Details

analyze432.0ms (12.8%)

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
12.5%	87.4%	0.1%	7
25%	74.9%	0.1%	8
31.2%	62.4%	6.4%	9
46.8%	46.8%	6.4%	10
53.8%	39.8%	6.4%	11
57.3%	33.2%	9.5%	12
66.9%	23.6%	9.5%	13
70.3%	20.2%	9.5%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.0s (29.7%)

Symmetry

(sort x y)

Results

804.0ms	8256×	body	128	valid
98.0ms	288×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify25.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

192×	`fma-def_binary64`
125×	`fma-neg_binary64`
44×	`distribute-rgt-neg-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
27×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10

prune3.0ms (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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (.f64 (.f64 x 3) y) z)

Compiler

Compiled 30 to 21 computations (30% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 x 3) y)

series10.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(*.f64 (*.f64 x 3) y)

rewrite54.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

510×	`log1p-expm1-u_binary64`
510×	`expm1-log1p-u_binary64`
385×	`unpow-prod-down_binary64`
298×	`log-prod_binary64`
169×	`pow2_binary64`

Counts

1 → 17

Calls

1 calls:

53.0ms

(*.f64 (*.f64 x 3) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1355	7
3	5019	7
0	0	0
1	0	0

simplify18.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

41 → 18

Iterations

Useful iterations: 0 (0.0ms)

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

prune25.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	4	19

Error

0.0b

Counts

19 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (.f64 (.f64 x 3) y) z)
	33.8b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 x 3) y)) 2) z)
▶	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
	0.8b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)

Compiler

Compiled 281 to 197 computations (29.9% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (.f64 y x))

series10.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

10.0ms

(*.f64 3 (*.f64 y x))

rewrite65.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

511×	`log1p-expm1-u_binary64`
511×	`expm1-log1p-u_binary64`
387×	`unpow-prod-down_binary64`
299×	`log-prod_binary64`
169×	`pow2_binary64`

Counts

1 → 17

Calls

1 calls:

64.0ms

(*.f64 3 (*.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1357	7
3	5027	7
0	0	0
1	0	0

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune23.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	17	4	21

Error

0.0b

Counts

21 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (.f64 (.f64 x 3) y) z)
	33.8b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 x 3) y)) 2) z)
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
▶	0.8b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)

Compiler

Compiled 256 to 166 computations (35.2% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(.f64 (.f64 x 3) y)
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3)
✓	9.3b	(cbrt.f64 (.f64 (.f64 x 3) y))

series1.1s (31.4%)

Counts

2 → 48

Calls

2 calls:

609.0ms	(cbrt.f64 (.f64 (.f64 x 3) y))
447.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3)

rewrite80.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

617×	`log1p-expm1-u_binary64`
617×	`expm1-log1p-u_binary64`
357×	`log-prod_binary64`
123×	`expm1-udef_binary64`
123×	`log1p-udef_binary64`

Counts

2 → 71

Calls

2 calls:

79.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3)
79.0ms	(cbrt.f64 (.f64 (.f64 x 3) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	149	16
2	1644	16
3	4982	16
4	4924	16
0	0	0
1	0	0

simplify65.0ms (1.9%)

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 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	936
1	124	936
2	215	824
3	568	480
4	1843	480
5	4611	480
6	5077	480

prune62.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	101	5	106

Error

Counts

106 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 x (.f64 3 y)) z)
	33.8b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 x 3) y)) 2) z)
✓	0.3b	(-.f64 (.f64 (.f64 x 3) y) z)
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.8b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)

Compiler

Compiled 1519 to 1079 computations (29% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (.f64 3 y))

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(*.f64 x (*.f64 3 y))

rewrite54.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

511×	`log1p-expm1-u_binary64`
511×	`expm1-log1p-u_binary64`
387×	`unpow-prod-down_binary64`
299×	`log-prod_binary64`
169×	`pow2_binary64`

Counts

1 → 17

Calls

1 calls:

53.0ms

(*.f64 x (*.f64 3 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1357	7
3	5027	7
0	0	0
1	0	0

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

41 → 18

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 (0.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	18	0	18
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	18	5	23

Error

Counts

23 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 x (.f64 3 y)) z)
	33.8b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 x 3) y)) 2) z)
✓	0.3b	(-.f64 (.f64 (.f64 x 3) y) z)
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.8b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)

Compiler

Compiled 255 to 176 computations (31% saved)

regimes106.0ms (3.2%)

Accuracy

Total 0.1b remaining (92.1%)

Threshold costs 0.1b (92.1%)

Counts

5 → 1

Compiler

Compiled 508 to 376 computations (26% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	12	10
2	17	10
3	19	10
4	20	10
5	20	10

end201.0ms (6%)

Compiler: Compiled 96 to 69 computations (28.1% saved)

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10

Details

analyze432.0ms (12.8%)

sample1.0s (29.7%)

simplify25.0ms (0.8%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series10.0ms (0.3%)

rewrite54.0ms (1.6%)

simplify18.0ms (0.5%)

prune25.0ms (0.7%)

localize9.0ms (0.3%)

series10.0ms (0.3%)

rewrite65.0ms (1.9%)

simplify12.0ms (0.4%)

prune23.0ms (0.7%)

localize13.0ms (0.4%)

series1.1s (31.4%)

rewrite80.0ms (2.4%)

simplify65.0ms (1.9%)

prune62.0ms (1.9%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite54.0ms (1.6%)

simplify10.0ms (0.3%)

prune12.0ms (0.4%)

regimes106.0ms (3.2%)

simplify3.0ms (0.1%)

end201.0ms (6%)

Profiling

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10