Details

analyze65.0ms (2.9%)

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
25%	74.9%	0.1%	5
50%	50%	0.1%	6
62.4%	31.2%	6.3%	7
71.8%	21.9%	6.3%	8
76.5%	14%	9.5%	9
80.4%	10.1%	9.5%	10
82.3%	6.6%	11%	11
84.1%	4.9%	11%	12
85%	3.2%	11.8%	13
85.8%	2.4%	11.8%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample697.0ms (31.1%)

Symmetry

(sort x y)

Results

661.0ms	8256×	body	128	valid
5.0ms	75×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	10	7
2	16	7
3	16	7
4	16	7

prune2.0ms (0.1%)

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

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (.f64 x 27) y)

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 x 27) y)

series4.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(*.f64 (*.f64 x 27) y)

rewrite38.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

511×	`log1p-expm1-u_binary64`
511×	`expm1-log1p-u_binary64`
385×	`unpow-prod-down_binary64`
298×	`log-prod_binary64`
153×	`pow2_binary64`

Counts

1 → 18

Calls

1 calls:

38.0ms

(*.f64 (*.f64 x 27) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1356	7
3	5047	7
0	0	0
1	0	0

simplify10.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Counts

42 → 19

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	10	168
2	16	168
3	16	168
4	16	168

prune14.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	14	5	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	6	20

Error

0.0b

Counts

20 → 6

Alt Table

Status	Error	Program
	1.4b	(pow.f64 (cbrt.f64 (.f64 (.f64 x 27) y)) 3)
▶	0.2b	(.f64 27 (.f64 y x))
✓	0.4b	(.f64 (.f64 x 27) y)
	32.8b	(cbrt.f64 (.f64 19683 (pow.f64 (.f64 x y) 3)))
	39.2b	(sqrt.f64 (.f64 729 (pow.f64 (.f64 x y) 2)))
	29.2b	(pow.f64 (sqrt.f64 (.f64 (.f64 x 27) y)) 2)

Compiler

Compiled 268 to 197 computations (26.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 27 (.f64 y x))

series4.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

4.0ms

(*.f64 27 (*.f64 y x))

rewrite36.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
387×	`unpow-prod-down_binary64`
299×	`log-prod_binary64`
153×	`pow2_binary64`

Counts

1 → 18

Calls

1 calls:

36.0ms

(*.f64 27 (*.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1358	7
3	5055	7
0	0	0
1	0	0

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune12.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	18	6	24

Error

0.0b

Counts

24 → 6

Alt Table

Status	Error	Program
✓	0.2b	(.f64 27 (.f64 y x))
▶	1.2b	(pow.f64 (cbrt.f64 (.f64 27 (.f64 y x))) 3)
✓	0.4b	(.f64 (.f64 x 27) y)
	32.8b	(cbrt.f64 (.f64 19683 (pow.f64 (.f64 x y) 3)))
	39.2b	(sqrt.f64 (.f64 729 (pow.f64 (.f64 x y) 2)))
	29.2b	(pow.f64 (sqrt.f64 (.f64 (.f64 x 27) y)) 2)

Compiler

Compiled 256 to 177 computations (30.9% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(.f64 27 (.f64 y x))
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 27 (.f64 y x))) 3)
✓	10.0b	(cbrt.f64 (.f64 27 (.f64 y x)))

series730.0ms (32.6%)

Counts

2 → 48

Calls

2 calls:

380.0ms	(cbrt.f64 (.f64 27 (.f64 y x)))
350.0ms	(pow.f64 (cbrt.f64 (.f64 27 (.f64 y x))) 3)

rewrite47.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
372×	`log-prod_binary64`
133×	`expm1-udef_binary64`
133×	`log1p-udef_binary64`

Counts

2 → 71

Calls

2 calls:

45.0ms	(pow.f64 (cbrt.f64 (.f64 27 (.f64 y x))) 3)
45.0ms	(cbrt.f64 (.f64 27 (.f64 y x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	166	16
2	1769	16
3	5121	16
0	0	0
1	0	0

simplify67.0ms (3%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-def_binary64`
424×	`unswap-sqr_binary64`
273×	`exp-diff_binary64`
268×	`distribute-neg-out_binary64`
267×	`associate-l_binary64`

Counts

119 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	904
1	124	904
2	215	856
3	568	448
4	1843	448
5	4611	448
6	5077	448

prune64.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	3	0	3
Picked	1	0	1
Done	0	2	2
Total	103	6	109

Error

0.0b

Counts

109 → 6

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (.f64 x 27) y)
	1.4b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 27 (.f64 y x)))) 2) (.f64 (cbrt.f64 (cbrt.f64 (.f64 27 (.f64 y x)))) (pow.f64 (cbrt.f64 (.f64 27 (.f64 y x))) 2)))
✓	0.2b	(.f64 27 (.f64 y x))
	29.0b	(.f64 (.f64 27 (sqrt.f64 (.f64 y x))) (sqrt.f64 (.f64 y x)))
	1.2b	(.f64 (cbrt.f64 (.f64 27 (.f64 y x))) (pow.f64 (cbrt.f64 (.f64 27 (*.f64 y x))) 2))
▶	0.2b	(.f64 x (.f64 27 y))

Compiler

Compiled 1404 to 939 computations (33.1% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (.f64 27 y))

series4.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(*.f64 x (*.f64 27 y))

rewrite42.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
387×	`unpow-prod-down_binary64`
299×	`log-prod_binary64`
153×	`pow2_binary64`

Counts

1 → 18

Calls

1 calls:

42.0ms

(*.f64 x (*.f64 27 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1358	7
3	5055	7
0	0	0
1	0	0

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Counts

42 → 19

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	10	168
2	16	168
3	16	168
4	16	168

prune12.0ms (0.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	19	0	19
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	19	6	25

Error

0.0b

Counts

25 → 6

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (.f64 x 27) y)
	1.4b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 27 (.f64 y x)))) 2) (.f64 (cbrt.f64 (cbrt.f64 (.f64 27 (.f64 y x)))) (pow.f64 (cbrt.f64 (.f64 27 (.f64 y x))) 2)))
✓	0.2b	(.f64 27 (.f64 y x))
	29.0b	(.f64 (.f64 27 (sqrt.f64 (.f64 y x))) (sqrt.f64 (.f64 y x)))
	1.2b	(.f64 (cbrt.f64 (.f64 27 (.f64 y x))) (pow.f64 (cbrt.f64 (.f64 27 (*.f64 y x))) 2))
✓	0.2b	(.f64 x (.f64 27 y))

Compiler

Compiled 246 to 171 computations (30.5% saved)

regimes123.0ms (5.5%)

Accuracy

Total 0.3b remaining (93.8%)

Threshold costs 0.3b (93.8%)

Counts

27 → 1

Compiler

Compiled 1410 to 1058 computations (25% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7
2	8	7

end215.0ms (9.6%)

Compiler: Compiled 107 to 74 computations (30.8% saved)

Details

analyze65.0ms (2.9%)

sample697.0ms (31.1%)

simplify10.0ms (0.4%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

series4.0ms (0.2%)

rewrite38.0ms (1.7%)

simplify10.0ms (0.5%)

prune14.0ms (0.6%)

localize3.0ms (0.1%)

series4.0ms (0.2%)

rewrite36.0ms (1.6%)

simplify7.0ms (0.3%)

prune12.0ms (0.5%)

localize9.0ms (0.4%)

series730.0ms (32.6%)

rewrite47.0ms (2.1%)

simplify67.0ms (3%)

prune64.0ms (2.9%)

localize3.0ms (0.1%)

series4.0ms (0.2%)

rewrite42.0ms (1.9%)

simplify13.0ms (0.6%)

prune12.0ms (0.5%)

regimes123.0ms (5.5%)

simplify2.0ms (0.1%)

end215.0ms (9.6%)

Profiling