Details

analyze1.2s (22.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
12.5%	87.3%	0.2%	8
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
23.4%	76.4%	0.2%	11
31.6%	68.2%	0.2%	12
34.5%	64.9%	0.6%	13
40.3%	59.2%	0.6%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample1.5s (27.6%)

Results

1.1s	8256×	body	128	valid
400.0ms	3170×	body	128	invalid

Compiler

Compiled 40 to 28 computations (30% saved)

preprocess37.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

447×	`distribute-neg-frac_binary64`
318×	`sub-neg_binary64`
281×	`div-sub_binary64`
279×	`fma-def_binary64`
225×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	154
1	122	154
2	290	154
3	609	154
4	1387	133
5	3618	133
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify38.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

587×	`div-sub_binary64`
387×	`fma-def_binary64`
326×	`fma-neg_binary64`
244×	`distribute-neg-frac_binary64`
227×	`associate-/l*_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	22
2	59	22
3	116	22
4	255	20
5	552	16
6	1238	14
7	3482	14
8	4716	14

Stop Event

1×	node limit

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
▶	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
✓	0.2b	(.f64 (.f64 z 3) y)
✓	0.4b	(/.f64 y (*.f64 z 3))
✓	5.6b	(/.f64 t (.f64 (.f64 z 3) y))

series62.0ms (1.1%)

Counts

4 → 132

Calls

33 calls:

8.0ms	(/.f64 t (.f64 (.f64 z 3) y))	t	0
5.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))	t	inf
5.0ms	(.f64 (.f64 z 3) y)	y	-inf
3.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))	x	0
2.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))	t	-inf

rewrite76.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

264×	`log1p-udef_binary64`
155×	`egg-rr`
144×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`
138×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	278	44
2	4554	44

Stop Event

1×	node limit

Counts

4 → 155

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-neg_binary64`
475×	`fma-def_binary64`
274×	`cancel-sign-sub-inv_binary64`
264×	`div-sub_binary64`
224×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	1477
1	63	1339
2	135	1333
3	233	1267
4	409	1267
5	724	1267
6	1280	1267
7	2122	1267
8	3631	1267

Stop Event

1×	node limit

Counts

287 → 170

prune188.0ms (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	160	10	170
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	161	11	172

Error

0.0b

Counts

172 → 11

Alt Table

Status	Error	Program
	33.6b	(+.f64 (-.f64 x (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (/.f64 1/3 z)))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
	3.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (pow.f64 (cbrt.f64 t) 2) (*.f64 (cbrt.f64 t) (/.f64 (/.f64 1/3 z) y))))
	25.9b	(/.f64 (-.f64 (.f64 1/3 (/.f64 t y)) (.f64 1/3 y)) z)
	2.9b	(+.f64 (-.f64 x (pow.f64 (cbrt.f64 (.f64 y (/.f64 1/3 z))) 3)) (/.f64 t (.f64 (*.f64 z 3) y)))
▶	2.6b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	44.3b	(.f64 (+.f64 (pow.f64 (-.f64 x (.f64 y (/.f64 1/3 z))) 3) (pow.f64 (.f64 t (/.f64 (/.f64 1/3 z) y)) 3)) (/.f64 1 (+.f64 (pow.f64 (-.f64 x (.f64 y (/.f64 1/3 z))) 2) (.f64 (.f64 t (/.f64 (/.f64 1/3 z) y)) (-.f64 (.f64 t (/.f64 (/.f64 1/3 z) y)) (-.f64 x (.f64 y (/.f64 1/3 z))))))))
	3.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (pow.f64 (cbrt.f64 (.f64 t (/.f64 (/.f64 1/3 z) y))) 3))
	33.8b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 (sqrt.f64 t) 1) (/.f64 (sqrt.f64 t) (.f64 z (.f64 3 y)))))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	2.9b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 1/3 (/.f64 t (*.f64 y z))))

Compiler

Compiled 4538 to 2885 computations (36.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	0.2b	(.f64 (.f64 z 3) y)
✓	0.3b	(*.f64 (/.f64 1 z) (/.f64 y 3))
	5.6b	(/.f64 t (.f64 (.f64 z 3) y))

series30.0ms (0.6%)

Counts

2 → 72

Calls

18 calls:

3.0ms	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))	x	0
3.0ms	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))	z	-inf
2.0ms	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))	t	-inf
2.0ms	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))	x	-inf
2.0ms	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))	t	inf

rewrite39.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

173×	`add-sqr-sqrt_binary64`
164×	`add-cbrt-cube_binary64`
164×	`log1p-expm1-u_binary64`
164×	`expm1-log1p-u_binary64`
160×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	345	29

Stop Event

1×	node limit

Counts

2 → 108

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-neg_binary64`
467×	`fma-def_binary64`
343×	`div-sub_binary64`
274×	`cancel-sign-sub-inv_binary64`
224×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	949
1	58	811
2	123	805
3	219	739
4	395	739
5	710	739
6	1257	739
7	2100	739
8	3582	739
9	4984	739

Stop Event

1×	node limit

Counts

180 → 124

prune181.0ms (3.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	179	5	184
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	188	7	195

Error

Counts

195 → 7

Alt Table

Status	Error	Program
	22.1b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (expm1.f64 (log1p.f64 (.f64 z (*.f64 3 y))))))
	3.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (pow.f64 (cbrt.f64 (.f64 t (/.f64 (/.f64 1/3 z) y))) 3))
▶	2.5b	(-.f64 x (-.f64 (.f64 1/3 (/.f64 y z)) (/.f64 (.f64 1/3 (/.f64 t z)) y)))
	2.6b	(+.f64 (-.f64 x (/.f64 (/.f64 1 z) (/.f64 3 y))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (.f64 (/.f64 1 z) (/.f64 t (*.f64 3 y))))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	40.3b	(/.f64 (+.f64 (+.f64 x (.f64 1/3 (/.f64 y z))) (.f64 (.f64 z (/.f64 (.f64 3 y) t)) (-.f64 (.f64 x x) (pow.f64 (.f64 1/3 (/.f64 y z)) 2)))) (.f64 (.f64 z (/.f64 (.f64 3 y) t)) (+.f64 x (.f64 1/3 (/.f64 y z)))))

Compiler

Compiled 4672 to 2788 computations (40.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/3 (/.f64 y z)) (/.f64 (.f64 1/3 (/.f64 t z)) y))
✓	0.3b	(*.f64 1/3 (/.f64 t z))
✓	0.3b	(*.f64 1/3 (/.f64 y z))
✓	5.3b	(/.f64 (*.f64 1/3 (/.f64 t z)) y)

series51.0ms (0.9%)

Counts

4 → 72

Calls

30 calls:

4.0ms	(-.f64 (.f64 1/3 (/.f64 y z)) (/.f64 (.f64 1/3 (/.f64 t z)) y))	t	-inf
3.0ms	(*.f64 1/3 (/.f64 y z))	y	inf
2.0ms	(-.f64 (.f64 1/3 (/.f64 y z)) (/.f64 (.f64 1/3 (/.f64 t z)) y))	t	inf
2.0ms	(/.f64 (*.f64 1/3 (/.f64 t z)) y)	t	0
2.0ms	(-.f64 (.f64 1/3 (/.f64 y z)) (/.f64 (.f64 1/3 (/.f64 t z)) y))	z	0

rewrite79.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

299×	`fma-def_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
197×	`egg-rr`
169×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	252	41
2	3813	41

Stop Event

1×	node limit

Counts

4 → 197

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Rules

739×	`times-frac_binary64`
676×	`fma-neg_binary64`
496×	`fma-def_binary64`
335×	`cancel-sign-sub-inv_binary64`
258×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	891
1	65	801
2	171	801
3	386	801
4	913	801
5	1665	801
6	3451	801

Stop Event

1×	node limit

Counts

269 → 207

prune219.0ms (4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	208	6	214

Error

Counts

214 → 6

Alt Table

Status	Error	Program
	22.1b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (expm1.f64 (log1p.f64 (.f64 z (*.f64 3 y))))))
▶	2.4b	(-.f64 x (fma.f64 (.f64 (/.f64 t z) -1/3) (/.f64 1 y) (.f64 1/3 (/.f64 y z))))
	2.7b	(-.f64 x (-.f64 (.f64 1/3 (/.f64 y z)) (.f64 1/3 (/.f64 (/.f64 t z) y))))
	2.6b	(+.f64 (-.f64 x (/.f64 (/.f64 1 z) (/.f64 3 y))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	40.3b	(/.f64 (+.f64 (+.f64 x (.f64 1/3 (/.f64 y z))) (.f64 (.f64 z (/.f64 (.f64 3 y) t)) (-.f64 (.f64 x x) (pow.f64 (.f64 1/3 (/.f64 y z)) 2)))) (.f64 (.f64 z (/.f64 (.f64 3 y) t)) (+.f64 x (.f64 1/3 (/.f64 y z)))))

Compiler

Compiled 5460 to 3085 computations (43.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (fma.f64 (.f64 (/.f64 t z) -1/3) (/.f64 1 y) (.f64 1/3 (/.f64 y z))))
✓	0.3b	(*.f64 (/.f64 t z) -1/3)
	0.3b	(*.f64 1/3 (/.f64 y z))
✓	5.1b	(fma.f64 (.f64 (/.f64 t z) -1/3) (/.f64 1 y) (.f64 1/3 (/.f64 y z)))

series55.0ms (1%)

Counts

3 → 108

Calls

27 calls:

5.0ms	(fma.f64 (.f64 (/.f64 t z) -1/3) (/.f64 1 y) (.f64 1/3 (/.f64 y z)))	z	-inf
5.0ms	(-.f64 x (fma.f64 (.f64 (/.f64 t z) -1/3) (/.f64 1 y) (.f64 1/3 (/.f64 y z))))	t	-inf
3.0ms	(-.f64 x (fma.f64 (.f64 (/.f64 t z) -1/3) (/.f64 1 y) (.f64 1/3 (/.f64 y z))))	x	0
2.0ms	(-.f64 x (fma.f64 (.f64 (/.f64 t z) -1/3) (/.f64 1 y) (.f64 1/3 (/.f64 y z))))	x	-inf
2.0ms	(-.f64 x (fma.f64 (.f64 (/.f64 t z) -1/3) (/.f64 1 y) (.f64 1/3 (/.f64 y z))))	x	inf

rewrite70.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

661×	`prod-diff_binary64`
160×	`add-sqr-sqrt_binary64`
150×	`add-cbrt-cube_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	322	48
2	4209	48

Stop Event

1×	node limit

Counts

3 → 95

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

551×	`fma-neg_binary64`
392×	`cancel-sign-sub-inv_binary64`
283×	`fma-def_binary64`
268×	`div-sub_binary64`
227×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	1480
1	90	1252
2	215	1246
3	462	1180
4	1088	1180
5	2137	1180
6	4306	1180

Stop Event

1×	node limit

Counts

203 → 118

prune114.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	140	6	146

Error

Counts

146 → 6

Alt Table

Status	Error	Program
	22.1b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (expm1.f64 (log1p.f64 (.f64 z (*.f64 3 y))))))
✓	2.4b	(-.f64 x (fma.f64 (.f64 (/.f64 t z) -1/3) (/.f64 1 y) (.f64 1/3 (/.f64 y z))))
	2.7b	(-.f64 x (-.f64 (.f64 1/3 (/.f64 y z)) (.f64 1/3 (/.f64 (/.f64 t z) y))))
	2.6b	(+.f64 (-.f64 x (/.f64 (/.f64 1 z) (/.f64 3 y))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	40.3b	(/.f64 (+.f64 (+.f64 x (.f64 1/3 (/.f64 y z))) (.f64 (.f64 z (/.f64 (.f64 3 y) t)) (-.f64 (.f64 x x) (pow.f64 (.f64 1/3 (/.f64 y z)) 2)))) (.f64 (.f64 z (/.f64 (.f64 3 y) t)) (+.f64 x (.f64 1/3 (/.f64 y z)))))

Compiler

Compiled 3530 to 1907 computations (46% saved)

regimes1.0s (18.6%)

Accuracy

Total 1.5b remaining (97.7%)

Threshold costs 0b (0%)

Counts

129 → 3

Compiler

Compiled 15724 to 10989 computations (30.1% saved)

bsearch62.0ms (1.1%)

Algorithm

2×	binary-search

Calls

2 calls:

36.0ms	t
19.0ms	t

Steps

Iters	Point		Range
6.568065307651204e+190	∈ [	6.472571550635483e+190	,	1.1958236452304568e+199	]
-1.3110050459942516e-113	∈ [	-2.1482505042311445e-113	,	-1.125250442704989e-121	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

42×	`distribute-rgt-neg-in_binary64`
26×	`distribute-lft-neg-in_binary64`
26×	`cancel-sign-sub-inv_binary64`
23×	`distribute-lft-neg-out_binary64`
21×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	83
1	56	81
2	72	81
3	96	81
4	116	81
5	132	81
6	162	81
7	206	81
8	247	81
9	278	81
10	295	81
11	299	81

Stop Event

1×

saturated

end107.0ms (2%)

Stop Event

1×

fuel

Compiler

Compiled 262 to 175 computations (33.2% saved)

Iter	Nodes	Cost
0	34	83
1	56	81
2	72	81
3	96	81
4	116	81
5	132	81
6	162	81
7	206	81
8	247	81
9	278	81
10	295	81
11	299	81

Iter	Nodes	Cost
0	34	83
1	56	81
2	72	81
3	96	81
4	116	81
5	132	81
6	162	81
7	206	81
8	247	81
9	278	81
10	295	81
11	299	81

Details

analyze1.2s (22.1%)

sample1.5s (27.6%)

preprocess37.0ms (0.7%)

simplify38.0ms (0.7%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series62.0ms (1.1%)

rewrite76.0ms (1.4%)

simplify79.0ms (1.4%)

prune188.0ms (3.5%)

localize12.0ms (0.2%)

series30.0ms (0.6%)

rewrite39.0ms (0.7%)

simplify69.0ms (1.3%)

prune181.0ms (3.3%)

localize9.0ms (0.2%)

series51.0ms (0.9%)

rewrite79.0ms (1.5%)

simplify52.0ms (1%)

prune219.0ms (4%)

localize10.0ms (0.2%)

series55.0ms (1%)

rewrite70.0ms (1.3%)

simplify64.0ms (1.2%)

prune114.0ms (2.1%)

regimes1.0s (18.6%)

bsearch62.0ms (1.1%)

simplify9.0ms (0.2%)

end107.0ms (2%)

Profiling

Iter	Nodes	Cost
0	34	83
1	56	81
2	72	81
3	96	81
4	116	81
5	132	81
6	162	81
7	206	81
8	247	81
9	278	81
10	295	81
11	299	81