Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.2s (30.9%)

Results

530.0ms	2087×	body	1024	valid
342.0ms	4406×	body	128	valid
198.0ms	1039×	body	512	valid
70.0ms	512×	body	256	valid
67.0ms	212×	body	2048	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

27.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.9b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f64 (+.f64 x 1))
✓	0.6b	(cbrt.f64 x)
✓	3.7b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series660.0ms (16.5%)

Counts

3 → 10

Calls

3 calls:

648.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
9.0ms	(cbrt.f64 x)
3.0ms	(cbrt.f64 (+.f64 x 1))

rewrite51.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

731×	`log1p-expm1-u_binary64`
731×	`expm1-log1p-u_binary64`
698×	`prod-diff_binary64`
130×	`egg-rr`
72×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	149	20
2	1939	20

Stop Event

1×	node limit

Counts

3 → 130

Calls

3 calls:

49.0ms	(cbrt.f64 (+.f64 x 1))
49.0ms	(cbrt.f64 x)
49.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

simplify27.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-def_binary64`
611×	`associate-l_binary64`
536×	`unswap-sqr_binary64`
374×	`associate-r_binary64`
222×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	59
1	51	53
2	124	47
3	392	43
4	1126	38
5	3765	38

Stop Event

1×	node limit

Counts

140 → 138

prune150.0ms (3.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	129	9	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	9	139

Error

26.2b

Counts

139 → 9

Alt Table

Status	Error	Program
	28.3b	(fma.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))
▶	26.9b	(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
	29.1b	(-.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 x))
	44.1b	(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 (sqrt.f64 x) 1/3)) (pow.f64 (sqrt.f64 x) 1/3) (cbrt.f64 x)))
	28.4b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (pow.f64 (cbrt.f64 x) 2)) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))
	28.1b	(+.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 x)))
	29.9b	1
	44.1b	(+.f64 (fma.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/3) (neg.f64 (cbrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/6)) (pow.f64 x 1/6) (cbrt.f64 x)))
	27.7b	(/.f64 (+.f64 (+.f64 x 1) (pow.f64 (neg.f64 (cbrt.f64 x)) 3)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (-.f64 (.f64 (neg.f64 (cbrt.f64 x)) (neg.f64 (cbrt.f64 x))) (.f64 (cbrt.f64 (+.f64 x 1)) (neg.f64 (cbrt.f64 x))))))

Compiler

Compiled 2884 to 1848 computations (35.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))
	0.6b	(cbrt.f64 x)
✓	2.7b	(-.f64 (+.f64 x 1) x)
✓	12.5b	(cbrt.f64 (pow.f64 (+.f64 x 1) 2))

series54.0ms (1.4%)

Counts

3 → 16

Calls

3 calls:

50.0ms	(*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))
3.0ms	(cbrt.f64 (pow.f64 (+.f64 x 1) 2))
1.0ms	(-.f64 (+.f64 x 1) x)

rewrite56.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

654×	`fma-def_binary64`
358×	`fma-neg_binary64`
204×	`log1p-udef_binary64`
203×	`expm1-udef_binary64`
193×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	263	32
2	3473	32

Stop Event

1×	node limit

Counts

3 → 193

Calls

3 calls:

53.0ms	(*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))
53.0ms	(-.f64 (+.f64 x 1) x)
53.0ms	(cbrt.f64 (pow.f64 (+.f64 x 1) 2))

simplify29.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
621×	`associate-l_binary64`
536×	`unswap-sqr_binary64`
380×	`associate-r_binary64`
222×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	59
1	51	55
2	124	49
3	396	45
4	1134	40
5	3786	40

Stop Event

1×	node limit

Counts

209 → 200

prune309.0ms (7.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	238	4	242
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	245	6	251

Error

12.5b

Counts

251 → 6

Alt Table

Status	Error	Program
▶	12.6b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
	26.9b	(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))) (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
	26.9b	(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 4))) (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
	26.9b	(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
	29.9b	1
	29.1b	(-.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 x))

Compiler

Compiled 7488 to 4945 computations (34% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(cbrt.f64 (+.f64 x 1))
	0.3b	(*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))
	0.6b	(cbrt.f64 x)
	12.5b	(cbrt.f64 (pow.f64 (+.f64 x 1) 2))

prune304.0ms (7.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	141	7	148
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	146	8	154

Error

0.2b

Counts

154 → 8

Alt Table

Status	Error	Program
	12.6b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (cbrt.f64 (*.f64 (pow.f64 (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x 1))) 3) x))))
	29.1b	(-.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 x))
	28.4b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (exp.f64 (log.f64 (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x 1))))))))
	0.5b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
▶	0.5b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
	0.6b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) 3) (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
	12.6b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (+.f64 (cbrt.f64 (*.f64 x (+.f64 x 1))) (pow.f64 (cbrt.f64 x) 2))))
	12.5b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (/.f64 (*.f64 (cbrt.f64 x) (+.f64 x (+.f64 x 1))) (fma.f64 (cbrt.f64 x) (-.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)))))

Compiler

Compiled 4560 to 2982 computations (34.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(cbrt.f64 (+.f64 x 1))
✓	0.3b	(pow.f64 (cbrt.f64 (+.f64 x 1)) 2)
	0.3b	(*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))
	0.6b	(cbrt.f64 x)

series5.0ms (0.1%)

Counts

1 → 4

Calls

1 calls:

5.0ms

(pow.f64 (cbrt.f64 (+.f64 x 1)) 2)

rewrite33.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

549×	`log1p-expm1-u_binary64`
549×	`expm1-log1p-u_binary64`
240×	`log-prod_binary64`
151×	`pow2_binary64`
114×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	144	9
2	1580	8

Stop Event

1×	node limit

Counts

1 → 21

Calls

1 calls:

33.0ms

(pow.f64 (cbrt.f64 (+.f64 x 1)) 2)

simplify25.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
621×	`associate-l_binary64`
536×	`unswap-sqr_binary64`
380×	`associate-r_binary64`
222×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	47
1	51	43
2	124	37
3	396	33
4	1134	28
5	3786	28

Stop Event

1×	node limit

Counts

25 → 28

prune286.0ms (7.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	167	4	171
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	170	9	179

Error

0.1b

Counts

179 → 9

Alt Table

Status	Error	Program
	0.6b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (pow.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x 1))))) 3)))
	0.6b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
	12.6b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (cbrt.f64 (*.f64 (pow.f64 (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x 1))) 3) x))))
	29.1b	(-.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 x))
	0.6b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) 3) (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
	8.0b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (/.f64 (*.f64 (cbrt.f64 x) (+.f64 x (+.f64 x 1))) (fma.f64 (cbrt.f64 x) (-.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)))))
	12.5b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (/.f64 (*.f64 (cbrt.f64 x) (+.f64 x (+.f64 x 1))) (fma.f64 (cbrt.f64 x) (-.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)))))
	15.5b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (pow.f64 (sqrt.f64 (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x 1))))) 2)))
	28.4b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (exp.f64 (log.f64 (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x 1))))))))

Compiler

Compiled 5029 to 3254 computations (35.3% saved)

regimes535.0ms (13.4%)

Accuracy

Total 0.4b remaining (66.8%)

Threshold costs 0.4b (66.8%)

Counts

228 → 1

Compiler

Compiled 10862 to 8037 computations (26% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	36
1	26	36
2	30	36
3	32	36
4	33	36

Stop Event

1×

saturated

end183.0ms (4.6%)

Compiler: Compiled 296 to 215 computations (27.4% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Details

analyze1.0ms (0%)

sample1.2s (30.9%)

simplify9.0ms (0.2%)

prune1.0ms (0%)

localize7.0ms (0.2%)

series660.0ms (16.5%)

rewrite51.0ms (1.3%)

simplify27.0ms (0.7%)

prune150.0ms (3.8%)

localize11.0ms (0.3%)

series54.0ms (1.4%)

rewrite56.0ms (1.4%)

simplify29.0ms (0.7%)

prune309.0ms (7.7%)

localize15.0ms (0.4%)

prune304.0ms (7.6%)

localize13.0ms (0.3%)

series5.0ms (0.1%)

rewrite33.0ms (0.8%)

simplify25.0ms (0.6%)

prune286.0ms (7.1%)

regimes535.0ms (13.4%)

simplify2.0ms (0.1%)

end183.0ms (4.6%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11