Details

analyze70.0ms (2.7%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample995.0ms (38.2%)

Results

915.0ms	8256×	body	128	valid
28.0ms	254×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify39.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

892×	`fma-def_binary64`
453×	`fma-neg_binary64`
318×	`cancel-sign-sub-inv_binary64`
251×	`distribute-rgt-neg-in_binary64`
168×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	28	18
2	69	18
3	194	16
4	402	16
5	586	16
6	1164	16
7	2527	16
8	4281	16
9	4905	16

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.5b	(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.2b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(*.f64 3 (sqrt.f64 x))

series35.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

24.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
1.0ms	(/.f64 1 (*.f64 x 9))

rewrite59.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`prod-diff_binary64`
226×	`log1p-udef_binary64`
134×	`add-sqr-sqrt_binary64`
130×	`add-cbrt-cube_binary64`
130×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	283	35
2	3707	35

Stop Event

1×	node limit

Counts

4 → 102

Calls

4 calls:

58.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
58.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
58.0ms	(/.f64 1 (*.f64 x 9))
58.0ms	(*.f64 3 (sqrt.f64 x))

simplify65.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

985×	`fma-def_binary64`
636×	`fma-neg_binary64`
234×	`distribute-rgt-in_binary64`
221×	`distribute-rgt-neg-in_binary64`
202×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	453
1	57	408
2	117	387
3	222	387
4	441	387
5	785	387
6	1535	387
7	2724	387
8	3683	387
9	4025	387
10	4790	387
11	4790	387

Stop Event

1×	node limit

Counts

150 → 113

prune102.0ms (3.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	103	10	113
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	104	11	115

Error

Counts

115 → 11

Alt Table

Status	Error	Program
	25.9b	(pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 2)
	1.4b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 3)
	0.6b	(pow.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 1)
	28.4b	(/.f64 (*.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1/9 x) y) 2) -1) (sqrt.f64 (/.f64 x 1/9))) (+.f64 1 (+.f64 (/.f64 1/9 x) y)))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (pow.f64 (sqrt.f64 (/.f64 1/9 x)) 2)) 1))
	0.6b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
✓	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	2.2b	(.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 x 1/9)))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
▶	0.3b	(.f64 (sqrt.f64 (/.f64 x 1/9)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.6b	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 x 1/9))) 2) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	34.6b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3))

Compiler

Compiled 2332 to 1737 computations (25.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 x 1/9))
✓	0.2b	(.f64 (sqrt.f64 (/.f64 x 1/9)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.2b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(/.f64 x 1/9)

series26.0ms (1%)

Counts

3 → 24

Calls

3 calls:

20.0ms	(.f64 (sqrt.f64 (/.f64 x 1/9)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
4.0ms	(sqrt.f64 (/.f64 x 1/9))
1.0ms	(/.f64 x 1/9)

rewrite55.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

639×	`prod-diff_binary64`
218×	`log1p-udef_binary64`
127×	`add-sqr-sqrt_binary64`
126×	`add-cbrt-cube_binary64`
126×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	295	28
2	3638	28

Stop Event

1×	node limit

Counts

3 → 93

Calls

3 calls:

54.0ms	(sqrt.f64 (/.f64 x 1/9))
54.0ms	(.f64 (sqrt.f64 (/.f64 x 1/9)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
54.0ms	(/.f64 x 1/9)

simplify48.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

949×	`fma-neg_binary64`
618×	`fma-def_binary64`
221×	`distribute-rgt-neg-in_binary64`
192×	`associate-/l*_binary64`
188×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	315
1	58	270
2	116	249
3	221	249
4	439	249
5	778	249
6	1523	249
7	2714	249
8	3669	249
9	4422	249

Stop Event

1×	node limit

Counts

117 → 100

prune126.0ms (4.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	3	6	9
Picked	0	1	1
Done	1	0	1
Total	127	10	137

Error

Counts

137 → 10

Alt Table

Status	Error	Program
	1.4b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 3)
	0.4b	(.f64 (sqrt.f64 (pow.f64 (/.f64 1/9 x) -1)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	25.9b	(pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 2)
	0.6b	(pow.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 1)
	28.4b	(/.f64 (*.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1/9 x) y) 2) -1) (sqrt.f64 (/.f64 x 1/9))) (+.f64 1 (+.f64 (/.f64 1/9 x) y)))
▶	0.3b	(.f64 (sqrt.f64 (.f64 9 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.4b	(*.f64 (sqrt.f64 (/.f64 x 1/9)) (-.f64 (+.f64 y (pow.f64 (sqrt.f64 (/.f64 1/9 x)) 2)) 1))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 x 1/9)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	34.6b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3))

Compiler

Compiled 2494 to 1921 computations (23% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.1b	(sqrt.f64 (*.f64 9 x))
✓	0.2b	(.f64 (sqrt.f64 (.f64 9 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.2b	(/.f64 1 (*.f64 x 9))

series25.0ms (1%)

Counts

2 → 12

Calls

2 calls:

21.0ms	(.f64 (sqrt.f64 (.f64 9 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
4.0ms	(sqrt.f64 (*.f64 9 x))

rewrite45.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`prod-diff_binary64`
201×	`log1p-udef_binary64`
200×	`expm1-udef_binary64`
117×	`add-sqr-sqrt_binary64`
114×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	265	24
2	3280	24

Stop Event

1×	node limit

Counts

2 → 50

Calls

2 calls:

44.0ms	(sqrt.f64 (*.f64 9 x))
44.0ms	(.f64 (sqrt.f64 (.f64 9 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))

simplify45.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary64`
618×	`fma-def_binary64`
230×	`distribute-rgt-in_binary64`
221×	`distribute-rgt-neg-in_binary64`
201×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	267
1	55	222
2	113	201
3	218	201
4	436	201
5	779	201
6	1524	201
7	2722	201
8	3671	201
9	4312	201

Stop Event

1×	node limit

Counts

62 → 57

prune107.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	126	9	135

Error

Counts

135 → 9

Alt Table

Status	Error	Program
	1.4b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 3)
	0.4b	(.f64 (sqrt.f64 (pow.f64 (/.f64 1/9 x) -1)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	25.9b	(pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 2)
	0.6b	(pow.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 1)
	28.4b	(/.f64 (*.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1/9 x) y) 2) -1) (sqrt.f64 (/.f64 x 1/9))) (+.f64 1 (+.f64 (/.f64 1/9 x) y)))
	0.6b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
▶	0.3b	(.f64 (sqrt.f64 (.f64 9 x)) (-.f64 (+.f64 y (pow.f64 (sqrt.f64 (/.f64 1/9 x)) 2)) 1))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 x 1/9)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	34.6b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3))

Compiler

Compiled 2480 to 1932 computations (22.1% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1/9 x))
✓	0.2b	(.f64 (sqrt.f64 (.f64 9 x)) (-.f64 (+.f64 y (pow.f64 (sqrt.f64 (/.f64 1/9 x)) 2)) 1))
✓	0.4b	(/.f64 1/9 x)
✓	0.5b	(pow.f64 (sqrt.f64 (/.f64 1/9 x)) 2)

series35.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 (.f64 9 x)) (-.f64 (+.f64 y (pow.f64 (sqrt.f64 (/.f64 1/9 x)) 2)) 1))
8.0ms	(pow.f64 (sqrt.f64 (/.f64 1/9 x)) 2)
6.0ms	(sqrt.f64 (/.f64 1/9 x))
1.0ms	(/.f64 1/9 x)

rewrite57.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

770×	`prod-diff_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
140×	`add-sqr-sqrt_binary64`
138×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	331	32
2	3886	32

Stop Event

1×	node limit

Counts

4 → 112

Calls

4 calls:

56.0ms	(sqrt.f64 (/.f64 1/9 x))
56.0ms	(.f64 (sqrt.f64 (.f64 9 x)) (-.f64 (+.f64 y (pow.f64 (sqrt.f64 (/.f64 1/9 x)) 2)) 1))
56.0ms	(/.f64 1/9 x)
56.0ms	(pow.f64 (sqrt.f64 (/.f64 1/9 x)) 2)

simplify46.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary64`
618×	`fma-def_binary64`
230×	`distribute-rgt-in_binary64`
221×	`distribute-rgt-neg-in_binary64`
201×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	267
1	55	222
2	113	201
3	218	201
4	436	201
5	779	201
6	1524	201
7	2722	201
8	3671	201
9	4312	201

Stop Event

1×	node limit

Counts

124 → 98

prune89.0ms (3.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	98	9	107

Error

Counts

107 → 9

Alt Table

Status	Error	Program
	1.4b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 3)
	0.4b	(.f64 (sqrt.f64 (pow.f64 (/.f64 1/9 x) -1)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	25.9b	(pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 2)
	0.6b	(pow.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 1)
	28.4b	(/.f64 (*.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1/9 x) y) 2) -1) (sqrt.f64 (/.f64 x 1/9))) (+.f64 1 (+.f64 (/.f64 1/9 x) y)))
	0.6b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
✓	0.3b	(.f64 (sqrt.f64 (.f64 9 x)) (-.f64 (+.f64 y (pow.f64 (sqrt.f64 (/.f64 1/9 x)) 2)) 1))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 x 1/9)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	34.6b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 x) (.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3))

Compiler

Compiled 1831 to 1396 computations (23.8% saved)

regimes364.0ms (14%)

Accuracy

Total 0.4b remaining (93.5%)

Threshold costs 0.4b (93.5%)

Counts

122 → 1

Compiler

Compiled 6026 to 4876 computations (19.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	28	21
2	36	21
3	39	21
4	40	21

Stop Event

1×

saturated

end130.0ms (5%)

Compiler: Compiled 194 to 157 computations (19.1% saved)

Details

analyze70.0ms (2.7%)

sample995.0ms (38.2%)

simplify39.0ms (1.5%)

prune4.0ms (0.1%)

localize8.0ms (0.3%)

series35.0ms (1.3%)

rewrite59.0ms (2.3%)

simplify65.0ms (2.5%)

prune102.0ms (3.9%)

localize8.0ms (0.3%)

series26.0ms (1%)

rewrite55.0ms (2.1%)

simplify48.0ms (1.9%)

prune126.0ms (4.8%)

localize8.0ms (0.3%)

series25.0ms (1%)

rewrite45.0ms (1.7%)

simplify45.0ms (1.7%)

prune107.0ms (4.1%)

localize9.0ms (0.4%)

series35.0ms (1.3%)

rewrite57.0ms (2.2%)

simplify46.0ms (1.8%)

prune89.0ms (3.4%)

regimes364.0ms (14%)

simplify2.0ms (0.1%)

end130.0ms (5%)

Profiling