Details

analyze1.7s (13.7%)

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
7.8%	92%	0.2%	8
15.6%	84.2%	0.2%	9
23.4%	76.4%	0.2%	10
25%	74.9%	0.2%	11
37.9%	59.6%	2.5%	12
41.4%	55.7%	2.9%	13
46.3%	50.6%	3.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample2.3s (18.6%)

Results

1.7s	8256×	body	128	valid
363.0ms	1822×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify314.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

2150×	`fma-neg_binary64`
1161×	`div-sub_binary64`
897×	`fma-def_binary64`
414×	`associate-/l*_binary64`
410×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	33	16
3	65	16
4	113	16
5	197	16
6	397	16
7	814	16
8	1449	16
9	1832	16
10	1941	16
11	2036	16
12	2110	16
13	2224	16
14	2174	16
15	2652	16
16	2330	16
17	2358	16
18	2376	16
19	2392	16
20	2384	16
21	2468	16
22	2468	16
23	2388	16
24	2450	16
25	2428	16
26	2426	16
27	2428	16
28	2430	16
29	2440	16
30	2440	16
31	2255	16

prune3.0ms (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

5.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	5.6b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series115.0ms (0.9%)

Counts

3 → 78

Calls

3 calls:

69.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
27.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
19.0ms	(/.f64 t (-.f64 1 z))

rewrite138.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

408×	`fma-def_binary64`
234×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
209×	`fma-neg_binary64`
187×	`egg-rr`

Counts

3 → 187

Calls

3 calls:

127.0ms	(/.f64 t (-.f64 1 z))
127.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
127.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	247	36
2	3576	36
3	5005	36
0	0	0
1	0	0

simplify150.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

395×	`cancel-sign-sub-inv_binary64`
301×	`fma-neg_binary64`
294×	`fma-def_binary64`
243×	`div-sub_binary64`
233×	`times-frac_binary64`

Counts

265 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1328
1	234	1302
2	664	1241
3	1912	1195
4	4198	1195
5	4681	1195
6	4952	1195

prune416.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	9	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	229	9	238

Error

0.0b

Counts

238 → 9

Alt Table

Status	Error	Program
▶	5.6b	(*.f64 x (-.f64 (/.f64 y z) (pow.f64 (/.f64 (-.f64 1 z) t) -1)))
	32.1b	(*.f64 x (pow.f64 (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) 2))
	28.1b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 2) (pow.f64 (/.f64 t (-.f64 1 z)) 2)) x) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	6.3b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	5.6b	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))
	23.8b	(.f64 x (/.f64 (-.f64 (-.f64 1 z) (.f64 (/.f64 z y) t)) (*.f64 (/.f64 z y) (-.f64 1 z))))
	39.7b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3)) x) (fma.f64 (/.f64 t (-.f64 1 z)) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (pow.f64 (/.f64 y z) 2)))
	23.4b	(/.f64 (.f64 (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t)) x) (.f64 z (-.f64 1 z)))
	6.5b	(.f64 x (.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) (pow.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) 2)))

Compiler

Compiled 5337 to 2836 computations (46.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series140.0ms (1.2%)

Counts

4 → 124

Calls

4 calls:

76.0ms	(*.f64 x (-.f64 (/.f64 y z) (pow.f64 (/.f64 (-.f64 1 z) t) -1)))
32.0ms	(-.f64 (/.f64 y z) (pow.f64 (/.f64 (-.f64 1 z) t) -1))
20.0ms	(pow.f64 (/.f64 (-.f64 1 z) t) -1)
12.0ms	(/.f64 (-.f64 1 z) t)

rewrite142.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

335×	`fma-def_binary64`
255×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
209×	`egg-rr`
200×	`fma-neg_binary64`

Counts

4 → 209

Calls

4 calls:

132.0ms	(/.f64 (-.f64 1 z) t)
132.0ms	(-.f64 (/.f64 y z) (pow.f64 (/.f64 (-.f64 1 z) t) -1))
132.0ms	(pow.f64 (/.f64 (-.f64 1 z) t) -1)
132.0ms	(*.f64 x (-.f64 (/.f64 y z) (pow.f64 (/.f64 (-.f64 1 z) t) -1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	286	43
2	3785	43
3	5029	43
0	0	0
1	0	0

simplify153.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

955×	`fma-neg_binary64`
403×	`cancel-sign-sub-inv_binary64`
299×	`fma-def_binary64`
283×	`times-frac_binary64`
249×	`associate-l_binary64`

Counts

333 → 271

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1800
1	265	1774
2	709	1674
3	2048	1616
4	4426	1616
5	5019	1616

prune404.0ms (3.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	271	9	280

Error

0.0b

Counts

280 → 9

Alt Table

Status	Error	Program
✓	5.6b	(*.f64 x (-.f64 (/.f64 y z) (pow.f64 (/.f64 (-.f64 1 z) t) -1)))
	32.1b	(*.f64 x (pow.f64 (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) 2))
	28.1b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 2) (pow.f64 (/.f64 t (-.f64 1 z)) 2)) x) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	6.3b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
▶	5.6b	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))
	23.8b	(.f64 x (/.f64 (-.f64 (-.f64 1 z) (.f64 (/.f64 z y) t)) (*.f64 (/.f64 z y) (-.f64 1 z))))
	39.7b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3)) x) (fma.f64 (/.f64 t (-.f64 1 z)) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (pow.f64 (/.f64 y z) 2)))
	23.4b	(/.f64 (.f64 (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t)) x) (.f64 z (-.f64 1 z)))
	6.5b	(.f64 x (.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) (pow.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) 2)))

Compiler

Compiled 5648 to 3087 computations (45.3% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (neg.f64 t) (-.f64 1 z))
✓	0.1b	(fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z)))
✓	5.3b	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))

series114.0ms (0.9%)

Counts

3 → 108

Calls

3 calls:

68.0ms	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))
29.0ms	(fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z)))
17.0ms	(/.f64 (neg.f64 t) (-.f64 1 z))

rewrite220.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

600×	`prod-diff_binary64`
246×	`egg-rr`
209×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
188×	`log-pow_binary64`

Counts

3 → 246

Calls

3 calls:

204.0ms	(/.f64 (neg.f64 t) (-.f64 1 z))
204.0ms	(fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z)))
204.0ms	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	44
1	255	36
2	2914	36
3	4911	36
4	5365	36
0	0	0
1	0	0

simplify156.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

678×	`fma-neg_binary64`
633×	`times-frac_binary64`
594×	`cancel-sign-sub-inv_binary64`
305×	`fma-def_binary64`
223×	`associate-+l+_binary64`

Counts

354 → 294

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1662
1	230	1636
2	659	1575
3	1912	1541
4	4354	1541
5	5029	1541

prune503.0ms (4.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	294	9	303

Error

0.0b

Counts

303 → 9

Alt Table

Status	Error	Program
✓	5.6b	(*.f64 x (-.f64 (/.f64 y z) (pow.f64 (/.f64 (-.f64 1 z) t) -1)))
	32.1b	(*.f64 x (pow.f64 (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) 2))
	28.1b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 2) (pow.f64 (/.f64 t (-.f64 1 z)) 2)) x) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
▶	6.3b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	5.6b	(*.f64 x (fma.f64 y (/.f64 1 z) (/.f64 (neg.f64 t) (-.f64 1 z))))
	23.8b	(.f64 x (/.f64 (-.f64 (-.f64 1 z) (.f64 (/.f64 z y) t)) (*.f64 (/.f64 z y) (-.f64 1 z))))
	39.7b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3)) x) (fma.f64 (/.f64 t (-.f64 1 z)) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (pow.f64 (/.f64 y z) 2)))
	23.4b	(/.f64 (.f64 (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t)) x) (.f64 z (-.f64 1 z)))
	6.5b	(.f64 x (.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) (pow.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) 2)))

Compiler

Compiled 10739 to 6392 computations (40.5% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	3.2b	(/.f64 (*.f64 t x) (-.f64 1 z))
✓	5.6b	(/.f64 (*.f64 y x) z)

series111.0ms (0.9%)

Counts

3 → 42

Calls

3 calls:

56.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
31.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
24.0ms	(/.f64 (*.f64 y x) z)

rewrite151.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

270×	`fma-neg_binary64`
256×	`expm1-udef_binary64`
255×	`log1p-udef_binary64`
168×	`egg-rr`
141×	`add-sqr-sqrt_binary64`

Counts

3 → 168

Calls

3 calls:

142.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
142.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
142.0ms	(/.f64 (*.f64 y x) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	271	36
2	4142	36
3	5203	36
0	0	0
1	0	0

simplify130.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

635×	`cancel-sign-sub-inv_binary64`
593×	`fma-neg_binary64`
462×	`times-frac_binary64`
365×	`fma-def_binary64`
294×	`div-sub_binary64`

Counts

210 → 204

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	63	857
1	197	845
2	603	717
3	1962	675
4	4104	673
5	4821	673
6	5045	673

prune322.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	204	9	213

Error

Counts

213 → 9

Alt Table

Status	Error	Program
✓	5.6b	(*.f64 x (-.f64 (/.f64 y z) (pow.f64 (/.f64 (-.f64 1 z) t) -1)))
	32.1b	(*.f64 x (pow.f64 (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) 2))
	28.1b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 2) (pow.f64 (/.f64 t (-.f64 1 z)) 2)) x) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
✓	6.3b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	20.4b	(*.f64 (/.f64 x z) (+.f64 t y))
	6.5b	(.f64 x (.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) (pow.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) 2)))
	6.9b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 y x) z)) 3) (/.f64 (.f64 t x) (-.f64 1 z)))
	39.7b	(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3)) x) (fma.f64 (/.f64 t (-.f64 1 z)) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (pow.f64 (/.f64 y z) 2)))
	7.8b	(-.f64 (.f64 (/.f64 y 1) (/.f64 x z)) (/.f64 (.f64 t x) (-.f64 1 z)))

Compiler

Compiled 4260 to 1740 computations (59.2% saved)

regimes4.1s (33.8%)

Accuracy

Total 1.9b remaining (98.7%)

Threshold costs 0b (0%)

Counts

177 → 3

Compiler

Compiled 21715 to 14637 computations (32.6% saved)

bsearch12.0ms (0.1%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

84×	`distribute-rgt-neg-in_binary64`
67×	`cancel-sign-sub-inv_binary64`
53×	`distribute-lft-neg-in_binary64`
50×	`neg-sub0_binary64`
50×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	109
1	73	109
2	119	107
3	165	105
4	201	105
5	219	105
6	244	105
7	269	105
8	292	105
9	316	105
10	335	105
11	364	105
12	391	105
13	415	105
14	426	105
15	428	105
16	424	105

end305.0ms (2.5%)

Compiler: Compiled 350 to 221 computations (36.9% saved)

Iter	Nodes	Cost
0	34	109
1	73	109
2	119	107
3	165	105
4	201	105
5	219	105
6	244	105
7	269	105
8	292	105
9	316	105
10	335	105
11	364	105
12	391	105
13	415	105
14	426	105
15	428	105
16	424	105

Iter	Nodes	Cost
0	34	109
1	73	109
2	119	107
3	165	105
4	201	105
5	219	105
6	244	105
7	269	105
8	292	105
9	316	105
10	335	105
11	364	105
12	391	105
13	415	105
14	426	105
15	428	105
16	424	105

Details

analyze1.7s (13.7%)

sample2.3s (18.6%)

simplify314.0ms (2.6%)

prune3.0ms (0%)

localize14.0ms (0.1%)

series115.0ms (0.9%)

rewrite138.0ms (1.1%)

simplify150.0ms (1.2%)

prune416.0ms (3.4%)

localize15.0ms (0.1%)

series140.0ms (1.2%)

rewrite142.0ms (1.2%)

simplify153.0ms (1.3%)

prune404.0ms (3.3%)

localize16.0ms (0.1%)

series114.0ms (0.9%)

rewrite220.0ms (1.8%)

simplify156.0ms (1.3%)

prune503.0ms (4.2%)

localize15.0ms (0.1%)

series111.0ms (0.9%)

rewrite151.0ms (1.2%)

simplify130.0ms (1.1%)

prune322.0ms (2.7%)

regimes4.1s (33.8%)

bsearch12.0ms (0.1%)

simplify40.0ms (0.3%)

end305.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	34	109
1	73	109
2	119	107
3	165	105
4	201	105
5	219	105
6	244	105
7	269	105
8	292	105
9	316	105
10	335	105
11	364	105
12	391	105
13	415	105
14	426	105
15	428	105
16	424	105