Details

analyze1.1s (7.9%)

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
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
14%	85.2%	0.8%	11
19.1%	79.1%	1.8%	12
25.5%	70.3%	4.1%	13
30.3%	64.6%	5.1%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (8.6%)

Results

923.0ms	8256×	body	128	valid
278.0ms	2316×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess40.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

474×	`unsub-neg_binary64`
459×	`div-sub_binary64`
340×	`fma-def_binary64`
337×	`cancel-sign-sub-inv_binary64`
283×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	91
1	70	91
2	146	77
3	357	77
4	844	77
5	2267	77
6	3971	77
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify52.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
660×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	64	11
4	150	11
5	309	11
6	545	11
7	995	11
8	1956	11
9	2893	11
10	3408	11
11	3457	11
12	3487	11
13	3492	11
14	3492	11

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.6b	(fma.f64 (-.f64 z x) (/.f64 y t) x)
	5.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.5b	(fma.f64 (-.f64 z x) (/.f64 y t) x)

series15.0ms (0.1%)

Counts

1 → 48

Calls

12 calls:

1.0ms	(fma.f64 (-.f64 z x) (/.f64 y t) x)	x	-inf
1.0ms	(fma.f64 (-.f64 z x) (/.f64 y t) x)	y	-inf
1.0ms	(fma.f64 (-.f64 z x) (/.f64 y t) x)	x	inf
1.0ms	(fma.f64 (-.f64 z x) (/.f64 y t) x)	z	-inf
1.0ms	(fma.f64 (-.f64 z x) (/.f64 y t) x)	z	0

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

455×	`log-prod_binary64`
446×	`prod-diff_binary64`
197×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	175	11
2	2476	11

Stop Event

1×	node limit

Counts

1 → 29

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-def_binary64`
737×	`fma-neg_binary64`
248×	`cancel-sign-sub-inv_binary64`
179×	`distribute-rgt-in_binary64`
131×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	777
1	71	561
2	166	552
3	387	480
4	832	480
5	1538	480
6	2608	480
7	3638	480
8	3678	480
9	3722	480
10	3780	480
11	3780	480

Stop Event

1×

saturated

Counts

77 → 42

prune25.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Error

0.0b

Counts

44 → 4

Alt Table

Status	Error	Program
	4.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	2.8b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z x) (/.f64 y t) x)) 3)
✓	1.6b	(fma.f64 (-.f64 z x) (/.f64 y t) x)
	5.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 624 to 186 computations (70.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 z x) (/.f64 y t) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z x) (/.f64 y t) x)) 3)
	1.5b	(fma.f64 (-.f64 z x) (/.f64 y t) x)

series9.8s (68.8%)

Counts

2 → 40

Calls

24 calls:

2.5s	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z x) (/.f64 y t) x)) 3)	y	0
2.4s	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z x) (/.f64 y t) x)) 3)	t	inf
2.4s	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z x) (/.f64 y t) x)) 3)	t	-inf
2.2s	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z x) (/.f64 y t) x)) 3)	x	0
286.0ms	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z x) (/.f64 y t) x)) 3)	z	0

rewrite50.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

446×	`prod-diff_binary64`
207×	`fma-def_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
177×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	235	24
2	2954	24

Stop Event

1×	node limit

Counts

2 → 68

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

347×	`cancel-sign-sub-inv_binary64`
294×	`unswap-sqr_binary64`
183×	`associate-r_binary64`
182×	`associate-/r/_binary64`
175×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	3534
1	688	3518
2	2714	3465

Stop Event

1×	node limit

Counts

108 → 103

prune88.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	143	6	149

Error

0.0b

Counts

149 → 6

Alt Table

Status	Error	Program
	4.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	5.8b	(fma.f64 (*.f64 (-.f64 z x) y) (/.f64 1 t) x)
▶	2.2b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z x)) 2) (*.f64 (cbrt.f64 (-.f64 z x)) (/.f64 y t)) x)
✓	2.8b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z x) (/.f64 y t) x)) 3)
✓	1.6b	(fma.f64 (-.f64 z x) (/.f64 y t) x)
	5.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 4062 to 1879 computations (53.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 z x)) 2)
✓	0.5b	(cbrt.f64 (-.f64 z x))
✓	0.7b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z x)) 2) (*.f64 (cbrt.f64 (-.f64 z x)) (/.f64 y t)) x)
✓	2.9b	(*.f64 (cbrt.f64 (-.f64 z x)) (/.f64 y t))

series707.0ms (5%)

Counts

4 → 84

Calls

36 calls:

219.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z x)) 2) (*.f64 (cbrt.f64 (-.f64 z x)) (/.f64 y t)) x)	x
94.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z x)) 2) (*.f64 (cbrt.f64 (-.f64 z x)) (/.f64 y t)) x)	z
23.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z x)) 2) (*.f64 (cbrt.f64 (-.f64 z x)) (/.f64 y t)) x)	t
23.0ms	(*.f64 (cbrt.f64 (-.f64 z x)) (/.f64 y t))	z
22.0ms	(pow.f64 (cbrt.f64 (-.f64 z x)) 2)	z

rewrite59.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

451×	`prod-diff_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`
124×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	258	40
2	3375	40

Stop Event

1×	node limit

Counts

4 → 90

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

492×	`cancel-sign-sub-inv_binary64`
410×	`times-frac_binary64`
244×	`distribute-rgt-neg-in_binary64`
236×	`associate-r_binary64`
200×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	2570
1	701	2414
2	2629	2408

Stop Event

1×	node limit

Counts

174 → 161

prune174.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	201	7	208

Error

Counts

208 → 7

Alt Table

Status	Error	Program
▶	4.3b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	4.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	5.8b	(fma.f64 (*.f64 (-.f64 z x) y) (/.f64 1 t) x)
✓	2.2b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z x)) 2) (*.f64 (cbrt.f64 (-.f64 z x)) (/.f64 y t)) x)
✓	2.8b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z x) (/.f64 y t) x)) 3)
✓	1.6b	(fma.f64 (-.f64 z x) (/.f64 y t) x)
	5.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 5872 to 2952 computations (49.7% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
✓	0.0b	(/.f64 t (-.f64 z x))
✓	4.6b	(/.f64 y (/.f64 t (-.f64 z x)))

series56.0ms (0.4%)

Counts

3 → 120

Calls

33 calls:

3.0ms	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))	y	-inf
3.0ms	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))	x	-inf
3.0ms	(/.f64 y (/.f64 t (-.f64 z x)))	z	-inf
3.0ms	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))	y	inf
2.0ms	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))	z	-inf

rewrite73.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

384×	`fma-def_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
205×	`fma-neg_binary64`
178×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	211	28
2	3385	28

Stop Event

1×	node limit

Counts

3 → 148

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

556×	`cancel-sign-sub-inv_binary64`
521×	`fma-neg_binary64`
198×	`fma-def_binary64`
192×	`times-frac_binary64`
180×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	1842
1	209	1626
2	600	1518
3	2472	1482

Stop Event

1×	node limit

Counts

268 → 181

prune100.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	2	1	3
Picked	0	1	1
Done	2	1	3
Total	184	4	188

Error

Counts

188 → 4

Alt Table

Status	Error	Program
✓	4.3b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	1.6b	(+.f64 x (/.f64 (-.f64 z x) (/.f64 t y)))
✓	1.6b	(fma.f64 (-.f64 z x) (/.f64 y t) x)
	5.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 2751 to 879 computations (68% saved)

regimes262.0ms (1.8%)

Accuracy

Total 1.2b remaining (98.8%)

Threshold costs 0b (0%)

Counts

33 → 3

Compiler

Compiled 2156 to 1383 computations (35.9% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
0.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Steps

Iters	Point		Range
9.012799917002246e+291	∈ [	9.012799917002246e+291	,	2.1878371153038434e+304	]
-1.3132758008782921e+247	∈ [	-1.3132758008782921e+247	,	-1.1132485234492941e+246	]

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	73
1	26	73
2	31	73
3	33	73
4	34	73

Stop Event

1×

saturated

end63.0ms (0.4%)

Stop Event

1×

fuel

Compiler

Compiled 159 to 69 computations (56.6% saved)

Details

analyze1.1s (7.9%)

sample1.2s (8.6%)

preprocess40.0ms (0.3%)

simplify52.0ms (0.4%)

prune3.0ms (0%)

localize5.0ms (0%)

series15.0ms (0.1%)

rewrite40.0ms (0.3%)

simplify75.0ms (0.5%)

prune25.0ms (0.2%)

localize8.0ms (0.1%)

series9.8s (68.8%)

rewrite50.0ms (0.4%)

simplify66.0ms (0.5%)

prune88.0ms (0.6%)

localize11.0ms (0.1%)

series707.0ms (5%)

rewrite59.0ms (0.4%)

simplify61.0ms (0.4%)

prune174.0ms (1.2%)

localize7.0ms (0%)

series56.0ms (0.4%)

rewrite73.0ms (0.5%)

simplify61.0ms (0.4%)

prune100.0ms (0.7%)

regimes262.0ms (1.8%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end63.0ms (0.4%)

Profiling