Details

analyze492.0ms (15.8%)

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
18.7%	81.1%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
45.2%	53.8%	0.9%	9
50.3%	47.8%	1.9%	10
54%	43.6%	2.4%	11
61.7%	32.9%	5.4%	12
64.1%	28.3%	7.6%	13
66.2%	24.7%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (37%)

Results

960.0ms	8256×	body	128	valid
144.0ms	1272×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify45.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1128×	`fma-def_binary64`
1073×	`fma-neg_binary64`
226×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
162×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	46	18
3	78	18
4	141	16
5	274	16
6	443	16
7	744	16
8	1785	13
9	3544	13
10	4642	13
11	4838	13
12	4935	13
13	4935	13

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.3b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))
▶	0.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	3.1b	(*.f64 (/.f64 x y) z)

series54.0ms (1.7%)

Counts

3 → 96

Calls

3 calls:

36.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
12.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 (+.f64 x 4) y)

rewrite70.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

334×	`fma-def_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
202×	`fma-neg_binary64`
184×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	236	27
2	3526	27

Stop Event

1×	node limit

Counts

3 → 176

Calls

3 calls:

66.0ms	(/.f64 (+.f64 x 4) y)
66.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
66.0ms	(*.f64 (/.f64 x y) z)

simplify78.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-neg_binary64`
323×	`fma-def_binary64`
185×	`distribute-rgt-in_binary64`
176×	`cancel-sign-sub-inv_binary64`
160×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	1102
1	78	1102
2	186	952
3	442	860
4	951	790
5	2039	790
6	3042	790
7	3589	790
8	3601	790
9	3601	790

Stop Event

1×

saturated

Counts

272 → 194

prune114.0ms (3.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	191	3	194
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	192	4	196

Error

0.0b

Counts

196 → 4

Alt Table

Status	Error	Program
	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	4.3b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))
	39.9b	(fabs.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)) 2))
▶	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x))))

Compiler

Compiled 4092 to 1986 computations (51.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x)))
✓	3.2b	(/.f64 z (/.f64 y x))

series31.0ms (1%)

Counts

2 → 72

Calls

2 calls:

19.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x)))
12.0ms	(/.f64 z (/.f64 y x))

rewrite60.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`fma-neg_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
127×	`add-sqr-sqrt_binary64`
124×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	245	23
2	4002	23

Stop Event

1×	node limit

Counts

2 → 108

Calls

2 calls:

57.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x)))
57.0ms	(/.f64 z (/.f64 y x))

simplify65.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-neg_binary64`
323×	`fma-def_binary64`
185×	`distribute-rgt-in_binary64`
178×	`cancel-sign-sub-inv_binary64`
160×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	880
1	78	880
2	186	730
3	442	638
4	952	631
5	2050	631
6	3051	631
7	3597	631
8	3609	631
9	3609	631

Stop Event

1×

saturated

Counts

180 → 122

prune95.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	156	5	161

Error

Counts

161 → 5

Alt Table

Status	Error	Program
▶	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	27.4b	(fabs.f64 (/.f64 (-.f64 (.f64 (/.f64 y x) (+.f64 x 4)) (.f64 z y)) (*.f64 y (/.f64 y x))))
	4.3b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))
	39.9b	(fabs.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)) 2))
✓	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x))))

Compiler

Compiled 3052 to 1525 computations (50% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z)))
✓	5.2b	(/.f64 x (/.f64 y z))

series32.0ms (1%)

Counts

2 → 72

Calls

2 calls:

19.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z)))
12.0ms	(/.f64 x (/.f64 y z))

rewrite60.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`fma-neg_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
127×	`add-sqr-sqrt_binary64`
124×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	245	23
2	4001	23

Stop Event

1×	node limit

Counts

2 → 108

Calls

2 calls:

58.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z)))
58.0ms	(/.f64 x (/.f64 y z))

simplify63.0ms (2%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-neg_binary64`
323×	`fma-def_binary64`
185×	`distribute-rgt-in_binary64`
178×	`cancel-sign-sub-inv_binary64`
160×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	880
1	78	880
2	186	730
3	442	638
4	952	631
5	2050	631
6	3051	631
7	3597	631
8	3609	631
9	3609	631

Stop Event

1×

saturated

Counts

180 → 122

prune95.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	157	5	162

Error

Counts

162 → 5

Alt Table

Status	Error	Program
✓	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	27.4b	(fabs.f64 (/.f64 (-.f64 (.f64 (/.f64 y x) (+.f64 x 4)) (.f64 z y)) (*.f64 y (/.f64 y x))))
▶	4.3b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))
	39.9b	(fabs.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)) 2))
✓	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x))))

Compiler

Compiled 3037 to 1516 computations (50.1% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.1b	(/.f64 (-.f64 (fma.f64 x z -4) x) y)

series15.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

15.0ms

(/.f64 (-.f64 (fma.f64 x z -4) x) y)

rewrite76.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

541×	`prod-diff_binary64`
232×	`fma-def_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
169×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	180	11
2	2573	11

Stop Event

1×	node limit

Counts

1 → 169

Calls

1 calls:

69.0ms

(/.f64 (-.f64 (fma.f64 x z -4) x) y)

simplify54.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-neg_binary64`
321×	`fma-def_binary64`
203×	`cancel-sign-sub-inv_binary64`
178×	`unsub-neg_binary64`
166×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	617
1	85	617
2	203	375
3	451	375
4	1032	375
5	2193	375
6	3268	375
7	3474	375
8	3480	375
9	3480	375

Stop Event

1×

saturated

Counts

205 → 182

prune168.0ms (5.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	182	5	187

Error

Counts

187 → 5

Alt Table

Status	Error	Program
✓	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	27.4b	(fabs.f64 (/.f64 (-.f64 (.f64 (/.f64 y x) (+.f64 x 4)) (.f64 z y)) (*.f64 y (/.f64 y x))))
✓	4.3b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))
	39.9b	(fabs.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)) 2))
✓	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x))))

Compiler

Compiled 7161 to 3370 computations (52.9% saved)

regimes183.0ms (5.9%)

Accuracy

Total 1.6b remaining (99%)

Threshold costs 0b (0%)

Counts

29 → 1

Compiler

Compiled 1972 to 1341 computations (32% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	20	18
2	36	18
3	49	18
4	63	18
5	69	18
6	70	18

Stop Event

1×

saturated

end81.0ms (2.6%)

Compiler: Compiled 109 to 72 computations (33.9% saved)

Details

analyze492.0ms (15.8%)

sample1.2s (37%)

simplify45.0ms (1.5%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series54.0ms (1.7%)

rewrite70.0ms (2.2%)

simplify78.0ms (2.5%)

prune114.0ms (3.6%)

localize8.0ms (0.2%)

series31.0ms (1%)

rewrite60.0ms (1.9%)

simplify65.0ms (2.1%)

prune95.0ms (3%)

localize7.0ms (0.2%)

series32.0ms (1%)

rewrite60.0ms (1.9%)

simplify63.0ms (2%)

prune95.0ms (3.1%)

localize7.0ms (0.2%)

series15.0ms (0.5%)

rewrite76.0ms (2.4%)

simplify54.0ms (1.7%)

prune168.0ms (5.4%)

regimes183.0ms (5.9%)

simplify3.0ms (0.1%)

end81.0ms (2.6%)

Profiling