Details

analyze61.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.0s (32.7%)

Results

991.0ms	8256×	body	128	valid
10.0ms	96×	body	128	invalid

Compiler

Compiled 34 to 28 computations (17.6% saved)

preprocess51.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

980×	`fma-neg_binary64`
456×	`cancel-sign-sub-inv_binary64`
286×	`fma-def_binary64`
206×	`div-sub_binary64`
204×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	46	36
2	100	36
3	209	36
4	445	32
5	834	32
6	1729	32
7	3228	32
8	4595	32
9	4872	32
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify24.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-neg_binary64`
309×	`fma-def_binary64`
228×	`cancel-sign-sub-inv_binary64`
83×	`associate-/l*_binary64`
72×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	114	18
4	234	16
5	440	16
6	866	16
7	1567	16
8	2339	16
9	2371	16
10	2394	16

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
	0.3b	(+.f64 1 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 -1/9 x)))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))

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 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
✓	0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.4b	(/.f64 1 (*.f64 x 9))

series60.0ms (1.9%)

Counts

4 → 38

Calls

18 calls:

10.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))	x	-inf
9.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))	y	0
8.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))	y	inf
8.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))	x	-inf
3.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))	y	0

rewrite73.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

240×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
185×	`fma-neg_binary64`
139×	`add-sqr-sqrt_binary64`
136×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	291	37
2	4103	37

Stop Event

1×	node limit

Counts

4 → 136

simplify40.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

341×	`fma-def_binary64`
277×	`fma-neg_binary64`
124×	`cancel-sign-sub-inv_binary64`
55×	`distribute-rgt-neg-in_binary64`
49×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	417
1	40	399
2	88	399
3	180	399
4	380	399
5	666	399
6	1080	399
7	1319	399
8	1389	399
9	1396	399

Stop Event

1×

saturated

Counts

174 → 147

prune202.0ms (6.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	141	8	149

Error

0.0b

Counts

149 → 8

Alt Table

Status	Error	Program
	21.2b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (.f64 3 (/.f64 (sqrt.f64 x) y))) (.f64 (+.f64 1 (/.f64 1/9 x)) 1)) (.f64 (+.f64 1 (/.f64 1/9 x)) (*.f64 3 (/.f64 (sqrt.f64 x) y))))
	0.4b	(-.f64 (-.f64 1 (pow.f64 (/.f64 1/3 (sqrt.f64 x)) 2)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.3b	(+.f64 1 (fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) -1/3) (/.f64 -1/9 x)))
	0.3b	(-.f64 1 (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))))))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (pow.f64 (cbrt.f64 (.f64 y (/.f64 1/3 (sqrt.f64 x)))) 3))
	16.9b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -3)) (.f64 3 (sqrt.f64 x))) (.f64 (+.f64 1 (+.f64 (/.f64 1/9 x) (pow.f64 (/.f64 x 1/9) -2))) y)) (.f64 (+.f64 1 (+.f64 (/.f64 1/9 x) (pow.f64 (/.f64 x 1/9) -2))) (*.f64 3 (sqrt.f64 x))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (*.f64 y 1/3) (/.f64 1 (sqrt.f64 x))))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (/.f64 1/3 (sqrt.f64 x)))))

Compiler

Compiled 3341 to 2452 computations (26.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 x))
✓	0.3b	(.f64 (.f64 y 1/3) (/.f64 1 (sqrt.f64 x)))
✓	0.4b	(*.f64 y 1/3)
	0.4b	(/.f64 1 (*.f64 x 9))

series37.0ms (1.2%)

Counts

3 → 24

Calls

12 calls:

8.0ms	(.f64 (.f64 y 1/3) (/.f64 1 (sqrt.f64 x)))	x	-inf
7.0ms	(/.f64 1 (sqrt.f64 x))	x	-inf
5.0ms	(/.f64 1 (sqrt.f64 x))	x	inf
3.0ms	(.f64 (.f64 y 1/3) (/.f64 1 (sqrt.f64 x)))	x	inf
3.0ms	(.f64 (.f64 y 1/3) (/.f64 1 (sqrt.f64 x)))	x	0

rewrite52.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

749×	`log1p-expm1-u_binary64`
749×	`expm1-log1p-u_binary64`
147×	`log1p-udef_binary64`
86×	`add-sqr-sqrt_binary64`
80×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	183	17
2	2151	17

Stop Event

1×	node limit

Counts

3 → 65

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	192
1	16	192
2	22	192
3	23	192

Stop Event

1×

saturated

Counts

89 → 68

prune145.0ms (4.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	97	7	104

Error

0.0b

Counts

104 → 7

Alt Table

Status	Error	Program
	21.2b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (.f64 3 (/.f64 (sqrt.f64 x) y))) (.f64 (+.f64 1 (/.f64 1/9 x)) 1)) (.f64 (+.f64 1 (/.f64 1/9 x)) (*.f64 3 (/.f64 (sqrt.f64 x) y))))
	0.4b	(-.f64 (-.f64 1 (pow.f64 (/.f64 1/3 (sqrt.f64 x)) 2)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
▶	0.3b	(+.f64 1 (fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) -1/3) (/.f64 -1/9 x)))
	0.3b	(-.f64 1 (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))))))
	0.6b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (*.f64 y 1/3) (pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)))
	0.4b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (pow.f64 (cbrt.f64 (*.f64 y 1/3)) 3) (/.f64 1 (sqrt.f64 x))))
	16.9b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -3)) (.f64 3 (sqrt.f64 x))) (.f64 (+.f64 1 (+.f64 (/.f64 1/9 x) (pow.f64 (/.f64 x 1/9) -2))) y)) (.f64 (+.f64 1 (+.f64 (/.f64 1/9 x) (pow.f64 (/.f64 x 1/9) -2))) (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 2078 to 1613 computations (22.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) -1/3) (/.f64 -1/9 x))
✓	0.1b	(sqrt.f64 (/.f64 1 x))
✓	0.3b	(/.f64 -1/9 x)
✓	0.4b	(*.f64 (sqrt.f64 (/.f64 1 x)) -1/3)

series29.0ms (0.9%)

Counts

4 → 13

Calls

15 calls:

6.0ms	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) -1/3) (/.f64 -1/9 x))	y	inf
3.0ms	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) -1/3) (/.f64 -1/9 x))	x	-inf
3.0ms	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) -1/3) (/.f64 -1/9 x))	x	inf
2.0ms	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) -1/3) (/.f64 -1/9 x))	y	-inf
2.0ms	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) -1/3) (/.f64 -1/9 x))	y	0

rewrite60.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

893×	`log1p-expm1-u_binary64`
893×	`expm1-log1p-u_binary64`
149×	`prod-diff_binary64`
105×	`add-sqr-sqrt_binary64`
98×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	225	27
2	2528	27

Stop Event

1×	node limit

Counts

4 → 90

simplify23.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

157×	`fma-def_binary64`
140×	`fma-neg_binary64`
58×	`cancel-sign-sub-inv_binary64`
46×	`distribute-rgt-neg-in_binary64`
29×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	212
1	37	194
2	83	176
3	183	176
4	341	176
5	559	176
6	734	176
7	819	176
8	830	176
9	831	176

Stop Event

1×

saturated

Counts

103 → 95

prune116.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Error

0.0b

Counts

102 → 7

Alt Table

Status	Error	Program
	21.2b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (.f64 3 (/.f64 (sqrt.f64 x) y))) (.f64 (+.f64 1 (/.f64 1/9 x)) 1)) (.f64 (+.f64 1 (/.f64 1/9 x)) (*.f64 3 (/.f64 (sqrt.f64 x) y))))
	0.4b	(-.f64 (-.f64 1 (pow.f64 (/.f64 1/3 (sqrt.f64 x)) 2)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
✓	0.3b	(+.f64 1 (fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) -1/3) (/.f64 -1/9 x)))
▶	0.3b	(-.f64 1 (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))))))
	0.6b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (*.f64 y 1/3) (pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)))
	0.4b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (pow.f64 (cbrt.f64 (*.f64 y 1/3)) 3) (/.f64 1 (sqrt.f64 x))))
	16.9b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -3)) (.f64 3 (sqrt.f64 x))) (.f64 (+.f64 1 (+.f64 (/.f64 1/9 x) (pow.f64 (/.f64 x 1/9) -2))) y)) (.f64 (+.f64 1 (+.f64 (/.f64 1/9 x) (pow.f64 (/.f64 x 1/9) -2))) (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 1818 to 1390 computations (23.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (/.f64 1 x))
✓	0.2b	(*.f64 y (sqrt.f64 (/.f64 1 x)))
✓	0.3b	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))
✓	0.4b	(*.f64 1/9 (/.f64 1 x))

series29.0ms (0.9%)

Counts

3 → 12

Calls

15 calls:

3.0ms	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))	x	inf
3.0ms	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))	x	-inf
3.0ms	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))	x	0
2.0ms	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))	y	-inf
2.0ms	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))	y	inf

rewrite63.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

855×	`log1p-expm1-u_binary64`
855×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
95×	`add-cbrt-cube_binary64`
95×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	222	19
2	2463	19

Stop Event

1×	node limit

Counts

3 → 49

simplify17.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48

Stop Event

1×

saturated

Counts

61 → 49

prune111.0ms (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	78	7	85

Error

0.0b

Counts

85 → 7

Alt Table

Status	Error	Program
	21.2b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (.f64 3 (/.f64 (sqrt.f64 x) y))) (.f64 (+.f64 1 (/.f64 1/9 x)) 1)) (.f64 (+.f64 1 (/.f64 1/9 x)) (*.f64 3 (/.f64 (sqrt.f64 x) y))))
	0.4b	(-.f64 (-.f64 1 (pow.f64 (/.f64 1/3 (sqrt.f64 x)) 2)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
✓	0.3b	(+.f64 1 (fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) -1/3) (/.f64 -1/9 x)))
✓	0.3b	(-.f64 1 (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))))))
	0.6b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (*.f64 y 1/3) (pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)))
	0.4b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (pow.f64 (cbrt.f64 (*.f64 y 1/3)) 3) (/.f64 1 (sqrt.f64 x))))
	0.3b	(-.f64 1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) (.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))))

Compiler

Compiled 1507 to 1166 computations (22.6% saved)

regimes705.0ms (22.7%)

Accuracy

Total 0.2b remaining (87.2%)

Threshold costs 0.2b (87.2%)

Counts

195 → 1

Compiler

Compiled 10856 to 8902 computations (18% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	20	21
2	31	21
3	37	21
4	41	21
5	42	21

Stop Event

1×

saturated

end133.0ms (4.3%)

Stop Event

1×

fuel

Compiler

Compiled 180 to 144 computations (20% saved)

Iter	Nodes	Cost
0	17	212
1	37	194
2	83	176
3	183	176
4	341	176
5	559	176
6	734	176
7	819	176
8	830	176
9	831	176

Iter	Nodes	Cost
0	17	212
1	37	194
2	83	176
3	183	176
4	341	176
5	559	176
6	734	176
7	819	176
8	830	176
9	831	176

Details

analyze61.0ms (2%)

sample1.0s (32.7%)

preprocess51.0ms (1.6%)

simplify24.0ms (0.8%)

prune5.0ms (0.2%)

localize8.0ms (0.3%)

series60.0ms (1.9%)

rewrite73.0ms (2.4%)

simplify40.0ms (1.3%)

prune202.0ms (6.5%)

localize9.0ms (0.3%)

series37.0ms (1.2%)

rewrite52.0ms (1.7%)

simplify12.0ms (0.4%)

prune145.0ms (4.7%)

localize10.0ms (0.3%)

series29.0ms (0.9%)

rewrite60.0ms (1.9%)

simplify23.0ms (0.7%)

prune116.0ms (3.7%)

localize9.0ms (0.3%)

series29.0ms (0.9%)

rewrite63.0ms (2%)

simplify17.0ms (0.6%)

prune111.0ms (3.6%)

regimes705.0ms (22.7%)

simplify3.0ms (0.1%)

end133.0ms (4.3%)

Profiling

Iter	Nodes	Cost
0	17	212
1	37	194
2	83	176
3	183	176
4	341	176
5	559	176
6	734	176
7	819	176
8	830	176
9	831	176