Details

analyze396.0ms (14.1%)

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)

sample894.0ms (31.8%)

Results

827.0ms	8256×	body	128	valid
51.0ms	464×	body	128	invalid

Compiler

Compiled 38 to 18 computations (52.6% saved)

preprocess21.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

96×	`fma-def_binary64`
15×	`*-commutative_binary64`
14×	`associate-+l+_binary64`
12×	`+-commutative_binary64`
12×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	80
1	51	60
2	99	44
3	162	44
4	212	44
5	230	44
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x y)

Compiler

Compiled 18 to 8 computations (55.6% saved)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	17	15
2	34	11
3	57	11
4	75	11
5	81	11

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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 x y (.f64 z (.f64 z 3)))
▶	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 84 to 42 computations (50% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x y) (.f64 z z))
✓	0.0b	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

series34.0ms (1.2%)

Counts

3 → 108

Calls

27 calls:

6.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))	y	-inf
1.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))	x	0
1.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))	y	-inf
1.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))	x	inf
1.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))	x	-inf

rewrite72.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

853×	`fma-def_binary64`
351×	`fma-neg_binary64`
237×	`egg-rr`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	42
1	210	34
2	3206	34

Stop Event

1×	node limit

Counts

3 → 237

simplify110.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
398×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
242×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	942
1	27	942
2	51	942
3	88	942
4	196	942
5	553	942
6	769	942
7	1190	942
8	1310	942
9	1443	942
10	1612	942
11	1853	942
12	2168	942
13	2538	942
14	2994	942
15	3575	942
16	4283	942

Stop Event

1×	node limit

Counts

345 → 250

prune150.0ms (5.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	246	4	250
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	247	5	252

Error

Counts

252 → 5

Alt Table

Status	Error	Program
	13.3b	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 x y (.f64 z z)))) (.f64 z z)) (*.f64 z z))
	1.1b	(fma.f64 (cbrt.f64 (fma.f64 z (+.f64 z z) (.f64 x y))) (pow.f64 (cbrt.f64 (fma.f64 z (+.f64 z z) (.f64 x y))) 2) (*.f64 z z))
	0.1b	(fma.f64 x y (.f64 z (.f64 z 3)))
	0.3b	(+.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) z) (.f64 x y)) (.f64 z z)) (.f64 z z))
▶	0.0b	(fma.f64 x y (fma.f64 z z (*.f64 z (+.f64 z z))))

Compiler

Compiled 5088 to 1263 computations (75.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (fma.f64 z z (*.f64 z (+.f64 z z))))
✓	0.1b	(fma.f64 z z (*.f64 z (+.f64 z z)))

series17.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

3.0ms	(fma.f64 x y (fma.f64 z z (*.f64 z (+.f64 z z))))	x	-inf
1.0ms	(fma.f64 x y (fma.f64 z z (*.f64 z (+.f64 z z))))	y	inf
1.0ms	(fma.f64 x y (fma.f64 z z (*.f64 z (+.f64 z z))))	y	-inf
1.0ms	(fma.f64 x y (fma.f64 z z (*.f64 z (+.f64 z z))))	x	inf
1.0ms	(fma.f64 x y (fma.f64 z z (*.f64 z (+.f64 z z))))	x	0

rewrite39.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

677×	`log1p-expm1-u_binary64`
677×	`expm1-log1p-u_binary64`
128×	`expm1-udef_binary64`
128×	`log1p-udef_binary64`
87×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	168	20
2	2267	20

Stop Event

1×	node limit

Counts

2 → 48

simplify78.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
443×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	429
1	19	429
2	33	429
3	57	429
4	119	429
5	320	429
6	1229	429
7	2130	429
8	2294	429
9	2478	429
10	2686	429
11	2978	429
12	3369	429
13	3849	429
14	4408	429

Stop Event

1×	node limit

Counts

96 → 53

prune24.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	53	5	58

Error

Counts

58 → 5

Alt Table

Status	Error	Program
	13.3b	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 x y (.f64 z z)))) (.f64 z z)) (*.f64 z z))
	1.1b	(fma.f64 (cbrt.f64 (fma.f64 z (+.f64 z z) (.f64 x y))) (pow.f64 (cbrt.f64 (fma.f64 z (+.f64 z z) (.f64 x y))) 2) (*.f64 z z))
▶	0.1b	(fma.f64 x y (.f64 z (.f64 z 3)))
	0.3b	(+.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) z) (.f64 x y)) (.f64 z z)) (.f64 z z))
✓	0.0b	(fma.f64 x y (fma.f64 z z (*.f64 z (+.f64 z z))))

Compiler

Compiled 890 to 529 computations (40.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (.f64 z (.f64 z 3)))
✓	0.2b	(.f64 z (.f64 z 3))

series18.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

6.0ms	(fma.f64 x y (.f64 z (.f64 z 3)))	y	-inf
1.0ms	(fma.f64 x y (.f64 z (.f64 z 3)))	x	-inf
1.0ms	(fma.f64 x y (.f64 z (.f64 z 3)))	y	inf
1.0ms	(fma.f64 x y (.f64 z (.f64 z 3)))	x	inf
1.0ms	(fma.f64 x y (.f64 z (.f64 z 3)))	x	0

rewrite42.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`log1p-expm1-u_binary64`
680×	`expm1-log1p-u_binary64`
200×	`prod-diff_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	160	18
2	1860	18

Stop Event

1×	node limit

Counts

2 → 38

simplify80.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
443×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	429
1	19	429
2	33	429
3	57	429
4	119	429
5	320	429
6	1229	429
7	2130	429
8	2294	429
9	2478	429
10	2686	429
11	2978	429
12	3369	429
13	3849	429
14	4408	429

Stop Event

1×	node limit

Counts

86 → 43

prune29.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	43	5	48

Error

Counts

48 → 5

Alt Table

Status	Error	Program
	13.3b	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 x y (.f64 z z)))) (.f64 z z)) (*.f64 z z))
	1.1b	(fma.f64 (cbrt.f64 (fma.f64 z (+.f64 z z) (.f64 x y))) (pow.f64 (cbrt.f64 (fma.f64 z (+.f64 z z) (.f64 x y))) 2) (*.f64 z z))
✓	0.1b	(fma.f64 x y (.f64 z (.f64 z 3)))
▶	0.3b	(+.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) z) (.f64 x y)) (.f64 z z)) (.f64 z z))
✓	0.0b	(fma.f64 x y (fma.f64 z z (*.f64 z (+.f64 z z))))

Compiler

Compiled 684 to 391 computations (42.8% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) z) (.f64 x y))
✓	0.2b	(*.f64 (cbrt.f64 z) z)
✓	0.5b	(pow.f64 (cbrt.f64 z) 2)
✓	0.7b	(cbrt.f64 z)

series206.0ms (7.3%)

Counts

4 → 28

Calls

18 calls:

27.0ms	(fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) z) (.f64 x y))	x	inf
26.0ms	(fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) z) (.f64 x y))	y	0
23.0ms	(fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) z) (.f64 x y))	x	0
22.0ms	(fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) z) (.f64 x y))	y	-inf
22.0ms	(fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) z) (.f64 x y))	y	inf

rewrite52.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

764×	`log1p-expm1-u_binary64`
764×	`expm1-log1p-u_binary64`
338×	`prod-diff_binary64`
96×	`add-sqr-sqrt_binary64`
89×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	199	25
2	2299	25

Stop Event

1×	node limit

Counts

4 → 82

simplify61.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

783×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
354×	`cube-prod_binary64`
345×	`fabs-mul_binary64`
312×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	184
1	16	184
2	26	184
3	37	184
4	66	184
5	154	184
6	576	184
7	1445	184
8	1629	184
9	1813	184
10	2021	184
11	2308	184
12	2699	184
13	3179	184
14	3740	184
15	4428	184

Stop Event

1×	node limit

Counts

110 → 87

prune88.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	110	5	115

Error

Counts

115 → 5

Alt Table

Status	Error	Program
	0.1b	(+.f64 (+.f64 (fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) z) (.f64 x y)) (.f64 z z)) (*.f64 z z))
	13.3b	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 x y (.f64 z z)))) (.f64 z z)) (*.f64 z z))
✓	0.1b	(fma.f64 x y (.f64 z (.f64 z 3)))
✓	0.3b	(+.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) z) (.f64 x y)) (.f64 z z)) (.f64 z z))
✓	0.0b	(fma.f64 x y (fma.f64 z z (*.f64 z (+.f64 z z))))

Compiler

Compiled 2530 to 829 computations (67.2% saved)

regimes270.0ms (9.6%)

Accuracy

Total 0.0b remaining (79.2%)

Threshold costs 0.0b (79.2%)

Counts

45 → 1

Compiler

Compiled 5497 to 2984 computations (45.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	9	15

Stop Event

1×

saturated

end85.0ms (3%)

Stop Event

1×

fuel

Remove

(sort x y)

Compiler

Compiled 146 to 74 computations (49.3% saved)

Details

analyze396.0ms (14.1%)

sample894.0ms (31.8%)

preprocess21.0ms (0.8%)

simplify11.0ms (0.4%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series34.0ms (1.2%)

rewrite72.0ms (2.6%)

simplify110.0ms (3.9%)

prune150.0ms (5.3%)

localize6.0ms (0.2%)

series17.0ms (0.6%)

rewrite39.0ms (1.4%)

simplify78.0ms (2.8%)

prune24.0ms (0.9%)

localize5.0ms (0.2%)

series18.0ms (0.6%)

rewrite42.0ms (1.5%)

simplify80.0ms (2.9%)

prune29.0ms (1%)

localize13.0ms (0.4%)

series206.0ms (7.3%)

rewrite52.0ms (1.8%)

simplify61.0ms (2.2%)

prune88.0ms (3.1%)

regimes270.0ms (9.6%)

simplify2.0ms (0.1%)

end85.0ms (3%)

Profiling