Details

analyze9.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.6s (55.9%)

Results

521.0ms	4547×	body	128	valid
449.0ms	1582×	body	512	valid
446.0ms	1335×	body	1024	valid
141.0ms	792×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify18.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
42×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	64	22
4	122	22
5	237	22
6	388	22
7	509	22
8	615	22
9	635	22

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

9.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	1.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series9.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite76.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
152×	`egg-rr`
136×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	273	49
2	4302	49

Stop Event

1×	node limit

Counts

4 → 152

Calls

4 calls:

73.0ms	(/.f64 1 (+.f64 x 1))
73.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
73.0ms	(/.f64 1 (-.f64 x 1))
73.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

simplify35.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-neg_binary64`
489×	`cancel-sign-sub-inv_binary64`
255×	`associate-l_binary64`
254×	`fma-def_binary64`
246×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	752
1	247	726
2	724	720
3	2230	717

Stop Event

1×	node limit

Counts

200 → 205

prune155.0ms (5.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	202	3	205
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	203	3	206

Error

0.2b

Counts

206 → 3

Alt Table

Status	Error	Program
	24.9b	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))
▶	9.2b	(-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))
	32.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))

Compiler

Compiled 4825 to 3810 computations (21% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 1 x))
✓	0.0b	(-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1)))
✓	0.0b	(/.f64 1 (+.f64 x -1))
✓	1.3b	(-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))

series11.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1)))
3.0ms	(-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))
2.0ms	(/.f64 1 (+.f64 x -1))
2.0ms	(/.f64 1 (+.f64 1 x))

rewrite70.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
146×	`egg-rr`
145×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	293	49
2	4510	49

Stop Event

1×	node limit

Counts

4 → 146

Calls

4 calls:

65.0ms	(/.f64 1 (+.f64 1 x))
65.0ms	(-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1)))
65.0ms	(/.f64 1 (+.f64 x -1))
65.0ms	(-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))

simplify37.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-neg_binary64`
472×	`cancel-sign-sub-inv_binary64`
264×	`associate-l_binary64`
256×	`fma-def_binary64`
208×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	748
1	241	726
2	708	720
3	2169	717

Stop Event

1×	node limit

Counts

194 → 197

prune148.0ms (5.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	197	3	200

Error

0.2b

Counts

200 → 3

Alt Table

Status	Error	Program
▶	24.9b	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))
✓	9.2b	(-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))
	32.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))

Compiler

Compiled 4575 to 3594 computations (21.4% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 1 x))
✓	0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
✓	0.1b	(.f64 (+.f64 x -1) (.f64 x (+.f64 1 x)))
✓	16.5b	(+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (*.f64 (+.f64 1 x) 2))))

series11.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(.f64 (+.f64 x -1) (.f64 x (+.f64 1 x)))
2.0ms	(*.f64 x (+.f64 1 x))
1.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
1.0ms	(+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (*.f64 (+.f64 1 x) 2))))

rewrite67.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`expm1-udef_binary64`
257×	`log1p-udef_binary64`
145×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	53
1	297	53
2	4220	53

Stop Event

1×	node limit

Counts

4 → 135

Calls

4 calls:

65.0ms	(*.f64 x (+.f64 1 x))
65.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
65.0ms	(.f64 (+.f64 x -1) (.f64 x (+.f64 1 x)))
65.0ms	(+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (*.f64 (+.f64 1 x) 2))))

simplify23.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

536×	`unswap-sqr_binary64`
505×	`fma-def_binary64`
274×	`distribute-rgt-neg-in_binary64`
262×	`cancel-sign-sub-inv_binary64`
238×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	219
1	35	183
2	66	183
3	137	183
4	358	183
5	1396	183

Stop Event

1×	node limit

Counts

183 → 148

prune146.0ms (5.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	179	3	182

Error

0.2b

Counts

182 → 3

Alt Table

Status	Error	Program
✓	9.2b	(-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))
	32.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
▶	0.2b	(/.f64 2 (.f64 (+.f64 x -1) (.f64 x (+.f64 1 x))))

Compiler

Compiled 6063 to 3994 computations (34.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 x (+.f64 1 x))
	0.1b	(.f64 (+.f64 x -1) (.f64 x (+.f64 1 x)))
✓	0.2b	(/.f64 2 (.f64 (+.f64 x -1) (.f64 x (+.f64 1 x))))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 2 (*.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))

rewrite49.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

489×	`log-prod_binary64`
282×	`fma-def_binary64`
248×	`prod-diff_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	222	16
2	2874	11

Stop Event

1×	node limit

Counts

1 → 26

Calls

1 calls:

49.0ms

(/.f64 2 (*.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))

simplify32.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-def_binary64`
448×	`fma-neg_binary64`
277×	`cancel-sign-sub-inv_binary64`
228×	`distribute-rgt-neg-in_binary64`
210×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	223
1	127	217
2	375	211
3	1222	211
4	3953	211

Stop Event

1×	node limit

Counts

38 → 40

prune82.0ms (2.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	104	5	109

Error

0.0b

Counts

109 → 5

Alt Table

Status	Error	Program
	1.2b	(/.f64 2 (.f64 (+.f64 x -1) (pow.f64 (cbrt.f64 (+.f64 x (.f64 x x))) 3)))
	22.8b	(pow.f64 (sqrt.f64 (/.f64 2 (*.f64 x (fma.f64 x x -1)))) 2)
✓	0.2b	(/.f64 2 (.f64 (+.f64 x -1) (.f64 x (+.f64 1 x))))
	0.1b	(*.f64 (/.f64 2 (-.f64 x 1)) (/.f64 1 (fma.f64 x x x)))
	0.2b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 1560 to 1047 computations (32.9% saved)

regimes160.0ms (5.6%)

Accuracy

Total 0.1b remaining (82.8%)

Threshold costs 0.1b (82.8%)

Counts

80 → 1

Compiler

Compiled 2442 to 1876 computations (23.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	15	17
2	16	17

Stop Event

1×

saturated

end74.0ms (2.6%)

Compiler: Compiled 86 to 62 computations (27.9% saved)

Details

analyze9.0ms (0.3%)

sample1.6s (55.9%)

simplify18.0ms (0.6%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

series9.0ms (0.3%)

rewrite76.0ms (2.7%)

simplify35.0ms (1.2%)

prune155.0ms (5.5%)

localize8.0ms (0.3%)

series11.0ms (0.4%)

rewrite70.0ms (2.5%)

simplify37.0ms (1.3%)

prune148.0ms (5.2%)

localize10.0ms (0.4%)

series11.0ms (0.4%)

rewrite67.0ms (2.4%)

simplify23.0ms (0.8%)

prune146.0ms (5.1%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite49.0ms (1.7%)

simplify32.0ms (1.1%)

prune82.0ms (2.9%)

regimes160.0ms (5.6%)

simplify2.0ms (0.1%)

end74.0ms (2.6%)

Profiling