Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	50%	50%	2
25%	25%	50%	3
25%	12.5%	62.5%	4
25%	6.2%	68.8%	5
25%	3.1%	71.9%	6
25%	1.6%	73.5%	7
25%	0.8%	74.2%	8
25%	0.4%	74.6%	9
25%	0.2%	74.8%	10
25%	0.1%	74.9%	11
25%	0%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample1.0s (25.7%)

Results

850.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 23 to 14 computations (39.1% saved)

simplify158.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1887×	`fma-neg_binary64`
921×	`unsub-neg_binary64`
788×	`associate-+l+_binary64`
692×	`fma-def_binary64`
383×	`associate-+r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	7	10
2	12	10
3	19	10
4	26	10
5	43	10
6	69	10
7	94	10
8	140	10
9	261	10
10	495	10
11	1237	10
12	2158	10
13	2012	10
14	2131	10
15	2179	10
16	2189	10
17	2189	10
18	3301	10
19	3309	10
20	3361	10
21	3361	10
22	3885	10
23	4995	10
24	4994	10

prune1.0ms (0%)

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 (log.f64 x) (log.f64 (log.f64 x)))

Compiler

Compiled 21 to 12 computations (42.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(log.f64 (log.f64 x))
✓	0.3b	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))

series560.0ms (14%)

Counts

2 → 16

Calls

2 calls:

294.0ms	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
266.0ms	(log.f64 (log.f64 x))

rewrite55.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

560×	`log1p-expm1-u_binary64`
560×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
260×	`log-prod_binary64`
167×	`fma-def_binary64`

Counts

2 → 124

Calls

2 calls:

53.0ms	(log.f64 (log.f64 x))
53.0ms	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	105	13
2	1378	13
3	5175	13
0	0	0
1	0	0

simplify157.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1676×	`fma-def_binary64`
1385×	`associate--r-_binary64`
669×	`distribute-rgt-in_binary64`
625×	`fma-neg_binary64`
487×	`distribute-lft-in_binary64`

Counts

140 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	216
1	41	136
2	81	120
3	182	120
4	391	120
5	866	120
6	1405	120
7	1676	120
8	1791	120
9	1951	120
10	2100	120
11	2170	120
12	3345	120
13	3349	120
14	3349	120
15	3677	120
16	3689	120
17	3667	120
18	3733	120
19	3777	120
20	5120	120

prune58.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	2	130

Error

Counts

130 → 2

Alt Table

Status	Error	Program
	0.0b	(log.f64 (*.f64 (exp.f64 (neg.f64 (log.f64 (log.f64 x)))) x))
▶	0.0b	(neg.f64 (log.f64 (/.f64 (log.f64 x) x)))

Compiler

Compiled 1918 to 627 computations (67.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 (log.f64 x) x))
✓	0.3b	(/.f64 (log.f64 x) x)

series239.0ms (6%)

Counts

2 → 20

Calls

2 calls:

211.0ms	(log.f64 (/.f64 (log.f64 x) x))
28.0ms	(/.f64 (log.f64 x) x)

rewrite54.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

473×	`log1p-expm1-u_binary64`
473×	`expm1-log1p-u_binary64`
333×	`unpow-prod-down_binary64`
257×	`log-prod_binary64`
153×	`egg-rr`

Counts

2 → 153

Calls

2 calls:

50.0ms	(log.f64 (/.f64 (log.f64 x) x))
50.0ms	(/.f64 (log.f64 x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
1	98	14
2	1237	14
3	5010	14
0	0	0
1	0	0

simplify155.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1047×	`div-sub_binary64`
942×	`fma-neg_binary64`
590×	`sub-neg_binary64`
394×	`associate-/l*_binary64`
382×	`fma-def_binary64`

Counts

173 → 157

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	200
1	45	168
2	87	168
3	224	168
4	487	168
5	799	168
6	1301	168
7	2214	168
8	2382	168
9	2698	168
10	2835	168
11	3081	168
12	3169	168
13	3477	168
14	3669	168
15	4173	168
16	4957	168
17	4727	168

prune68.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	157	2	159

Error

Counts

159 → 2

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (*.f64 (exp.f64 (neg.f64 (log.f64 (log.f64 x)))) x))
✓	0.0b	(neg.f64 (log.f64 (/.f64 (log.f64 x) x)))

Compiler

Compiled 2263 to 1004 computations (55.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (*.f64 (exp.f64 (neg.f64 (log.f64 (log.f64 x)))) x))
	0.1b	(log.f64 (log.f64 x))
✓	0.2b	(*.f64 (exp.f64 (neg.f64 (log.f64 (log.f64 x)))) x)
✓	1.1b	(exp.f64 (neg.f64 (log.f64 (log.f64 x))))

series1.1s (27.2%)

Counts

3 → 28

Calls

3 calls:

536.0ms	(log.f64 (*.f64 (exp.f64 (neg.f64 (log.f64 (log.f64 x)))) x))
286.0ms	(*.f64 (exp.f64 (neg.f64 (log.f64 (log.f64 x)))) x)
268.0ms	(exp.f64 (neg.f64 (log.f64 (log.f64 x))))

rewrite52.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

493×	`log1p-expm1-u_binary64`
493×	`expm1-log1p-u_binary64`
369×	`unpow-prod-down_binary64`
286×	`log-prod_binary64`
144×	`pow2_binary64`

Counts

3 → 129

Calls

3 calls:

45.0ms	(log.f64 (*.f64 (exp.f64 (neg.f64 (log.f64 (log.f64 x)))) x))
45.0ms	(*.f64 (exp.f64 (neg.f64 (log.f64 (log.f64 x)))) x)
45.0ms	(exp.f64 (neg.f64 (log.f64 (log.f64 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	148	17
2	1354	17
3	4980	17
0	0	0
1	0	0

simplify172.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

767×	`log-prod_binary64`
715×	`fma-def_binary64`
555×	`fma-neg_binary64`
544×	`exp-sum_binary64`
427×	`sub-neg_binary64`

Counts

157 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	352
1	61	240
2	109	216
3	227	216
4	562	216
5	1426	216
6	3675	216
7	3181	216
8	3736	216
9	4216	216
10	4557	216
11	4927	216
12	4968	216
13	4992	216
14	4852	216

prune55.0ms (1.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	162	2	164

Error

Counts

164 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (*.f64 (exp.f64 (neg.f64 (log.f64 (log.f64 x)))) x))
✓	0.0b	(neg.f64 (log.f64 (/.f64 (log.f64 x) x)))

Compiler

Compiled 1758 to 795 computations (54.8% saved)

regimes43.0ms (1.1%)

Accuracy

Total 0.0b remaining (40.7%)

Threshold costs 0.0b (40.7%)

Counts

12 → 1

Compiler

Compiled 406 to 271 computations (33.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	10	10
2	12	10
3	13	10
4	13	10

end37.0ms (0.9%)

Compiler: Compiled 30 to 22 computations (26.7% saved)

Details

analyze3.0ms (0.1%)

sample1.0s (25.7%)

simplify158.0ms (4%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series560.0ms (14%)

rewrite55.0ms (1.4%)

simplify157.0ms (3.9%)

prune58.0ms (1.4%)

localize6.0ms (0.2%)

series239.0ms (6%)

rewrite54.0ms (1.3%)

simplify155.0ms (3.9%)

prune68.0ms (1.7%)

localize9.0ms (0.2%)

series1.1s (27.2%)

rewrite52.0ms (1.3%)

simplify172.0ms (4.3%)

prune55.0ms (1.4%)

regimes43.0ms (1.1%)

simplify2.0ms (0%)

end37.0ms (0.9%)

Profiling