Details

analyze359.0ms (15.5%)

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%	62.4%	6.4%	9
46.8%	46.8%	6.4%	10
53.8%	39.8%	6.4%	11
57.3%	33.2%	9.5%	12
66.9%	23.6%	9.5%	13
70.3%	20.2%	9.5%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample912.0ms (39.4%)

Symmetry

(sort x y)

Results

827.0ms	8256×	body	128	valid
27.0ms	287×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify16.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

192×	`fma-def_binary64`
125×	`fma-neg_binary64`
44×	`distribute-rgt-neg-in_binary64`
37×	`cancel-sign-sub-inv_binary64`
27×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	15	10
2	29	10
3	42	10
4	76	10
5	133	10
6	246	10
7	423	10
8	577	10
9	696	10
10	746	10
11	748	10

Stop Event

1×

saturated

Counts

1 → 2

prune5.0ms (0.2%)

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
▶	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
	0.1b	(neg.f64 (fma.f64 x (*.f64 y -3) z))

Compiler

Compiled 57 to 39 computations (31.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 x 3) y) z)
✓	0.3b	(.f64 (.f64 x 3) y)

series10.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

6.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
4.0ms	(.f64 (.f64 x 3) y)

rewrite53.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

832×	`expm1-log1p-u_binary64`
768×	`prod-diff_binary64`
130×	`egg-rr`
87×	`add-sqr-sqrt_binary64`
83×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	172	17
2	2226	17

Stop Event

1×	node limit

Counts

2 → 130

Calls

2 calls:

51.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
51.0ms	(.f64 (.f64 x 3) y)

simplify38.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

192×	`fma-def_binary64`
125×	`fma-neg_binary64`
44×	`distribute-rgt-neg-in_binary64`
37×	`cancel-sign-sub-inv_binary64`
27×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	485
1	18	485
2	30	485
3	43	485
4	76	485
5	133	485
6	246	485
7	422	485
8	576	485
9	695	485
10	745	485
11	747	485

Stop Event

1×

saturated

Counts

190 → 136

prune74.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	134	4	138

Error

0.0b

Counts

138 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
	16.2b	(+.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 x 3)) (neg.f64 z)) (fma.f64 -1 z z))
▶	0.1b	(fma.f64 3 (*.f64 y x) (neg.f64 z))
	0.1b	(neg.f64 (fma.f64 x (*.f64 y -3) z))

Compiler

Compiled 2338 to 1231 computations (47.3% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

6.0ms

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

rewrite45.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

617×	`log1p-expm1-u_binary64`
617×	`expm1-log1p-u_binary64`
328×	`log-prod_binary64`
133×	`prod-diff_binary64`
130×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	162	8
2	1928	8

Stop Event

1×	node limit

Counts

1 → 78

Calls

1 calls:

43.0ms

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

simplify32.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

192×	`fma-def_binary64`
125×	`fma-neg_binary64`
44×	`distribute-rgt-neg-in_binary64`
37×	`cancel-sign-sub-inv_binary64`
27×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	317
1	18	317
2	30	317
3	43	317
4	76	317
5	133	317
6	246	317
7	422	317
8	576	317
9	695	317
10	745	317
11	747	317

Stop Event

1×

saturated

Counts

114 → 84

prune51.0ms (2.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	84	4	88

Error

0.0b

Counts

88 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
	16.2b	(+.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 x 3)) (neg.f64 z)) (fma.f64 -1 z z))
✓	0.1b	(fma.f64 3 (*.f64 y x) (neg.f64 z))
▶	0.1b	(neg.f64 (fma.f64 x (*.f64 y -3) z))

Compiler

Compiled 1923 to 1040 computations (45.9% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

6.0ms

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

rewrite36.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

589×	`log1p-expm1-u_binary64`
589×	`expm1-log1p-u_binary64`
312×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	139	8
2	1594	8

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

35.0ms

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

simplify27.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

285×	`fma-def_binary64`
110×	`fma-neg_binary64`
57×	`cancel-sign-sub-inv_binary64`
36×	`distribute-rgt-neg-in_binary64`
27×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	309
1	21	309
2	49	255
3	107	255
4	150	255
5	198	255
6	292	255
7	371	255
8	469	255
9	665	255
10	829	255
11	841	255

Stop Event

1×

saturated

Counts

65 → 34

prune23.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	34	4	38

Error

0.0b

Counts

38 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
▶	16.2b	(+.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 x 3)) (neg.f64 z)) (fma.f64 -1 z z))
✓	0.1b	(fma.f64 3 (*.f64 y x) (neg.f64 z))
✓	0.1b	(neg.f64 (fma.f64 x (*.f64 y -3) z))

Compiler

Compiled 479 to 309 computations (35.5% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 x 3)) (neg.f64 z))
✓	0.3b	(.f64 (sqrt.f64 y) (.f64 x 3))

series33.0ms (1.4%)

Counts

2 → 37

Calls

2 calls:

23.0ms	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 x 3)) (neg.f64 z))
10.0ms	(.f64 (sqrt.f64 y) (.f64 x 3))

rewrite69.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

797×	`log1p-expm1-u_binary64`
797×	`expm1-log1p-u_binary64`
196×	`egg-rr`
172×	`prod-diff_binary64`
101×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	204	19
2	2454	19

Stop Event

1×	node limit

Counts

2 → 196

Calls

2 calls:

63.0ms	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 x 3)) (neg.f64 z))
63.0ms	(.f64 (sqrt.f64 y) (.f64 x 3))

simplify46.0ms (2%)

Algorithm

1×	egg-herbie

Rules

432×	`fma-def_binary64`
139×	`fma-neg_binary64`
63×	`associate-l_binary64`
61×	`associate-r_binary64`
53×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	321
1	25	321
2	42	321
3	57	321
4	90	321
5	147	321
6	260	321
7	437	321
8	655	321
9	969	321
10	1331	321
11	1337	321
12	1341	321
13	1357	321
14	1371	321

Stop Event

1×

saturated

Counts

233 → 204

prune115.0ms (5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	203	5	208

Error

Counts

208 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
✓	16.2b	(+.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 x 3)) (neg.f64 z)) (fma.f64 -1 z z))
✓	0.1b	(fma.f64 3 (*.f64 y x) (neg.f64 z))
✓	0.1b	(neg.f64 (fma.f64 x (*.f64 y -3) z))
	16.4b	(+.f64 (fma.f64 (sqrt.f64 y) (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 y) (.f64 x 3))) 3) (neg.f64 z)) (fma.f64 -1 z z))

Compiler

Compiled 5890 to 3100 computations (47.4% saved)

regimes120.0ms (5.2%)

Accuracy

Total 0.1b remaining (93.2%)

Threshold costs 0.1b (93.2%)

Counts

20 → 1

Compiler

Compiled 1458 to 1032 computations (29.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	12	10
2	17	10
3	19	10
4	20	10

Stop Event

1×

saturated

end211.0ms (9.1%)

Compiler: Compiled 111 to 76 computations (31.5% saved)

Iter	Nodes	Cost
0	8	10
1	15	10
2	29	10
3	42	10
4	76	10
5	133	10
6	246	10
7	423	10
8	577	10
9	696	10
10	746	10
11	748	10

Iter	Nodes	Cost
0	10	485
1	18	485
2	30	485
3	43	485
4	76	485
5	133	485
6	246	485
7	422	485
8	576	485
9	695	485
10	745	485
11	747	485

Iter	Nodes	Cost
0	10	317
1	18	317
2	30	317
3	43	317
4	76	317
5	133	317
6	246	317
7	422	317
8	576	317
9	695	317
10	745	317
11	747	317

Iter	Nodes	Cost
0	10	309
1	21	309
2	49	255
3	107	255
4	150	255
5	198	255
6	292	255
7	371	255
8	469	255
9	665	255
10	829	255
11	841	255

Iter	Nodes	Cost
0	8	10
1	15	10
2	29	10
3	42	10
4	76	10
5	133	10
6	246	10
7	423	10
8	577	10
9	696	10
10	746	10
11	748	10

Iter	Nodes	Cost
0	10	485
1	18	485
2	30	485
3	43	485
4	76	485
5	133	485
6	246	485
7	422	485
8	576	485
9	695	485
10	745	485
11	747	485

Iter	Nodes	Cost
0	10	317
1	18	317
2	30	317
3	43	317
4	76	317
5	133	317
6	246	317
7	422	317
8	576	317
9	695	317
10	745	317
11	747	317

Iter	Nodes	Cost
0	10	309
1	21	309
2	49	255
3	107	255
4	150	255
5	198	255
6	292	255
7	371	255
8	469	255
9	665	255
10	829	255
11	841	255

Details

analyze359.0ms (15.5%)

sample912.0ms (39.4%)

simplify16.0ms (0.7%)

prune5.0ms (0.2%)

localize4.0ms (0.2%)

series10.0ms (0.4%)

rewrite53.0ms (2.3%)

simplify38.0ms (1.6%)

prune74.0ms (3.2%)

localize6.0ms (0.2%)

series7.0ms (0.3%)

rewrite45.0ms (2%)

simplify32.0ms (1.4%)

prune51.0ms (2.2%)

localize7.0ms (0.3%)

series6.0ms (0.3%)

rewrite36.0ms (1.5%)

simplify27.0ms (1.2%)

prune23.0ms (1%)

localize10.0ms (0.4%)

series33.0ms (1.4%)

rewrite69.0ms (3%)

simplify46.0ms (2%)

prune115.0ms (5%)

regimes120.0ms (5.2%)

simplify3.0ms (0.1%)

end211.0ms (9.1%)

Profiling

Iter	Nodes	Cost
0	8	10
1	15	10
2	29	10
3	42	10
4	76	10
5	133	10
6	246	10
7	423	10
8	577	10
9	696	10
10	746	10
11	748	10

Iter	Nodes	Cost
0	10	485
1	18	485
2	30	485
3	43	485
4	76	485
5	133	485
6	246	485
7	422	485
8	576	485
9	695	485
10	745	485
11	747	485

Iter	Nodes	Cost
0	10	317
1	18	317
2	30	317
3	43	317
4	76	317
5	133	317
6	246	317
7	422	317
8	576	317
9	695	317
10	745	317
11	747	317

Iter	Nodes	Cost
0	10	309
1	21	309
2	49	255
3	107	255
4	150	255
5	198	255
6	292	255
7	371	255
8	469	255
9	665	255
10	829	255
11	841	255