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)

sample1.3s (33.8%)

Results

542.0ms	2087×	body	1024	valid
358.0ms	4406×	body	128	valid
204.0ms	1039×	body	512	valid
72.0ms	212×	body	2048	valid
71.0ms	512×	body	256	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

prune2.0ms (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))

series45.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

33.0ms	(cbrt.f64 x)
8.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
4.0ms	(cbrt.f64 (+.f64 x 1))

rewrite54.0ms (1.4%)

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:

51.0ms	(cbrt.f64 (+.f64 x 1))
51.0ms	(cbrt.f64 x)
51.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

simplify35.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

415×	`cancel-sign-sub-inv_binary64`
382×	`fma-neg_binary64`
355×	`associate-l_binary64`
282×	`fma-def_binary64`
253×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	843
1	253	825
2	704	649
3	2200	533

Stop Event

1×	node limit

Counts

166 → 177

prune169.0ms (4.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	171	6	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	172	6	178

Error

12.6b

Counts

178 → 6

Alt Table

Status	Error	Program
	28.1b	(-.f64 (cbrt.f64 (+.f64 x 1)) (*.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)))
▶	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)))))
	46.5b	(fma.f64 1/3 (cbrt.f64 (/.f64 (/.f64 1 x) x)) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 11))) -10/243))))
	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)))
	28.1b	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3))
	27.9b	(-.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3) (cbrt.f64 x))

Compiler

Compiled 3626 to 2437 computations (32.8% 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))

series28.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

22.0ms	(*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))
5.0ms	(cbrt.f64 (pow.f64 (+.f64 x 1) 2))
1.0ms	(-.f64 (+.f64 x 1) x)

rewrite59.0ms (1.6%)

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:

56.0ms	(*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))
56.0ms	(-.f64 (+.f64 x 1) x)
56.0ms	(cbrt.f64 (pow.f64 (+.f64 x 1) 2))

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-def_binary64`
452×	`fma-neg_binary64`
429×	`unswap-sqr_binary64`
291×	`associate-r_binary64`
289×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	824
1	320	759
2	932	668
3	3593	624

Stop Event

1×	node limit

Counts

229 → 232

prune393.0ms (10.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	276	4	280
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	277	9	286

Error

12.5b

Counts

286 → 9

Alt Table

Status	Error	Program
	26.9b	(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 2) 1/3) (*.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))))
	46.5b	(fma.f64 1/3 (cbrt.f64 (/.f64 (/.f64 1 x) x)) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 11))) -10/243))))
	28.1b	(-.f64 (cbrt.f64 (+.f64 x 1)) (*.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)))
▶	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)))))
	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)))
	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)))))
	28.1b	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3))
	27.9b	(-.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3) (cbrt.f64 x))

Compiler

Compiled 9090 to 6145 computations (32.4% saved)

localize14.0ms (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))

prune303.0ms (8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	195	7	202
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	202	9	211

Error

0.2b

Counts

211 → 9

Alt Table

Status	Error	Program
	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)))))
	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))))
	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)))))
	46.5b	(fma.f64 1/3 (cbrt.f64 (/.f64 (/.f64 1 x) x)) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 11))) -10/243))))
▶	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)))))
	14.9b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (.f64 2 (cbrt.f64 (.f64 x 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)))))
	28.1b	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3))

Compiler

Compiled 6675 to 4505 computations (32.5% saved)

localize12.0ms (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)

series6.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

6.0ms

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

rewrite30.0ms (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:

29.0ms

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

simplify36.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

902×	`fma-def_binary64`
808×	`times-frac_binary64`
452×	`associate-/l*_binary64`
167×	`cancel-sign-sub-inv_binary64`
159×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	383
1	161	375
2	442	255
3	1549	200

Stop Event

1×	node limit

Counts

33 → 44

prune415.0ms (11%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	245	4	249
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	248	10	258

Error

0.1b

Counts

258 → 10

Alt Table

Status	Error	Program
	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)))))
	46.5b	(fma.f64 1/3 (cbrt.f64 (/.f64 (/.f64 1 x) x)) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 11))) -10/243))))
	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))))
	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)))))
	14.9b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) (.f64 2 (cbrt.f64 (.f64 x x)))))
	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)))
	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)))
	28.1b	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 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)))))

Compiler

Compiled 8076 to 5423 computations (32.9% saved)

regimes616.0ms (16.3%)

Accuracy

Total 0.4b remaining (69.5%)

Threshold costs 0.4b (69.5%)

Counts

265 → 1

Compiler

Compiled 12374 to 9167 computations (25.9% 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

end218.0ms (5.8%)

Compiler: Compiled 324 to 240 computations (25.9% 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%)

sample1.3s (33.8%)

simplify9.0ms (0.2%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series45.0ms (1.2%)

rewrite54.0ms (1.4%)

simplify35.0ms (0.9%)

prune169.0ms (4.5%)

localize11.0ms (0.3%)

series28.0ms (0.7%)

rewrite59.0ms (1.6%)

simplify41.0ms (1.1%)

prune393.0ms (10.4%)

localize14.0ms (0.4%)

prune303.0ms (8%)

localize12.0ms (0.3%)

series6.0ms (0.2%)

rewrite30.0ms (0.8%)

simplify36.0ms (0.9%)

prune415.0ms (11%)

regimes616.0ms (16.3%)

simplify2.0ms (0.1%)

end218.0ms (5.8%)

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