Details

analyze4.0ms (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)

sample798.0ms (20.5%)

Results

785.0ms	8256×	body	128	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 16 to 10 computations (37.5% saved)

preprocess62.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

1835×	`fma-neg_binary64`
684×	`fma-def_binary64`
317×	`unsub-neg_binary64`
293×	`distribute-rgt-in_binary64`
245×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	7	10
2	12	10
3	19	10
4	28	10
5	45	10
6	83	10
7	124	10
8	201	10
9	395	10
10	833	10
11	2189	10
12	4247	10
13	4737	10
14	4911	10
15	4966	10
16	4976	10
17	4976	10
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify56.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1835×	`fma-neg_binary64`
684×	`fma-def_binary64`
317×	`unsub-neg_binary64`
293×	`distribute-rgt-in_binary64`
245×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	7	10
2	12	10
3	19	10
4	28	10
5	45	10
6	83	10
7	124	10
8	201	10
9	395	10
10	833	10
11	2189	10
12	4247	10
13	4737	10
14	4911	10
15	4966	10
16	4976	10
17	4976	10

Stop Event

1×	node limit

Counts

1 → 1

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
✓	0.0b	(log.f64 (log.f64 x))
✓	0.3b	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))

series543.0ms (14%)

Counts

2 → 16

Calls

6 calls:

104.0ms	(log.f64 (log.f64 x))	x	-inf
104.0ms	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))	x	-inf
90.0ms	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))	x	inf
89.0ms	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))	x	0
83.0ms	(log.f64 (log.f64 x))	x	inf

rewrite43.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

560×	`log1p-expm1-u_binary64`
560×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
167×	`fma-def_binary64`
110×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	107	13
2	1463	13

Stop Event

1×	node limit

Counts

2 → 110

simplify55.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1648×	`fma-def_binary64`
625×	`fma-neg_binary64`
583×	`distribute-rgt-in_binary64`
397×	`distribute-lft-in_binary64`
316×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	216
1	41	136
2	87	120
3	256	120
4	688	120
5	1585	120
6	2866	120
7	3700	120
8	3915	120
9	4529	120
10	4807	120
11	4914	120

Stop Event

1×	node limit

Counts

126 → 116

prune79.0ms (2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	2	117

Error

Counts

117 → 2

Alt Table

Status	Error	Program
	0.3b	(*.f64 -1 (+.f64 (log.f64 (/.f64 1 x)) (log.f64 (neg.f64 (log.f64 (/.f64 1 x))))))
▶	0.0b	(neg.f64 (log.f64 (/.f64 (log.f64 x) x)))

Compiler

Compiled 1745 to 576 computations (67% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 (log.f64 x) x))
✓	0.2b	(/.f64 (log.f64 x) x)

series247.0ms (6.4%)

Counts

2 → 20

Calls

6 calls:

85.0ms	(log.f64 (/.f64 (log.f64 x) x))	x	-inf
69.0ms	(log.f64 (/.f64 (log.f64 x) x))	x	inf
65.0ms	(log.f64 (/.f64 (log.f64 x) x))	x	0
13.0ms	(/.f64 (log.f64 x) x)	x	inf
10.0ms	(/.f64 (log.f64 x) x)	x	-inf

rewrite43.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

473×	`log1p-expm1-u_binary64`
473×	`expm1-log1p-u_binary64`
338×	`unpow-prod-down_binary64`
257×	`log-prod_binary64`
135×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
1	100	14
2	1288	14

Stop Event

1×	node limit

Counts

2 → 135

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

942×	`fma-neg_binary64`
374×	`fma-def_binary64`
293×	`unsub-neg_binary64`
236×	`div-sub_binary64`
235×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	200
1	45	168
2	97	168
3	265	168
4	637	168
5	1531	168
6	2772	168
7	4249	168
8	4886	168

Stop Event

1×	node limit

Counts

155 → 140

prune72.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	140	2	142

Error

Counts

142 → 2

Alt Table

Status	Error	Program
▶	0.2b	(neg.f64 (-.f64 (log.f64 (/.f64 (log.f64 x) (sqrt.f64 x))) (log.f64 (sqrt.f64 x))))
✓	0.0b	(neg.f64 (log.f64 (/.f64 (log.f64 x) x)))

Compiler

Compiled 1908 to 892 computations (53.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (sqrt.f64 x))
✓	0.0b	(log.f64 (/.f64 (log.f64 x) (sqrt.f64 x)))
✓	0.2b	(-.f64 (log.f64 (/.f64 (log.f64 x) (sqrt.f64 x))) (log.f64 (sqrt.f64 x)))
✓	0.4b	(/.f64 (log.f64 x) (sqrt.f64 x))

series1.4s (36.3%)

Counts

4 → 0

Calls

12 calls:

725.0ms	(-.f64 (log.f64 (/.f64 (log.f64 x) (sqrt.f64 x))) (log.f64 (sqrt.f64 x)))	x	inf
634.0ms	(-.f64 (log.f64 (/.f64 (log.f64 x) (sqrt.f64 x))) (log.f64 (sqrt.f64 x)))	x	0
13.0ms	(-.f64 (log.f64 (/.f64 (log.f64 x) (sqrt.f64 x))) (log.f64 (sqrt.f64 x)))	x	-inf
11.0ms	(/.f64 (log.f64 x) (sqrt.f64 x))	x	-inf
9.0ms	(log.f64 (/.f64 (log.f64 x) (sqrt.f64 x)))	x	-inf

rewrite70.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

879×	`log1p-expm1-u_binary64`
879×	`expm1-log1p-u_binary64`
506×	`prod-diff_binary64`
168×	`egg-rr`
84×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	38
1	171	31
2	2344	31

Stop Event

1×	node limit

Counts

4 → 168

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

168 → 168

prune76.0ms (2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	168	2	170

Error

Counts

170 → 2

Alt Table

Status	Error	Program
✓	0.2b	(neg.f64 (-.f64 (log.f64 (/.f64 (log.f64 x) (sqrt.f64 x))) (log.f64 (sqrt.f64 x))))
✓	0.0b	(neg.f64 (log.f64 (/.f64 (log.f64 x) x)))

Compiler

Compiled 3388 to 1175 computations (65.3% saved)

regimes214.0ms (5.5%)

Accuracy

Total 0.0b remaining (76.1%)

Threshold costs 0.0b (76.1%)

Counts

71 → 1

Compiler

Compiled 2581 to 1775 computations (31.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	19	13
2	26	13
3	29	13
4	30	13

Stop Event

1×

saturated

end43.0ms (1.1%)

Stop Event

1×

done

Compiler

Compiled 37 to 27 computations (27% saved)

Details

analyze4.0ms (0.1%)

sample798.0ms (20.5%)

preprocess62.0ms (1.6%)

simplify56.0ms (1.4%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series543.0ms (14%)

rewrite43.0ms (1.1%)

simplify55.0ms (1.4%)

prune79.0ms (2%)

localize5.0ms (0.1%)

series247.0ms (6.4%)

rewrite43.0ms (1.1%)

simplify41.0ms (1.1%)

prune72.0ms (1.9%)

localize9.0ms (0.2%)

series1.4s (36.3%)

rewrite70.0ms (1.8%)

simplify8.0ms (0.2%)

prune76.0ms (2%)

regimes214.0ms (5.5%)

simplify2.0ms (0.1%)

end43.0ms (1.1%)

Profiling