Details

analyze398.0ms (10.9%)

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
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%	64%	4.8%	9
31.2%	42.1%	26.7%	10
35.9%	37.1%	27.1%	11
38.2%	32.2%	29.6%	12
47.8%	21.6%	30.6%	13
50.2%	19%	30.8%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample931.0ms (25.5%)

Symmetry

(sort x y)

Results

856.0ms	8256×	body	128	valid
41.0ms	434×	body	128	invalid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
5×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	17	15
2	34	11
3	54	11
4	68	11
5	72	11
6	70	11

prune5.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 84 to 41 computations (51.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))

series9.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

9.0ms

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

rewrite40.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

678×	`log1p-expm1-u_binary64`
678×	`expm1-log1p-u_binary64`
191×	`prod-diff_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`

Counts

1 → 24

Calls

1 calls:

39.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	159	11
2	1785	11
3	4975	11

simplify166.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

60 → 29

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	345
1	19	345
2	32	345
3	53	345
4	101	345
5	238	345
6	718	345
7	1143	345
8	1145	345
9	1293	345
10	1463	345
11	1645	345
12	1868	345
13	2153	345
14	2572	345
15	3137	345
16	3823	345
17	4041	345
18	4285	345
19	4367	345
20	4400	345
21	4421	345
22	4990	345

prune20.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	27	4	31

Error

0.0b

Counts

31 → 4

Alt Table

Status	Error	Program
	37.5b	(cbrt.f64 (pow.f64 (fma.f64 z (.f64 z 3) (.f64 x y)) 3))
	1.2b	(.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (pow.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))) 2))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))

Compiler

Compiled 470 to 265 computations (43.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (.f64 z z))

series2.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(*.f64 3 (*.f64 z z))

rewrite77.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`log1p-udef_binary64`
400×	`log1p-expm1-u_binary64`
400×	`expm1-log1p-u_binary64`
347×	`pow1_binary64`
279×	`unpow-prod-down_binary64`

Counts

1 → 24

Calls

1 calls:

76.0ms

(*.f64 3 (*.f64 z z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1071	7
3	4741	7
4	5869	7

simplify152.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

36 → 25

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	22	84
3	41	84
4	87	84
5	220	84
6	692	84
7	1097	84
8	1099	84
9	1247	84
10	1417	84
11	1599	84
12	1824	84
13	2109	84
14	2528	84
15	3093	84
16	3779	84
17	3997	84
18	4241	84
19	4323	84
20	4356	84
21	4377	84
22	4946	84

prune20.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	25	4	29

Error

0.0b

Counts

29 → 4

Alt Table

Status	Error	Program
▶	1.2b	(.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (pow.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))) 2))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))
	20.8b	(fma.f64 y x (cbrt.f64 (*.f64 27 (pow.f64 z 6))))

Compiler

Compiled 391 to 240 computations (38.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (pow.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) 2)
✓	4.4b	(cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y)))

series305.0ms (8.3%)

Counts

3 → 108

Calls

3 calls:

155.0ms

(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z 3) (*.f64 x y))) 2)

110.0ms

(*.f64 (cbrt.f64 (fma.f64 z (*.f64 z 3) (*.f64 x y))) (pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z 3) (*.f64 x y))) 2))

40.0ms

(cbrt.f64 (fma.f64 z (*.f64 z 3) (*.f64 x y)))

rewrite52.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

857×	`log1p-expm1-u_binary64`
857×	`expm1-log1p-u_binary64`
191×	`prod-diff_binary64`
105×	`add-sqr-sqrt_binary64`
99×	`add-log-exp_binary64`

Counts

3 → 62

Calls

3 calls:

51.0ms

(*.f64 (cbrt.f64 (fma.f64 z (*.f64 z 3) (*.f64 x y))) (pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z 3) (*.f64 x y))) 2))

51.0ms

(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z 3) (*.f64 x y))) 2)

51.0ms

(cbrt.f64 (fma.f64 z (*.f64 z 3) (*.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	222	40
2	2273	40
3	5566	40

simplify111.0ms (3%)

Algorithm

1×	egg-herbie

Rules

499×	`unswap-sqr_binary64`
303×	`associate-r_binary64`
292×	`times-frac_binary64`
255×	`associate-/r*_binary64`
242×	`associate-/l*_binary64`

Counts

170 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	325	4904
1	1103	4724
2	3924	4602
3	5212	4602

prune345.0ms (9.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	328	1	329
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	328	5	333

Error

0.0b

Counts

333 → 5

Alt Table

Status	Error	Program
▶	1.6b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y)))) 3) (pow.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))) 2))
✓	1.2b	(.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (pow.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))) 2))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))
	20.8b	(fma.f64 y x (cbrt.f64 (*.f64 27 (pow.f64 z 6))))

Compiler

Compiled 13030 to 8171 computations (37.3% saved)

localize41.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))))
	0.5b	(pow.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) 2)
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y)))) 3)
	4.4b	(cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y)))

series152.0ms (4.2%)

Counts

2 → 72

Calls

2 calls:

111.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y)))) 3)
40.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))))

rewrite49.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

833×	`log1p-expm1-u_binary64`
833×	`expm1-log1p-u_binary64`
191×	`prod-diff_binary64`
97×	`add-sqr-sqrt_binary64`
91×	`add-cbrt-cube_binary64`

Counts

2 → 48

Calls

2 calls:

47.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))))
47.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y)))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	202	28
2	2212	28
3	5443	28

simplify114.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

576×	`unswap-sqr_binary64`
374×	`associate-r_binary64`
316×	`times-frac_binary64`
267×	`associate-/l*_binary64`
259×	`associate-l_binary64`

Counts

120 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	5209
1	1135	5021
2	4349	5015
3	5728	5015

prune393.0ms (10.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	409	0	409
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	409	5	414

Error

0.0b

Counts

414 → 5

Alt Table

Status	Error	Program
✓	1.6b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y)))) 3) (pow.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))) 2))
✓	1.2b	(.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (pow.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))) 2))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))
	20.8b	(fma.f64 y x (cbrt.f64 (*.f64 27 (pow.f64 z 6))))

Compiler

Compiled 20272 to 13471 computations (33.5% saved)

regimes158.0ms (4.3%)

Accuracy

Total 0.1b remaining (75.5%)

Threshold costs 0.1b (75.5%)

Counts

25 → 1

Compiler

Compiled 2633 to 1827 computations (30.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end90.0ms (2.5%)

Remove: (sort x y)
Compiler: Compiled 129 to 84 computations (34.9% saved)

Details

analyze398.0ms (10.9%)

sample931.0ms (25.5%)

simplify7.0ms (0.2%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite40.0ms (1.1%)

simplify166.0ms (4.5%)

prune20.0ms (0.5%)

localize5.0ms (0.1%)

series2.0ms (0.1%)

rewrite77.0ms (2.1%)

simplify152.0ms (4.1%)

prune20.0ms (0.6%)

localize9.0ms (0.2%)

series305.0ms (8.3%)

rewrite52.0ms (1.4%)

simplify111.0ms (3%)

prune345.0ms (9.4%)

localize41.0ms (1.1%)

series152.0ms (4.2%)

rewrite49.0ms (1.3%)

simplify114.0ms (3.1%)

prune393.0ms (10.8%)

regimes158.0ms (4.3%)

simplify2.0ms (0.1%)

end90.0ms (2.5%)

Profiling