1×	`flip-+_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 15

Calls

1 calls:

3.0ms

(+.f64 (*.f64 d1 d2) (*.f64 d1 d3))

simplify76.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

791×	`unsub-neg_binary64`
551×	`distribute-rgt-out_binary64`
343×	`distribute-rgt-in_binary64`
309×	`distribute-lft-in_binary64`
288×	`unswap-sqr_binary64`

Counts

51 → 28

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	420
1	116	402
2	419	401
3	1259	398
4	2596	398
5	3843	398
6	4403	398
7	5351	398

prune15.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	28	2	30

Error

0.0b

Counts

30 → 2

Alt Table

Status	Error	Program
	30.0b	(.f64 (sqrt.f64 (+.f64 (.f64 d1 d2) (.f64 d1 d3))) (sqrt.f64 (+.f64 (.f64 d1 d2) (*.f64 d1 d3))))
▶	0.0b	(fma.f64 d1 d2 (*.f64 d1 d3))

Compiler

Compiled 395 to 109 computations (72.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 d1 d2 (*.f64 d1 d3))

series8.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(fma.f64 d1 d2 (*.f64 d1 d3))

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 d1 d2 (*.f64 d1 d3))

simplify86.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
773×	`distribute-rgt-in_binary64`
765×	`distribute-lft-in_binary64`
405×	`*-commutative_binary64`
380×	`distribute-rgt-out_binary64`

Counts

46 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	346
1	26	331
2	78	331
3	295	331
4	778	331
5	2919	331
6	3117	331
7	3288	331
8	3563	331
9	4329	331
10	4791	331

prune10.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	22	2	24

Error

0.0b

Counts

24 → 2

Alt Table

Status	Error	Program
▶	30.0b	(.f64 (sqrt.f64 (fma.f64 d1 d2 (.f64 d1 d3))) (sqrt.f64 (fma.f64 d1 d2 (*.f64 d1 d3))))
✓	0.0b	(fma.f64 d1 d2 (*.f64 d1 d3))

Compiler

Compiled 252 to 66 computations (73.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 d1 d2 (*.f64 d1 d3))
✓	0.2b	(.f64 (sqrt.f64 (fma.f64 d1 d2 (.f64 d1 d3))) (sqrt.f64 (fma.f64 d1 d2 (*.f64 d1 d3))))
✓	4.2b	(sqrt.f64 (fma.f64 d1 d2 (*.f64 d1 d3)))

series102.0ms (3%)

Counts

2 → 44

Calls

2 calls:

93.0ms	(sqrt.f64 (fma.f64 d1 d2 (*.f64 d1 d3)))
8.0ms	(.f64 (sqrt.f64 (fma.f64 d1 d2 (.f64 d1 d3))) (sqrt.f64 (fma.f64 d1 d2 (*.f64 d1 d3))))

rewrite13.0ms (0.4%)

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:

7.0ms	(.f64 (sqrt.f64 (fma.f64 d1 d2 (.f64 d1 d3))) (sqrt.f64 (fma.f64 d1 d2 (*.f64 d1 d3))))
1.0ms	(sqrt.f64 (fma.f64 d1 d2 (*.f64 d1 d3)))

simplify65.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

706×	`distribute-lft-in_binary64`
706×	`distribute-rgt-in_binary64`
455×	`associate-l_binary64`
350×	`associate-r_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

112 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	1379
1	209	1241
2	595	1197
3	2061	1169
4	5322	1169

prune68.0ms (2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	189	2	191

Error

0.0b

Counts

191 → 2

Alt Table

Status	Error	Program
✓	30.0b	(.f64 (sqrt.f64 (fma.f64 d1 d2 (.f64 d1 d3))) (sqrt.f64 (fma.f64 d1 d2 (*.f64 d1 d3))))
✓	0.0b	(fma.f64 d1 d2 (*.f64 d1 d3))

Compiler

Compiled 3856 to 735 computations (80.9% saved)

regimes99.0ms (2.9%)

Accuracy

Total 0.0b remaining (6.1%)

Threshold costs 0.0b (6.1%)

Counts

21 → 1

Compiler

Compiled 1110 to 648 computations (41.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end48.0ms (1.4%)

Remove: (sort d2 d3)
Compiler: Compiled 63 to 32 computations (49.2% saved)

Details

analyze1.2s (35.8%)

sample1.5s (45.5%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series8.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify76.0ms (2.2%)

prune15.0ms (0.4%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite1.0ms (0%)

simplify86.0ms (2.6%)

prune10.0ms (0.3%)

localize7.0ms (0.2%)

series102.0ms (3%)

rewrite13.0ms (0.4%)

simplify65.0ms (1.9%)

prune68.0ms (2%)

regimes99.0ms (2.9%)

simplify2.0ms (0.1%)

end48.0ms (1.4%)

Profiling