Details

analyze396.0ms (11.2%)

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
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
46.8%	44.5%	8.7%	10
51.5%	39%	9.5%	11
57.3%	32.6%	10.1%	12
63.8%	21.6%	14.7%	13
66.2%	18.7%	15.1%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample983.0ms (27.8%)

Symmetry

(sort x y)

Results

806.0ms	8256×	body	128	valid
83.0ms	621×	body	128	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`
1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7
2	16	7
3	18	7
4	18	7

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (+.f64 x y) z)

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) z)

series6.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

6.0ms

(*.f64 (+.f64 x y) z)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
3×	`associate-r_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 23

Calls

1 calls:

7.0ms

(*.f64 (+.f64 x y) z)

simplify100.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-def_binary64`
448×	`associate-+l+_binary64`
431×	`fma-neg_binary64`
402×	`associate-+r+_binary64`
300×	`distribute-rgt-out_binary64`

Counts

59 → 41

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	490
1	115	460
2	370	460
3	930	460
4	1654	460
5	2723	460
6	3208	460
7	4769	460
8	4995	460
9	4860	460

prune26.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Error

Counts

42 → 3

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) (cbrt.f64 (.f64 (+.f64 x y) z))) (cbrt.f64 (*.f64 (+.f64 x y) z)))
▶	0.0b	(+.f64 (.f64 y z) (.f64 z x))
	41.7b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) z) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y))))

Compiler

Compiled 548 to 177 computations (67.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y z) (.f64 z x))

series9.0ms (0.3%)

Counts

1 → 18

Calls

1 calls:

9.0ms

(+.f64 (*.f64 y z) (*.f64 z x))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`+-commutative_binary64`
1×	`flip-+_binary64`
1×	`*-un-lft-identity_binary64`
1×	`flip3-+_binary64`

Counts

1 → 14

Calls

1 calls:

3.0ms

(+.f64 (*.f64 y z) (*.f64 z x))

simplify70.0ms (2%)

Algorithm

1×	egg-herbie

Rules

801×	`unsub-neg_binary64`
588×	`distribute-rgt-out_binary64`
339×	`distribute-rgt-in_binary64`
307×	`distribute-lft-in_binary64`
288×	`associate-l_binary64`

Counts

32 → 28

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	296
1	115	272
2	397	271
3	1233	271
4	2569	268
5	3818	268
6	4353	268
7	5317	268

prune14.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	28	3	31

Error

Counts

31 → 3

Alt Table

Status	Error	Program
▶	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) (cbrt.f64 (.f64 (+.f64 x y) z))) (cbrt.f64 (*.f64 (+.f64 x y) z)))
✓	0.0b	(+.f64 (.f64 y z) (.f64 z x))
	41.7b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) z) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y))))

Compiler

Compiled 439 to 136 computations (69% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 x y) z)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) (cbrt.f64 (.f64 (+.f64 x y) z))) (cbrt.f64 (*.f64 (+.f64 x y) z)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) (cbrt.f64 (*.f64 (+.f64 x y) z)))
✓	3.7b	(cbrt.f64 (*.f64 (+.f64 x y) z))

series797.0ms (22.5%)

Counts

3 → 108

Calls

3 calls:

395.0ms

(*.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) (cbrt.f64 (*.f64 (+.f64 x y) z)))

382.0ms

(cbrt.f64 (*.f64 (+.f64 x y) z))

20.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) (cbrt.f64 (*.f64 (+.f64 x y) z))) (cbrt.f64 (*.f64 (+.f64 x y) z)))

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`associate-*l/_binary64`
68×	`cbrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) (cbrt.f64 (*.f64 (+.f64 x y) z))) (cbrt.f64 (*.f64 (+.f64 x y) z)))

6.0ms

(*.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) (cbrt.f64 (*.f64 (+.f64 x y) z)))

3.0ms

(cbrt.f64 (*.f64 (+.f64 x y) z))

simplify174.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

300×	`cancel-sign-sub-inv_binary64`
276×	`unswap-sqr_binary64`
269×	`associate-r_binary64`
240×	`associate-l_binary64`
227×	`fma-neg_binary64`

Counts

223 → 275

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	438	6452
1	1085	6010
2	3350	5651
3	4887	5651
4	4988	5651

prune271.0ms (7.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	547	1	548
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	548	3	551

Error

Counts

551 → 3

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) (cbrt.f64 (.f64 (+.f64 x y) z))) (cbrt.f64 (*.f64 (+.f64 x y) z)))
▶	41.7b	(/.f64 (.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 y (-.f64 y x) (.f64 x x)))
✓	0.0b	(+.f64 (.f64 y z) (.f64 z x))

Compiler

Compiled 18580 to 5892 computations (68.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (-.f64 y x) (*.f64 x x))
✓	2.1b	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
✓	7.0b	(*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
✓	35.4b	(/.f64 (.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 y (-.f64 y x) (.f64 x x)))

series166.0ms (4.7%)

Counts

4 → 120

Calls

4 calls:

117.0ms	(/.f64 (.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 y (-.f64 y x) (.f64 x x)))
32.0ms	(*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
10.0ms	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
6.0ms	(fma.f64 y (-.f64 y x) (*.f64 x x))

rewrite38.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`fma-def_binary64`
11×	`cube-prod_binary64`
11×	`unpow-prod-down_binary64`

Counts

4 → 96

Calls

4 calls:

14.0ms	(/.f64 (.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 y (-.f64 y x) (.f64 x x)))
11.0ms	(*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
8.0ms	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
0.0ms	(fma.f64 y (-.f64 y x) (*.f64 x x))

simplify103.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

588×	`distribute-rgt-in_binary64`
571×	`distribute-lft-in_binary64`
499×	`fma-def_binary64`
469×	`times-frac_binary64`
191×	`fma-neg_binary64`

Counts

216 → 154

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	126	3127
1	323	2829
2	1508	2829
3	4908	2829
4	5013	2829

prune78.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	154	3	157

Error

Counts

157 → 3

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) (cbrt.f64 (.f64 (+.f64 x y) z))) (cbrt.f64 (*.f64 (+.f64 x y) z)))
✓	41.7b	(/.f64 (.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 y (-.f64 y x) (.f64 x x)))
✓	0.0b	(+.f64 (.f64 y z) (.f64 z x))

Compiler

Compiled 3819 to 1704 computations (55.4% saved)

regimes167.0ms (4.7%)

Accuracy

Total 0.0b remaining (57.7%)

Threshold costs 0.0b (57.7%)

Counts

29 → 1

Compiler

Compiled 2464 to 1534 computations (37.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	10	10

end61.0ms (1.7%)

Remove: (sort x y)
Compiler: Compiled 94 to 51 computations (45.7% saved)

Details

analyze396.0ms (11.2%)

sample983.0ms (27.8%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify100.0ms (2.8%)

prune26.0ms (0.7%)

localize5.0ms (0.1%)

series9.0ms (0.3%)

rewrite3.0ms (0.1%)

simplify70.0ms (2%)

prune14.0ms (0.4%)

localize7.0ms (0.2%)

series797.0ms (22.5%)

rewrite32.0ms (0.9%)

simplify174.0ms (4.9%)

prune271.0ms (7.7%)

localize12.0ms (0.3%)

series166.0ms (4.7%)

rewrite38.0ms (1.1%)

simplify103.0ms (2.9%)

prune78.0ms (2.2%)

regimes167.0ms (4.7%)

simplify2.0ms (0.1%)

end61.0ms (1.7%)

Profiling