Details

analyze55.0ms (1.9%)

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)

sample997.0ms (33.7%)

Results

926.0ms	8256×	body	128	valid
11.0ms	107×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify27.0ms (0.9%)

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

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

series46.0ms (1.5%)

Counts

4 → 38

Calls

4 calls:

20.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
19.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
5.0ms	(*.f64 3 (sqrt.f64 x))
1.0ms	(/.f64 1 (*.f64 x 9))

rewrite65.0ms (2.2%)

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	4102	37

Stop Event

1×	node limit

Counts

4 → 136

Calls

4 calls:

63.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
63.0ms	(/.f64 1 (*.f64 x 9))
63.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
63.0ms	(*.f64 3 (sqrt.f64 x))

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	1077	399
7	1316	399
8	1386	399
9	1393	399

Stop Event

1×

saturated

Counts

174 → 147

prune158.0ms (5.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	141	8	149

Error

0.0b

Counts

149 → 8

Alt Table

Status	Error	Program
	0.7b	(-.f64 (-.f64 1 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 x 9)) 2) -1) (pow.f64 (cbrt.f64 (.f64 x 9)) -1))) (/.f64 y (.f64 3 (sqrt.f64 x))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (sqrt.f64 (.f64 x 9))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (/.f64 1 (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (/.f64 y (sqrt.f64 (.f64 3 (sqrt.f64 x))))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (*.f64 1/3 y) (sqrt.f64 (/.f64 1 x))))
	2.4b	(-.f64 (-.f64 1 (exp.f64 (log.f64 (/.f64 1/9 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	19.1b	(-.f64 1 (*.f64 1/9 (/.f64 1 x)))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (pow.f64 (cbrt.f64 (.f64 3 (sqrt.f64 x))) 3)))
	0.3b	(+.f64 1 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 -1/9 x)))

Compiler

Compiled 3243 to 2381 computations (26.6% 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 (sqrt.f64 (.f64 x 9))))
✓	0.1b	(sqrt.f64 (*.f64 x 9))
	0.2b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(/.f64 y (sqrt.f64 (*.f64 x 9)))

series45.0ms (1.5%)

Counts

3 → 26

Calls

3 calls:

21.0ms	(/.f64 y (sqrt.f64 (*.f64 x 9)))
19.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (sqrt.f64 (.f64 x 9))))
4.0ms	(sqrt.f64 (*.f64 x 9))

rewrite69.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

398×	`fma-def_binary64`
215×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
178×	`fma-neg_binary64`
166×	`egg-rr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	252	33
2	3584	31

Stop Event

1×	node limit

Counts

3 → 166

Calls

3 calls:

66.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (sqrt.f64 (.f64 x 9))))
66.0ms	(sqrt.f64 (*.f64 x 9))
66.0ms	(/.f64 y (sqrt.f64 (*.f64 x 9)))

simplify35.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	369
1	40	351
2	88	351
3	179	351
4	379	351
5	665	351
6	1079	351
7	1318	351
8	1388	351
9	1395	351

Stop Event

1×

saturated

Counts

192 → 176

prune227.0ms (7.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	207	5	212

Error

0.0b

Counts

212 → 5

Alt Table

Status	Error	Program
	2.4b	(-.f64 (-.f64 1 (exp.f64 (log.f64 (/.f64 1/9 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.7b	(-.f64 (-.f64 1 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 x 9)) 2) -1) (pow.f64 (cbrt.f64 (.f64 x 9)) -1))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(fma.f64 y (neg.f64 (sqrt.f64 (/.f64 1/9 x))) (-.f64 1 (/.f64 1/9 x)))
▶	0.2b	(-.f64 (-.f64 1 (.f64 1/9 (/.f64 1 x))) (/.f64 y (sqrt.f64 (.f64 x 9))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (pow.f64 (pow.f64 (/.f64 x 1/9) 1/4) 2)))

Compiler

Compiled 4901 to 3562 computations (27.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 1 (.f64 1/9 (/.f64 1 x))) (/.f64 y (sqrt.f64 (.f64 x 9))))
	0.1b	(sqrt.f64 (*.f64 x 9))
	0.3b	(/.f64 y (sqrt.f64 (*.f64 x 9)))
✓	0.4b	(*.f64 1/9 (/.f64 1 x))

series21.0ms (0.7%)

Counts

2 → 26

Calls

2 calls:

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

rewrite65.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

390×	`fma-def_binary64`
248×	`expm1-udef_binary64`
247×	`log1p-udef_binary64`
215×	`fma-neg_binary64`
139×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	298	22
2	3980	21

Stop Event

1×	node limit

Counts

2 → 122

Calls

2 calls:

61.0ms	(-.f64 (-.f64 1 (.f64 1/9 (/.f64 1 x))) (/.f64 y (sqrt.f64 (.f64 x 9))))
61.0ms	(*.f64 1/9 (/.f64 1 x))

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

148 → 130

prune194.0ms (6.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	194	5	199

Error

0.0b

Counts

199 → 5

Alt Table

Status	Error	Program
	0.7b	(-.f64 (-.f64 1 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 x 9)) 2) -1) (pow.f64 (cbrt.f64 (.f64 x 9)) -1))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	15.3b	(fma.f64 (cbrt.f64 (+.f64 1 (/.f64 -1/9 x))) (cbrt.f64 (pow.f64 (+.f64 1 (/.f64 -1/9 x)) 2)) (/.f64 (neg.f64 y) (*.f64 3 (sqrt.f64 x))))
	0.3b	(fma.f64 y (neg.f64 (sqrt.f64 (/.f64 1/9 x))) (-.f64 1 (/.f64 1/9 x)))
✓	0.2b	(-.f64 (-.f64 1 (.f64 1/9 (/.f64 1 x))) (/.f64 y (sqrt.f64 (.f64 x 9))))
▶	0.3b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (pow.f64 (pow.f64 (/.f64 x 1/9) 1/4) 2)))

Compiler

Compiled 4818 to 3514 computations (27.1% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(/.f64 y (pow.f64 (pow.f64 (/.f64 x 1/9) 1/4) 2))
✓	0.4b	(/.f64 x 1/9)
✓	0.5b	(pow.f64 (pow.f64 (/.f64 x 1/9) 1/4) 2)

series49.0ms (1.7%)

Counts

3 → 36

Calls

3 calls:

32.0ms	(pow.f64 (pow.f64 (/.f64 x 1/9) 1/4) 2)
16.0ms	(/.f64 y (pow.f64 (pow.f64 (/.f64 x 1/9) 1/4) 2))
1.0ms	(/.f64 x 1/9)

rewrite52.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

912×	`log1p-expm1-u_binary64`
912×	`expm1-log1p-u_binary64`
98×	`add-cbrt-cube_binary64`
98×	`add-log-exp_binary64`
97×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	226	19
2	2603	19

Stop Event

1×	node limit

Counts

3 → 92

Calls

3 calls:

51.0ms	(/.f64 y (pow.f64 (pow.f64 (/.f64 x 1/9) 1/4) 2))
51.0ms	(/.f64 x 1/9)
51.0ms	(pow.f64 (pow.f64 (/.f64 x 1/9) 1/4) 2)

simplify40.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

414×	`fma-neg_binary64`
403×	`associate-l_binary64`
342×	`associate-r_binary64`
288×	`fma-def_binary64`
275×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	384
1	73	384
2	146	348
3	380	264
4	1187	264
5	4447	264

Stop Event

1×	node limit

Counts

128 → 97

prune138.0ms (4.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	125	5	130

Error

0.0b

Counts

130 → 5

Alt Table

Status	Error	Program
	0.7b	(-.f64 (-.f64 1 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 x 9)) 2) -1) (pow.f64 (cbrt.f64 (.f64 x 9)) -1))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	15.3b	(fma.f64 (cbrt.f64 (+.f64 1 (/.f64 -1/9 x))) (cbrt.f64 (pow.f64 (+.f64 1 (/.f64 -1/9 x)) 2)) (/.f64 (neg.f64 y) (*.f64 3 (sqrt.f64 x))))
	0.3b	(fma.f64 y (neg.f64 (sqrt.f64 (/.f64 1/9 x))) (-.f64 1 (/.f64 1/9 x)))
✓	0.2b	(-.f64 (-.f64 1 (.f64 1/9 (/.f64 1 x))) (/.f64 y (sqrt.f64 (.f64 x 9))))
✓	0.3b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (pow.f64 (pow.f64 (/.f64 x 1/9) 1/4) 2)))

Compiler

Compiled 2543 to 2020 computations (20.6% saved)

regimes470.0ms (15.9%)

Accuracy

Total 0.2b remaining (78.2%)

Threshold costs 0.2b (78.2%)

Counts

145 → 1

Compiler

Compiled 7709 to 6325 computations (18% saved)

simplify2.0ms (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	11	21
1	18	21
2	29	21
3	35	21
4	39	21
5	40	21

Stop Event

1×

saturated

end92.0ms (3.1%)

Compiler: Compiled 131 to 108 computations (17.6% saved)

Details

analyze55.0ms (1.9%)

sample997.0ms (33.7%)

simplify27.0ms (0.9%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series46.0ms (1.5%)

rewrite65.0ms (2.2%)

simplify37.0ms (1.3%)

prune158.0ms (5.4%)

localize8.0ms (0.3%)

series45.0ms (1.5%)

rewrite69.0ms (2.3%)

simplify35.0ms (1.2%)

prune227.0ms (7.7%)

localize10.0ms (0.3%)

series21.0ms (0.7%)

rewrite65.0ms (2.2%)

simplify32.0ms (1.1%)

prune194.0ms (6.6%)

localize11.0ms (0.4%)

series49.0ms (1.7%)

rewrite52.0ms (1.8%)

simplify40.0ms (1.3%)

prune138.0ms (4.7%)

regimes470.0ms (15.9%)

simplify2.0ms (0.1%)

end92.0ms (3.1%)

Profiling