Details

analyze436.0ms (10.7%)

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)

sample1.2s (29.3%)

Symmetry

(sort d2 d3)

Results

952.0ms	7761×	body	128	valid
66.0ms	654×	body	128	invalid
56.0ms	172×	body	1024	valid
50.0ms	201×	body	512	valid
23.0ms	122×	body	256	valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify9.0ms (0.2%)

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

0.1b

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)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 28

Calls

1 calls:

7.0ms

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

rewrite7.0ms (0.2%)

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)))

simplify82.0ms (2%)

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

prune59.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	46	4	50

Error

Counts

50 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	32.2b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
▶	26.2b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	32.7b	(/.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)))))

Compiler

Compiled 751 to 411 computations (45.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
✓	8.7b	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
✓	15.9b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

series90.0ms (2.2%)

Counts

3 → 96

Calls

3 calls:

56.0ms	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
29.0ms	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
5.0ms	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`

Counts

3 → 108

Calls

3 calls:

10.0ms	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
6.0ms	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
5.0ms	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))

simplify114.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

245×	`fma-neg_binary64`
237×	`associate-/l*_binary64`
236×	`associate-r_binary64`
218×	`associate-l_binary64`
196×	`times-frac_binary64`

Counts

204 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	5107
1	958	4615
2	4155	4506
3	4970	4506

prune172.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	204	4	208

Error

Counts

208 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
▶	32.2b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
✓	26.2b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	32.7b	(/.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)))))

Compiler

Compiled 6111 to 2892 computations (52.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3)))
✓	0.2b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))

series34.0ms (0.8%)

Counts

2 → 56

Calls

2 calls:

21.0ms	(*.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3)))
13.0ms	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
12×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

2 → 59

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
7.0ms	(*.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3)))

simplify104.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
588×	`fma-neg_binary64`
361×	`+-commutative_binary64`
321×	`*-commutative_binary64`
269×	`unswap-sqr_binary64`

Counts

115 → 98

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	102	1512
1	257	1350
2	1035	1350
3	1582	1350
4	2664	1350
5	4281	1350
6	4984	1350
7	4932	1350

prune46.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	98	4	102

Error

Counts

102 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
✓	32.2b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
✓	26.2b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
▶	32.7b	(/.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)))))

Compiler

Compiled 1694 to 728 computations (57% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 3 (+.f64 d2 d3))
✓	0.2b	(-.f64 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)) (.f64 3 (+.f64 d2 d3)))
✓	4.9b	(*.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3)))
✓	28.9b	(/.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)))))

series373.0ms (9.2%)

Counts

4 → 120

Calls

4 calls:

280.0ms	(/.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)))))
80.0ms	(*.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3)))
9.0ms	(-.f64 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)) (.f64 3 (+.f64 d2 d3)))
3.0ms	(*.f64 3 (+.f64 d2 d3))

rewrite57.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`associate-*r/_binary64`
28×	`flip-+_binary64`
28×	`flip3-+_binary64`
16×	`frac-sub_binary64`
14×	`*-un-lft-identity_binary64`

Counts

4 → 118

Calls

4 calls:

22.0ms	(/.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)))))
8.0ms	(*.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3)))
8.0ms	(-.f64 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)) (.f64 3 (+.f64 d2 d3)))
4.0ms	(*.f64 3 (+.f64 d2 d3))

simplify176.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-def_binary64`
509×	`times-frac_binary64`
380×	`distribute-rgt-in_binary64`
364×	`distribute-lft-in_binary64`
170×	`*-commutative_binary64`

Counts

238 → 249

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	608	9613
1	2044	8608
2	5526	8608

prune371.0ms (9.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	249	4	253

Error

Counts

253 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
✓	32.2b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
✓	26.2b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
✓	32.7b	(/.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)))))

Compiler

Compiled 13627 to 7593 computations (44.3% saved)

regimes508.0ms (12.5%)

Accuracy

Total 0.1b remaining (82.2%)

Threshold costs 0.1b (82.2%)

Counts

95 → 1

Compiler

Compiled 7868 to 5260 computations (33.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

end135.0ms (3.3%)

Remove: (sort d2 d3)
Compiler: Compiled 114 to 73 computations (36% saved)

Details

analyze436.0ms (10.7%)

sample1.2s (29.3%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series7.0ms (0.2%)

rewrite7.0ms (0.2%)

simplify82.0ms (2%)

prune59.0ms (1.5%)

localize8.0ms (0.2%)

series90.0ms (2.2%)

rewrite31.0ms (0.8%)

simplify114.0ms (2.8%)

prune172.0ms (4.2%)

localize7.0ms (0.2%)

series34.0ms (0.8%)

rewrite20.0ms (0.5%)

simplify104.0ms (2.6%)

prune46.0ms (1.1%)

localize12.0ms (0.3%)

series373.0ms (9.2%)

rewrite57.0ms (1.4%)

simplify176.0ms (4.3%)

prune371.0ms (9.1%)

regimes508.0ms (12.5%)

simplify4.0ms (0.1%)

end135.0ms (3.3%)

Profiling