Details

analyze61.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample1.2s (38.9%)

Results

887.0ms	8256×	body	128	valid
7.0ms	62×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify119.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 m) v)
✓	0.1b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

series23.0ms (0.7%)

Counts

3 → 64

Calls

3 calls:

10.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
7.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
5.0ms	(/.f64 (-.f64 1 m) v)

rewrite98.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

451×	`log-prod_binary64`
326×	`prod-diff_binary64`
173×	`pow1/3_binary64`
165×	`expm1-udef_binary64`
164×	`log1p-udef_binary64`

Counts

3 → 128

Calls

3 calls:

95.0ms	(/.f64 (-.f64 1 m) v)
95.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
95.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	186	32
2	2360	32
3	4883	32
4	5141	32
0	0	0
1	0	0

simplify65.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

595×	`unswap-sqr_binary64`
582×	`associate-l_binary64`
406×	`fma-def_binary64`
291×	`associate-/l*_binary64`
282×	`fma-neg_binary64`

Counts

192 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	814
1	83	715
2	159	689
3	370	676
4	1002	676
5	3651	676
6	5359	676

prune114.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	147	6	153
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	148	7	155

Error

0.0b

Counts

155 → 7

Alt Table

Status	Error	Program
	32.1b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	35.1b	(pow.f64 (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) 2)
▶	0.2b	(fma.f64 m (/.f64 (-.f64 m (*.f64 m m)) v) (neg.f64 m))
	0.3b	(*.f64 m (fma.f64 m (+.f64 (/.f64 (-.f64 1 m) v) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))) -1))
	21.9b	(*.f64 m (cbrt.f64 (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3)))
	9.1b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 3433 to 1810 computations (47.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 m (*.f64 m m))
✓	0.0b	(/.f64 (-.f64 m (*.f64 m m)) v)
✓	0.2b	(fma.f64 m (/.f64 (-.f64 m (*.f64 m m)) v) (neg.f64 m))

series26.0ms (0.9%)

Counts

3 → 60

Calls

3 calls:

13.0ms	(fma.f64 m (/.f64 (-.f64 m (*.f64 m m)) v) (neg.f64 m))
11.0ms	(/.f64 (-.f64 m (*.f64 m m)) v)
2.0ms	(-.f64 m (*.f64 m m))

rewrite56.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

878×	`log1p-expm1-u_binary64`
878×	`expm1-log1p-u_binary64`
108×	`egg-rr`
96×	`add-sqr-sqrt_binary64`
89×	`add-cbrt-cube_binary64`

Counts

3 → 108

Calls

3 calls:

54.0ms	(-.f64 m (*.f64 m m))
54.0ms	(/.f64 (-.f64 m (*.f64 m m)) v)
54.0ms	(fma.f64 m (/.f64 (-.f64 m (*.f64 m m)) v) (neg.f64 m))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	33
1	185	31
2	2203	31
3	5236	31
0	0	0
1	0	0

simplify81.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

508×	`sub-neg_binary64`
438×	`fma-def_binary64`
382×	`associate-/l*_binary64`
378×	`unsub-neg_binary64`
370×	`div-sub_binary64`

Counts

168 → 131

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	624
1	65	624
2	140	624
3	365	624
4	1056	624
5	3939	624
6	4838	624
7	5353	624

prune72.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	2	3	5
Picked	0	1	1
Done	1	0	1
Total	133	5	138

Error

0.0b

Counts

138 → 5

Alt Table

Status	Error	Program
	35.1b	(pow.f64 (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) 2)
✓	0.2b	(fma.f64 m (/.f64 (-.f64 m (*.f64 m m)) v) (neg.f64 m))
	32.0b	(/.f64 (-.f64 (pow.f64 m 2) (pow.f64 m 3)) v)
▶	0.3b	(*.f64 m (fma.f64 m (+.f64 (/.f64 (-.f64 1 m) v) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))) -1))
	21.9b	(*.f64 m (cbrt.f64 (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3)))

Compiler

Compiled 2161 to 699 computations (67.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 m (+.f64 (/.f64 (-.f64 1 m) v) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))) -1)
✓	0.2b	(*.f64 m (fma.f64 m (+.f64 (/.f64 (-.f64 1 m) v) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))) -1))
✓	0.3b	(/.f64 (sqrt.f64 m) (sqrt.f64 v))
✓	61.3b	(fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))

series146.0ms (4.8%)

Counts

4 → 15

Calls

4 calls:

53.0ms	(*.f64 m (fma.f64 m (+.f64 (/.f64 (-.f64 1 m) v) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))) -1))
43.0ms	(fma.f64 m (+.f64 (/.f64 (-.f64 1 m) v) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))) -1)
32.0ms	(fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))
18.0ms	(/.f64 (sqrt.f64 m) (sqrt.f64 v))

rewrite84.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

278×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`

Counts

4 → 112

Calls

4 calls:

82.0ms	(fma.f64 m (+.f64 (/.f64 (-.f64 1 m) v) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))) -1)
82.0ms	(*.f64 m (fma.f64 m (+.f64 (/.f64 (-.f64 1 m) v) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))) -1))
82.0ms	(/.f64 (sqrt.f64 m) (sqrt.f64 v))
81.0ms	(fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	95
1	343	65
2	4265	65
3	5020	65
0	0	0
1	0	0

simplify180.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

467×	`sqr-pow_binary64`
461×	`sub-neg_binary64`
444×	`fma-def_binary64`
437×	`cube-prod_binary64`
434×	`unswap-sqr_binary64`

Counts

127 → 122

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	12	73
1	23	73
2	32	73
3	63	73
4	134	73
5	369	73
6	1489	73
7	4060	73
8	4330	73
9	4669	65
10	3440	65
11	4575	65
12	4644	65
13	4475	65
14	4885	65
15	4776	65

prune119.0ms (3.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	170	5	175

Error

0.0b

Counts

175 → 5

Alt Table

Status	Error	Program
	35.1b	(pow.f64 (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) 2)
✓	0.2b	(fma.f64 m (/.f64 (-.f64 m (*.f64 m m)) v) (neg.f64 m))
	32.0b	(/.f64 (-.f64 (pow.f64 m 2) (pow.f64 m 3)) v)
✓	0.3b	(*.f64 m (fma.f64 m (+.f64 (/.f64 (-.f64 1 m) v) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))) -1))
▶	21.9b	(*.f64 m (cbrt.f64 (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3)))

Compiler

Compiled 4525 to 1885 computations (58.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
✓	0.2b	(*.f64 m (cbrt.f64 (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3)))
✓	0.2b	(pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3)
✓	20.8b	(cbrt.f64 (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3))

series37.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

19.0ms	(pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3)
11.0ms	(*.f64 m (cbrt.f64 (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3)))
7.0ms	(cbrt.f64 (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3))

rewrite59.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

520×	`log-prod_binary64`
201×	`prod-diff_binary64`
194×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
166×	`log-pow_binary64`

Counts

3 → 94

Calls

3 calls:

57.0ms	(*.f64 m (cbrt.f64 (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3)))
57.0ms	(pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3)
57.0ms	(cbrt.f64 (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	232	39
2	2780	39
3	5119	39
0	0	0
1	0	0

simplify73.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

517×	`associate--r+_binary64`
455×	`fma-def_binary64`
312×	`associate-+l+_binary64`
304×	`associate--l+_binary64`
287×	`times-frac_binary64`

Counts

166 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1789
1	273	1672
2	1016	1554
3	4965	1551
4	5067	1551

prune130.0ms (4.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	175	7	182

Error

0.0b

Counts

182 → 7

Alt Table

Status	Error	Program
	35.1b	(pow.f64 (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) 2)
✓	0.2b	(fma.f64 m (/.f64 (-.f64 m (*.f64 m m)) v) (neg.f64 m))
	0.2b	(-.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) m)
	32.0b	(/.f64 (-.f64 (pow.f64 m 2) (pow.f64 m 3)) v)
	22.0b	(.f64 m (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) 2) (*.f64 (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 2)))))
✓	0.3b	(*.f64 m (fma.f64 m (+.f64 (/.f64 (-.f64 1 m) v) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 v))) (/.f64 (sqrt.f64 m) (sqrt.f64 v)) (/.f64 m v))) -1))
✓	21.9b	(*.f64 m (cbrt.f64 (pow.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) 3)))

Compiler

Compiled 3628 to 2461 computations (32.2% saved)

regimes195.0ms (6.4%)

Accuracy

Total 0.2b remaining (84%)

Threshold costs 0.2b (84%)

Counts

74 → 1

Compiler

Compiled 2885 to 1934 computations (33% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	20	16
2	23	16
3	24	16
4	23	16

end97.0ms (3.2%)

Compiler: Compiled 158 to 102 computations (35.4% saved)

Details

analyze61.0ms (2%)

sample1.2s (38.9%)

simplify119.0ms (3.9%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series23.0ms (0.7%)

rewrite98.0ms (3.2%)

simplify65.0ms (2.1%)

prune114.0ms (3.7%)

localize6.0ms (0.2%)

series26.0ms (0.9%)

rewrite56.0ms (1.8%)

simplify81.0ms (2.6%)

prune72.0ms (2.3%)

localize13.0ms (0.4%)

series146.0ms (4.8%)

rewrite84.0ms (2.7%)

simplify180.0ms (5.9%)

prune119.0ms (3.9%)

localize8.0ms (0.3%)

series37.0ms (1.2%)

rewrite59.0ms (1.9%)

simplify73.0ms (2.4%)

prune130.0ms (4.3%)

regimes195.0ms (6.4%)

simplify2.0ms (0.1%)

end97.0ms (3.2%)

Profiling