Details

analyze59.0ms (2.2%)

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
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)

sample746.0ms (28.1%)

Symmetry

(sort x y)

Results

615.0ms	8256×	body	128	valid
8.0ms	88×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify7.0ms (0.3%)

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

prune1.0ms (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

0.2b

Counts

2 → 1

Alt Table

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

series5.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite47.0ms (1.8%)

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 → 17

Calls

1 calls:

47.0ms

(*.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

simplify11.0ms (0.4%)

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

prune13.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	14	4	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	5	19

Error

0.1b

Counts

19 → 5

Alt Table

Status	Error	Program
	30.0b	(cbrt.f64 (.f64 19683 (pow.f64 (.f64 x y) 3)))
✓	0.2b	(.f64 (.f64 x 27) y)
	26.8b	(pow.f64 (sqrt.f64 (.f64 (.f64 x 27) y)) 2)
	1.2b	(pow.f64 (cbrt.f64 (.f64 (.f64 x 27) y)) 3)
▶	0.3b	(.f64 27 (.f64 y x))

Compiler

Compiled 243 to 178 computations (26.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 27 (.f64 y x))

series5.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

5.0ms

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

rewrite40.0ms (1.5%)

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 → 17

Calls

1 calls:

40.0ms

(*.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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune12.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	17	5	22

Error

0.1b

Counts

22 → 5

Alt Table

Status	Error	Program
	30.0b	(cbrt.f64 (.f64 19683 (pow.f64 (.f64 x y) 3)))
✓	0.2b	(.f64 (.f64 x 27) y)
	26.8b	(pow.f64 (sqrt.f64 (.f64 (.f64 x 27) y)) 2)
▶	1.2b	(pow.f64 (cbrt.f64 (.f64 (.f64 x 27) y)) 3)
✓	0.3b	(.f64 27 (.f64 y x))

Compiler

Compiled 231 to 159 computations (31.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 x 27) y)
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 (.f64 x 27) y)) 3)
✓	8.0b	(cbrt.f64 (.f64 (.f64 x 27) y))

series859.0ms (32.3%)

Counts

2 → 48

Calls

2 calls:

483.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x 27) y)) 3)
376.0ms	(cbrt.f64 (.f64 (.f64 x 27) y))

rewrite49.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

664×	`log1p-expm1-u_binary64`
664×	`expm1-log1p-u_binary64`
369×	`log-prod_binary64`
133×	`expm1-udef_binary64`
133×	`log1p-udef_binary64`

Counts

2 → 73

Calls

2 calls:

47.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x 27) y)) 3)
47.0ms	(cbrt.f64 (.f64 (.f64 x 27) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	166	16
2	1763	16
3	5103	16
0	0	0
1	0	0

simplify72.0ms (2.7%)

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

121 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	904
1	124	904
2	215	792
3	568	448
4	1843	448
5	4611	448
6	5077	448

prune72.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	2	0	2
Picked	0	1	1
Done	0	2	2
Total	102	7	109

Error

0.0b

Counts

109 → 7

Alt Table

Status	Error	Program
	18.3b	(.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 x 27)))
	23.5b	(.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 x 27)))
	26.4b	(.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (.f64 27 y)))
▶	0.3b	(.f64 x (.f64 27 y))
✓	1.2b	(pow.f64 (cbrt.f64 (.f64 (.f64 x 27) y)) 3)
✓	0.3b	(.f64 27 (.f64 y x))
✓	0.2b	(.f64 (.f64 x 27) y)

Compiler

Compiled 1379 to 1012 computations (26.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 x (.f64 27 y))

series5.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

5.0ms

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

rewrite46.0ms (1.7%)

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 → 17

Calls

1 calls:

45.0ms

(*.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

simplify19.0ms (0.7%)

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

prune26.0ms (1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	18	0	18
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	18	7	25

Error

0.0b

Counts

25 → 7

Alt Table

Status	Error	Program
	18.3b	(.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 x 27)))
	23.5b	(.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 x 27)))
	26.4b	(.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (.f64 27 y)))
✓	0.3b	(.f64 x (.f64 27 y))
✓	1.2b	(pow.f64 (cbrt.f64 (.f64 (.f64 x 27) y)) 3)
✓	0.3b	(.f64 27 (.f64 y x))
✓	0.2b	(.f64 (.f64 x 27) y)

Compiler

Compiled 230 to 162 computations (29.6% saved)

regimes100.0ms (3.8%)

Accuracy

Total 0.3b remaining (95.3%)

Threshold costs 0.3b (95.3%)

Counts

11 → 1

Compiler

Compiled 468 to 346 computations (26.1% saved)

simplify4.0ms (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

end439.0ms (16.5%)

Compiler: Compiled 96 to 68 computations (29.2% saved)

Details

analyze59.0ms (2.2%)

sample746.0ms (28.1%)

simplify7.0ms (0.3%)

prune1.0ms (0.1%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite47.0ms (1.8%)

simplify11.0ms (0.4%)

prune13.0ms (0.5%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite40.0ms (1.5%)

simplify6.0ms (0.2%)

prune12.0ms (0.4%)

localize6.0ms (0.2%)

series859.0ms (32.3%)

rewrite49.0ms (1.8%)

simplify72.0ms (2.7%)

prune72.0ms (2.7%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite46.0ms (1.7%)

simplify19.0ms (0.7%)

prune26.0ms (1%)

regimes100.0ms (3.8%)

simplify4.0ms (0.1%)

end439.0ms (16.5%)

Profiling