Details

analyze404.0ms (16.3%)

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
12.5%	87.4%	0.1%	7
37.4%	62.4%	0.1%	8
40.6%	57.7%	1.7%	9
45.2%	51.1%	3.7%	10
57.7%	33.5%	8.7%	11
59.7%	29.4%	10.9%	12
62%	25%	13%	13
68.3%	17.4%	14.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample991.0ms (40.1%)

Symmetry

(sort d2 d3)

Results

769.0ms	7782×	body	128	valid
72.0ms	699×	body	128	invalid
48.0ms	203×	body	512	valid
44.0ms	144×	body	1024	valid
23.0ms	127×	body	256	valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`distribute-lft-out_binary64`
6×	`associate-+r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	10
2	44	10
3	64	10
4	66	10
5	67	10
6	67	10

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
▶	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

Compiler

Compiled 69 to 45 computations (34.8% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

series7.0ms (0.3%)

Counts

1 → 28

Calls

1 calls:

7.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
5×	`associate-r_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`distribute-lft-out_binary64`
3×	`associate-l_binary64`

Counts

1 → 26

Calls

1 calls:

6.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

simplify88.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

949×	`distribute-rgt-in_binary64`
943×	`distribute-lft-in_binary64`
503×	`fma-neg_binary64`
394×	`associate-l_binary64`
294×	`associate-r_binary64`

Counts

54 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	601
1	162	559
2	683	559
3	2795	559
4	3172	559
5	4459	559
6	4975	559

prune35.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	45	5	50

Error

Counts

50 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
	21.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
	35.7b	(/.f64 (.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))) (+.f64 (.f64 3 3) (-.f64 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)) (.f64 3 (+.f64 d2 d3)))))
	29.6b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 3 (+.f64 d2 d3)))) (cbrt.f64 (.f64 d1 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))))

Compiler

Compiled 835 to 464 computations (44.4% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 d1 3) (.f64 d1 d2))
✓	0.0b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

series14.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

9.0ms	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
4.0ms	(+.f64 (.f64 d1 3) (.f64 d1 d2))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
5×	`fma-def_binary64`
4×	`sum-log_binary64`
4×	`distribute-lft-out_binary64`
3×	`*-un-lft-identity_binary64`

Counts

2 → 35

Calls

2 calls:

5.0ms	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
3.0ms	(+.f64 (.f64 d1 3) (.f64 d1 d2))

simplify106.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary64`
622×	`associate-l_binary64`
565×	`fma-neg_binary64`
499×	`associate-r_binary64`
492×	`distribute-rgt-in_binary64`

Counts

95 → 68

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	934
1	232	892
2	893	888
3	4255	888
4	4992	888
5	5184	888

prune69.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	69	4	73

Error

Counts

73 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
	21.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
	30.5b	(/.f64 (.f64 d1 (.f64 (.f64 d1 (+.f64 d2 (+.f64 3 d3))) (-.f64 (+.f64 d2 3) d3))) (.f64 d1 (-.f64 (+.f64 d2 3) d3)))
▶	0.0b	(fma.f64 d1 (+.f64 3 d2) (*.f64 d1 d3))

Compiler

Compiled 1174 to 598 computations (49.1% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 d1 (+.f64 3 d2) (*.f64 d1 d3))

series8.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(fma.f64 d1 (+.f64 3 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 (+.f64 3 d2) (*.f64 d1 d3))

simplify70.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1013×	`distribute-rgt-in_binary64`
985×	`distribute-lft-in_binary64`
731×	`associate-l_binary64`
686×	`associate-r_binary64`
359×	`fma-def_binary64`

Counts

46 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	494
1	50	460
2	122	460
3	567	460
4	4360	460
5	4533	460
6	4978	460
7	4994	460

prune16.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	27	4	31

Error

Counts

31 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
▶	21.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
	30.5b	(/.f64 (.f64 d1 (.f64 (.f64 d1 (+.f64 d2 (+.f64 3 d3))) (-.f64 (+.f64 d2 3) d3))) (.f64 d1 (-.f64 (+.f64 d2 3) d3)))
✓	0.0b	(fma.f64 d1 (+.f64 3 d2) (*.f64 d1 d3))

Compiler

Compiled 411 to 222 computations (46% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 3 (+.f64 d2 d3)))
✓	0.2b	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.3b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

series121.0ms (4.9%)

Counts

3 → 60

Calls

3 calls:

84.0ms	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
28.0ms	(sqrt.f64 (+.f64 3 (+.f64 d2 d3)))
9.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

rewrite32.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
16×	`sqrt-prod_binary64`
16×	`associate-r_binary64`
16×	`sqrt-div_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

3 → 81

Calls

3 calls:

13.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
7.0ms	(sqrt.f64 (+.f64 3 (+.f64 d2 d3)))
7.0ms	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

simplify128.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

644×	`fma-def_binary64`
436×	`fma-neg_binary64`
421×	`*-commutative_binary64`
307×	`cancel-sign-sub-inv_binary64`
244×	`associate-l_binary64`

Counts

141 → 133

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	195	2457
1	510	2313
2	1664	2269
3	3116	2260
4	4816	2258
5	4998	2258
6	4950	2258

prune95.0ms (3.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	168	4	172

Error

Counts

172 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
✓	21.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
	30.5b	(/.f64 (.f64 d1 (.f64 (.f64 d1 (+.f64 d2 (+.f64 3 d3))) (-.f64 (+.f64 d2 3) d3))) (.f64 d1 (-.f64 (+.f64 d2 3) d3)))
✓	0.0b	(fma.f64 d1 (+.f64 3 d2) (*.f64 d1 d3))

Compiler

Compiled 4408 to 2709 computations (38.5% saved)

regimes171.0ms (6.9%)

Accuracy

Total 0.0b remaining (62.4%)

Threshold costs 0.0b (62.4%)

Counts

47 → 1

Compiler

Compiled 2780 to 1872 computations (32.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end63.0ms (2.5%)

Remove: (sort d2 d3)
Compiler: Compiled 113 to 73 computations (35.4% saved)

Details

analyze404.0ms (16.3%)

sample991.0ms (40.1%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series7.0ms (0.3%)

rewrite7.0ms (0.3%)

simplify88.0ms (3.6%)

prune35.0ms (1.4%)

localize7.0ms (0.3%)

series14.0ms (0.6%)

rewrite9.0ms (0.4%)

simplify106.0ms (4.3%)

prune69.0ms (2.8%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite1.0ms (0%)

simplify70.0ms (2.8%)

prune16.0ms (0.6%)

localize6.0ms (0.3%)

series121.0ms (4.9%)

rewrite32.0ms (1.3%)

simplify128.0ms (5.2%)

prune95.0ms (3.9%)

regimes171.0ms (6.9%)

simplify2.0ms (0.1%)

end63.0ms (2.5%)

Profiling