Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.5s (39.7%)

Symmetry

(sort d2 d3)

Results

1.2s	7862×	body	128	valid
46.0ms	163×	body	512	valid
43.0ms	123×	body	1024	valid
22.0ms	108×	body	256	valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify14.0ms (0.4%)

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

prune6.0ms (0.2%)

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
	0.8b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
▶	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 69 to 45 computations (34.8% saved)

localize17.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

series13.0ms (0.4%)

Counts

1 → 28

Calls

1 calls:

13.0ms

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

rewrite13.0ms (0.4%)

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:

11.0ms

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

simplify161.0ms (4.4%)

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

prune71.0ms (1.9%)

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 (.f64 3 d1) (.f64 (+.f64 d2 d3) d1))
	29.1b	(cbrt.f64 (.f64 (.f64 (.f64 d1 (+.f64 3 (+.f64 d2 d3))) (.f64 d1 (+.f64 3 (+.f64 d2 d3)))) (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))))
	0.9b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
	32.5b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	19.8b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 819 to 455 computations (44.4% saved)

localize9.0ms (0.3%)

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))

series35.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

20.0ms	(*.f64 (+.f64 d2 d3) d1)
15.0ms	(+.f64 (.f64 3 d1) (.f64 (+.f64 d2 d3) d1))

rewrite21.0ms (0.6%)

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:

10.0ms	(*.f64 (+.f64 d2 d3) d1)
7.0ms	(+.f64 (.f64 3 d1) (.f64 (+.f64 d2 d3) d1))

simplify219.0ms (6%)

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

prune69.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	72	3	75

Error

Counts

75 → 3

Alt Table

Status	Error	Program
	19.8b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.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 1055 to 468 computations (55.6% saved)

localize14.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series18.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

18.0ms

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

rewrite2.0ms (0.1%)

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:

1.0ms

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

simplify163.0ms (4.4%)

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

prune121.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

66 → 3

Alt Table

Status	Error	Program
▶	19.8b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.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 857 to 343 computations (60% saved)

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
✓	7.6b	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
✓	12.1b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

series236.0ms (6.4%)

Counts

3 → 96

Calls

3 calls:

120.0ms	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
104.0ms	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
11.0ms	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))

rewrite53.0ms (1.5%)

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:

20.0ms	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
13.0ms	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
10.0ms	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))

simplify228.0ms (6.2%)

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

prune274.0ms (7.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	204	3	207

Error

Counts

207 → 3

Alt Table

Status	Error	Program
✓	19.8b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.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 6034 to 2845 computations (52.9% saved)

regimes330.0ms (9%)

Accuracy

Total 0.0b remaining (65%)

Threshold costs 0.0b (65%)

Counts

39 → 1

Compiler

Compiled 2544 to 1688 computations (33.6% saved)

simplify4.0ms (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

end106.0ms (2.9%)

Remove: (sort d2 d3)
Compiler: Compiled 85 to 53 computations (37.6% saved)

Details

analyze4.0ms (0.1%)

sample1.5s (39.7%)

simplify14.0ms (0.4%)

prune6.0ms (0.2%)

localize17.0ms (0.5%)

series13.0ms (0.4%)

rewrite13.0ms (0.4%)

simplify161.0ms (4.4%)

prune71.0ms (1.9%)

localize9.0ms (0.3%)

series35.0ms (0.9%)

rewrite21.0ms (0.6%)

simplify219.0ms (6%)

prune69.0ms (1.9%)

localize14.0ms (0.4%)

series18.0ms (0.5%)

rewrite2.0ms (0.1%)

simplify163.0ms (4.4%)

prune121.0ms (3.3%)

localize16.0ms (0.4%)

series236.0ms (6.4%)

rewrite53.0ms (1.5%)

simplify228.0ms (6.2%)

prune274.0ms (7.5%)

regimes330.0ms (9%)

simplify4.0ms (0.1%)

end106.0ms (2.9%)

Profiling