Details

analyze82.0ms (2.8%)

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
0%	50%	50%	4
12.5%	37.5%	50%	5
18.7%	31.2%	50%	6
28.1%	21.9%	50%	7
32.8%	17.2%	50%	8
37.5%	11.7%	50.8%	9
39.8%	9%	51.2%	10
42.1%	6%	51.8%	11
43.3%	4.6%	52.1%	12
44.5%	3.1%	52.4%	13
45.1%	2.3%	52.6%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample990.0ms (34.3%)

Results

965.0ms	8256×	body	128	valid
10.0ms	94×	body	128	invalid

Compiler

Compiled 34 to 28 computations (17.6% saved)

preprocess46.0ms (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)

simplify27.0ms (1%)

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

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(+.f64 1 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 -1/9 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))))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.3b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.5b	(/.f64 1 (*.f64 x 9))

series51.0ms (1.8%)

Counts

4 → 38

Calls

18 calls:

8.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))	x	-inf
8.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))	x	-inf
5.0ms	(*.f64 3 (sqrt.f64 x))	x	-inf
4.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))	y	-inf
3.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))	y	inf

rewrite66.0ms (2.3%)

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	4104	37

Stop Event

1×	node limit

Counts

4 → 136

simplify37.0ms (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

prune184.0ms (6.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	9	147
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	140	9	149

Error

0.0b

Counts

149 → 9

Alt Table

Status	Error	Program
	0.3b	(+.f64 1 (neg.f64 (+.f64 (/.f64 1/9 x) (/.f64 y (sqrt.f64 (/.f64 x 1/9))))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	20.9b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (/.f64 (sqrt.f64 x) (.f64 y 1/3))) (.f64 (+.f64 1 (/.f64 1/9 x)) 1)) (.f64 (+.f64 1 (/.f64 1/9 x)) (/.f64 (sqrt.f64 x) (*.f64 y 1/3))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (neg.f64 y) (/.f64 1 (*.f64 (sqrt.f64 x) -3))))
	12.9b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 x 1/9)) 3))))
	0.6b	(-.f64 (-.f64 1 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x 1/9)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x 1/9)) -1))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
	14.5b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (sqrt.f64 x)) (.f64 (+.f64 1 (/.f64 1/9 x)) (.f64 y 1/3))) (.f64 (+.f64 1 (/.f64 1/9 x)) (sqrt.f64 x)))
	18.4b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -3)) (sqrt.f64 x)) (.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (/.f64 1/9 x)) (.f64 y 1/3))) (.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (/.f64 1/9 x)) (sqrt.f64 x)))

Compiler

Compiled 3407 to 2592 computations (23.9% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (neg.f64 y) (/.f64 1 (.f64 (sqrt.f64 x) -3)))
✓	0.3b	(*.f64 (sqrt.f64 x) -3)
✓	0.3b	(/.f64 1 (*.f64 (sqrt.f64 x) -3))
	0.5b	(/.f64 1 (*.f64 x 9))

series38.0ms (1.3%)

Counts

3 → 12

Calls

12 calls:

9.0ms	(/.f64 1 (*.f64 (sqrt.f64 x) -3))	x	-inf
8.0ms	(.f64 (neg.f64 y) (/.f64 1 (.f64 (sqrt.f64 x) -3)))	x	-inf
4.0ms	(.f64 (neg.f64 y) (/.f64 1 (.f64 (sqrt.f64 x) -3)))	x	inf
2.0ms	(.f64 (neg.f64 y) (/.f64 1 (.f64 (sqrt.f64 x) -3)))	y	inf
2.0ms	(.f64 (neg.f64 y) (/.f64 1 (.f64 (sqrt.f64 x) -3)))	y	-inf

rewrite43.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

777×	`log1p-expm1-u_binary64`
777×	`expm1-log1p-u_binary64`
97×	`add-sqr-sqrt_binary64`
90×	`add-cbrt-cube_binary64`
90×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	206	21
2	2576	21

Stop Event

1×	node limit

Counts

3 → 77

simplify10.0ms (0.3%)

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	9	144
1	15	144
2	22	144
3	24	144

Stop Event

1×

saturated

Counts

89 → 79

prune138.0ms (4.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	107	9	116

Error

0.0b

Counts

116 → 9

Alt Table

Status	Error	Program
	0.3b	(+.f64 1 (neg.f64 (+.f64 (/.f64 1/9 x) (/.f64 y (sqrt.f64 (/.f64 x 1/9))))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	20.9b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (/.f64 (sqrt.f64 x) (.f64 y 1/3))) (.f64 (+.f64 1 (/.f64 1/9 x)) 1)) (.f64 (+.f64 1 (/.f64 1/9 x)) (/.f64 (sqrt.f64 x) (*.f64 y 1/3))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (neg.f64 y) (/.f64 1 (*.f64 (sqrt.f64 x) -3))))
	12.9b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 x 1/9)) 3))))
	0.6b	(-.f64 (-.f64 1 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x 1/9)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x 1/9)) -1))) (/.f64 y (.f64 3 (sqrt.f64 x))))
▶	0.2b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
	14.5b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (sqrt.f64 x)) (.f64 (+.f64 1 (/.f64 1/9 x)) (.f64 y 1/3))) (.f64 (+.f64 1 (/.f64 1/9 x)) (sqrt.f64 x)))
	18.4b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -3)) (sqrt.f64 x)) (.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (/.f64 1/9 x)) (.f64 y 1/3))) (.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (/.f64 1/9 x)) (sqrt.f64 x)))

Compiler

Compiled 2414 to 1797 computations (25.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(*.f64 3 (sqrt.f64 x))
	0.3b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.4b	(*.f64 (/.f64 1 x) 1/9)

series21.0ms (0.7%)

Counts

2 → 26

Calls

9 calls:

8.0ms	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))	x	-inf
3.0ms	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))	y	-inf
2.0ms	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))	y	0
2.0ms	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))	y	inf
2.0ms	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))	x	inf

rewrite59.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

250×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
214×	`fma-neg_binary64`
142×	`add-sqr-sqrt_binary64`
138×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	296	22
2	4075	22

Stop Event

1×	node limit

Counts

2 → 76

simplify32.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

341×	`fma-def_binary64`
275×	`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	273
1	40	255
2	88	255
3	180	255
4	380	255
5	666	255
6	1076	255
7	1315	255
8	1385	255
9	1392	255

Stop Event

1×

saturated

Counts

102 → 84

prune205.0ms (7.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	140	9	149

Error

0.0b

Counts

149 → 9

Alt Table

Status	Error	Program
	14.5b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (sqrt.f64 x)) (.f64 (+.f64 1 (/.f64 1/9 x)) (.f64 y 1/3))) (.f64 (+.f64 1 (/.f64 1/9 x)) (sqrt.f64 x)))
	0.3b	(-.f64 (-.f64 1 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	20.9b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (/.f64 (sqrt.f64 x) (.f64 y 1/3))) (.f64 (+.f64 1 (/.f64 1/9 x)) 1)) (.f64 (+.f64 1 (/.f64 1/9 x)) (/.f64 (sqrt.f64 x) (*.f64 y 1/3))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (neg.f64 y) (/.f64 1 (*.f64 (sqrt.f64 x) -3))))
▶	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	12.9b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 x 1/9)) 3))))
	0.3b	(+.f64 1 (-.f64 (/.f64 -1/9 x) (*.f64 y (/.f64 1/3 (sqrt.f64 x)))))
	0.6b	(-.f64 (-.f64 1 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x 1/9)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x 1/9)) -1))) (/.f64 y (.f64 3 (sqrt.f64 x))))
✓	0.2b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))

Compiler

Compiled 3196 to 2359 computations (26.2% 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)))
✓	0.4b	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))
	0.5b	(/.f64 1 (*.f64 x 9))

series30.0ms (1%)

Counts

3 → 0

Calls

15 calls:

4.0ms	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))	x	inf
2.0ms	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))	y	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))))	x	-inf
2.0ms	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))	y	-inf

rewrite41.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

718×	`log1p-expm1-u_binary64`
718×	`expm1-log1p-u_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`
85×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	181	19
2	2059	19

Stop Event

1×	node limit

Counts

3 → 60

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

60 → 60

prune114.0ms (3.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	89	8	97

Error

0.0b

Counts

97 → 8

Alt Table

Status	Error	Program
	14.5b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (sqrt.f64 x)) (.f64 (+.f64 1 (/.f64 1/9 x)) (.f64 y 1/3))) (.f64 (+.f64 1 (/.f64 1/9 x)) (sqrt.f64 x)))
	0.3b	(-.f64 (-.f64 1 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	20.9b	(/.f64 (-.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x 1/9) -2)) (/.f64 (sqrt.f64 x) (.f64 y 1/3))) (.f64 (+.f64 1 (/.f64 1/9 x)) 1)) (.f64 (+.f64 1 (/.f64 1/9 x)) (/.f64 (sqrt.f64 x) (*.f64 y 1/3))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (neg.f64 y) (/.f64 1 (*.f64 (sqrt.f64 x) -3))))
	12.9b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 x 1/9)) 3))))
	0.3b	(+.f64 1 (-.f64 (/.f64 -1/9 x) (*.f64 y (/.f64 1/3 (sqrt.f64 x)))))
✓	0.2b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.5b	(-.f64 (-.f64 1 (pow.f64 (/.f64 1/3 (sqrt.f64 x)) 2)) (.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x)))))

Compiler

Compiled 1744 to 1361 computations (22% saved)

regimes486.0ms (16.9%)

Accuracy

Total 0.2b remaining (88%)

Threshold costs 0.2b (88%)

Counts

150 → 1

Compiler

Compiled 8816 to 7219 computations (18.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`distribute-rgt-neg-in_binary64`
13×	`cancel-sign-sub-inv_binary64`
9×	`sub-neg_binary64`
8×	`*-commutative_binary64`
8×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	33	24
2	56	24
3	88	24
4	102	24
5	111	24
6	115	24

Stop Event

1×

saturated

end134.0ms (4.6%)

Stop Event

1×

fuel

Compiler

Compiled 209 to 167 computations (20.1% saved)

Details

analyze82.0ms (2.8%)

sample990.0ms (34.3%)

preprocess46.0ms (1.6%)

simplify27.0ms (1%)

prune4.0ms (0.1%)

localize8.0ms (0.3%)

series51.0ms (1.8%)

rewrite66.0ms (2.3%)

simplify37.0ms (1.3%)

prune184.0ms (6.4%)

localize10.0ms (0.4%)

series38.0ms (1.3%)

rewrite43.0ms (1.5%)

simplify10.0ms (0.3%)

prune138.0ms (4.8%)

localize9.0ms (0.3%)

series21.0ms (0.7%)

rewrite59.0ms (2%)

simplify32.0ms (1.1%)

prune205.0ms (7.1%)

localize9.0ms (0.3%)

series30.0ms (1%)

rewrite41.0ms (1.4%)

simplify6.0ms (0.2%)

prune114.0ms (3.9%)

regimes486.0ms (16.9%)

simplify3.0ms (0.1%)

end134.0ms (4.6%)

Profiling