Details

analyze1.7s (36.8%)

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%	99.1%	0.9%	9
0%	98.1%	1.9%	10
0%	95.6%	4.4%	11
0%	94.5%	5.5%	12
0%	93.4%	6.6%	13
0%	92.7%	7.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.8s (38.7%)

Symmetry

(sort d2 d3)

Results

905.0ms	7736×	body	128	valid
689.0ms	1138×	body	8192	exit
64.0ms	189×	body	1024	valid
56.0ms	351×	body	128	invalid
52.0ms	201×	body	512	valid
23.0ms	130×	body	256	valid

Compiler

Compiled 29 to 19 computations (34.5% saved)

simplify8.0ms (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)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.2%)

Counts

1 → 28

Calls

1 calls:

8.0ms

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

rewrite8.0ms (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:

7.0ms

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

simplify71.0ms (1.5%)

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

prune36.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	44	6	50

Error

Counts

50 → 6

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
▶	0.1b	(+.f64 (.f64 3 d1) (.f64 (+.f64 d2 d3) d1))
	1.5b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
	26.9b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	1.3b	(.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)))))
	19.2b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

Compiler

Compiled 815 to 453 computations (44.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series16.0ms (0.3%)

Counts

2 → 72

Calls

2 calls:

9.0ms	(+.f64 (.f64 3 d1) (.f64 (+.f64 d2 d3) d1))
6.0ms	(*.f64 (+.f64 d2 d3) d1)

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 38

Calls

2 calls:

6.0ms	(*.f64 (+.f64 d2 d3) d1)
3.0ms	(+.f64 (.f64 3 d1) (.f64 (+.f64 d2 d3) d1))

simplify83.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

621×	`distribute-rgt-in_binary64`
596×	`distribute-lft-in_binary64`
580×	`associate-r_binary64`
543×	`sub-neg_binary64`
401×	`fma-def_binary64`

Counts

110 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1036
1	236	1003
2	866	1002
3	3337	999
4	4712	999
5	5323	999

prune38.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	4	0	4
Picked	1	0	1
Done	0	1	1
Total	72	3	75

Error

Counts

75 → 3

Alt Table

Status	Error	Program
	32.0b	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d2 (+.f64 3 d3)))) (sqrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 3 d3)))))
▶	0.0b	(fma.f64 3 d1 (*.f64 (+.f64 d2 d3) d1))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 1055 to 474 computations (55.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 d2 d3) d1)
✓	0.1b	(fma.f64 3 d1 (*.f64 (+.f64 d2 d3) d1))

series10.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

10.0ms

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

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

simplify93.0ms (2%)

Algorithm

1×	egg-herbie

Rules

674×	`unswap-sqr_binary64`
473×	`associate-l_binary64`
428×	`+-commutative_binary64`
387×	`distribute-rgt-out_binary64`
358×	`associate-/l/_binary64`

Counts

46 → 28

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	479
1	48	457
2	112	457
3	532	457
4	1315	457
5	2331	457
6	2722	457
7	3156	457
8	3738	457
9	4861	457
10	5031	457

prune31.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Status	Error	Program
▶	29.4b	(fma.f64 3 d1 (.f64 (sqrt.f64 (.f64 d1 (+.f64 d2 d3))) (sqrt.f64 (*.f64 d1 (+.f64 d2 d3)))))
✓	0.0b	(fma.f64 3 d1 (*.f64 (+.f64 d2 d3) d1))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 855 to 339 computations (60.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3 d1 (.f64 (sqrt.f64 (.f64 d1 (+.f64 d2 d3))) (sqrt.f64 (*.f64 d1 (+.f64 d2 d3)))))
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
✓	0.2b	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d2 d3))) (sqrt.f64 (*.f64 d1 (+.f64 d2 d3))))
✓	3.8b	(sqrt.f64 (*.f64 d1 (+.f64 d2 d3)))

series188.0ms (4%)

Counts

4 → 97

Calls

4 calls:

102.0ms	(sqrt.f64 (*.f64 d1 (+.f64 d2 d3)))
44.0ms	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d2 d3))) (sqrt.f64 (*.f64 d1 (+.f64 d2 d3))))
31.0ms	(fma.f64 3 d1 (.f64 (sqrt.f64 (.f64 d1 (+.f64 d2 d3))) (sqrt.f64 (*.f64 d1 (+.f64 d2 d3)))))
10.0ms	(*.f64 d1 (+.f64 d2 d3))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`pow1_binary64`
30×	`sqrt-pow1_binary64`
22×	`pow-prod-down_binary64`
18×	`associate-*r/_binary64`
14×	`sqrt-div_binary64`

Counts

4 → 109

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d2 d3))) (sqrt.f64 (*.f64 d1 (+.f64 d2 d3))))
5.0ms	(*.f64 d1 (+.f64 d2 d3))
4.0ms	(sqrt.f64 (*.f64 d1 (+.f64 d2 d3)))
0.0ms	(fma.f64 3 d1 (.f64 (sqrt.f64 (.f64 d1 (+.f64 d2 d3))) (sqrt.f64 (*.f64 d1 (+.f64 d2 d3)))))

simplify113.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

512×	`times-frac_binary64`
400×	`fma-def_binary64`
398×	`distribute-rgt-in_binary64`
381×	`distribute-lft-in_binary64`
340×	`*-commutative_binary64`

Counts

206 → 162

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	168	2277
1	360	2167
2	1277	2127
3	3574	2086
4	4749	2002
5	4957	2002

prune100.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	222	3	225

Error

Counts

225 → 3

Alt Table

Status	Error	Program
✓	29.4b	(fma.f64 3 d1 (.f64 (sqrt.f64 (.f64 d1 (+.f64 d2 d3))) (sqrt.f64 (*.f64 d1 (+.f64 d2 d3)))))
✓	0.0b	(fma.f64 3 d1 (*.f64 (+.f64 d2 d3) d1))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 4907 to 1424 computations (71% saved)

regimes228.0ms (4.8%)

Accuracy

Total 0.0b remaining (45%)

Threshold costs 0.0b (45%)

Counts

59 → 1

Compiler

Compiled 3688 to 2424 computations (34.3% saved)

simplify2.0ms (0%)

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 (1.3%)

Remove: (sort d2 d3)
Compiler: Compiled 84 to 51 computations (39.3% saved)

Details

analyze1.7s (36.8%)

sample1.8s (38.7%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series8.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify71.0ms (1.5%)

prune36.0ms (0.8%)

localize7.0ms (0.1%)

series16.0ms (0.3%)

rewrite10.0ms (0.2%)

simplify83.0ms (1.8%)

prune38.0ms (0.8%)

localize5.0ms (0.1%)

series10.0ms (0.2%)

rewrite1.0ms (0%)

simplify93.0ms (2%)

prune31.0ms (0.7%)

localize7.0ms (0.2%)

series188.0ms (4%)

rewrite29.0ms (0.6%)

simplify113.0ms (2.4%)

prune100.0ms (2.1%)

regimes228.0ms (4.8%)

simplify2.0ms (0%)

end63.0ms (1.3%)

Profiling