Details

analyze661.0ms (11.6%)

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
49.1%	50.7%	0.2%	9
49.5%	50.3%	0.2%	10
49.7%	50.1%	0.2%	11
50.2%	49.6%	0.2%	12
60.5%	39.3%	0.2%	13
60.6%	37.9%	1.4%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.3s (22.3%)

Results

940.0ms	8256×	body	128	valid
307.0ms	2754×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

preprocess43.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

739×	`fma-neg_binary64`
711×	`div-sub_binary64`
668×	`sub-neg_binary64`
220×	`fma-def_binary64`
155×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	91
1	96	91
2	214	91
3	362	91
4	779	91
5	1787	91
6	3963	91
0	4	4
1	4	4

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort x y)

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify28.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-neg_binary64`
579×	`fma-def_binary64`
349×	`div-sub_binary64`
329×	`cancel-sign-sub-inv_binary64`
297×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	45	13
3	74	13
4	155	13
5	299	13
6	610	13
7	1305	13
8	2658	13

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 48 to 31 computations (35.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

series21.0ms (0.4%)

Counts

1 → 48

Calls

12 calls:

3.0ms	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))	z	0
2.0ms	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))	y	inf
2.0ms	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))	z	inf
2.0ms	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))	z	-inf
2.0ms	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))	x	-inf

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`fma-def_binary64`
245×	`fma-neg_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
121×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	232	13
2	3583	13

Stop Event

1×	node limit

Counts

1 → 60

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-neg_binary64`
431×	`fma-def_binary64`
296×	`div-sub_binary64`
210×	`cancel-sign-sub-inv_binary64`
183×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	930
1	109	735
2	271	696
3	555	579
4	1403	579
5	3111	579

Stop Event

1×	node limit

Counts

108 → 77

prune57.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	3	78

Error

Counts

78 → 3

Alt Table

Status	Error	Program
	0.4b	(pow.f64 (/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t)) -1)
	33.0b	(.f64 (/.f64 1 (sqrt.f64 (.f64 t 2))) (/.f64 (+.f64 x (-.f64 y z)) (sqrt.f64 (*.f64 t 2))))
▶	0.0b	(fma.f64 1/2 (/.f64 (+.f64 x y) t) (neg.f64 (*.f64 1/2 (/.f64 z t))))

Compiler

Compiled 1268 to 616 computations (51.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 (+.f64 x y) t) (neg.f64 (*.f64 1/2 (/.f64 z t))))
✓	0.0b	(/.f64 (+.f64 x y) t)

series36.0ms (0.6%)

Counts

2 → 84

Calls

21 calls:

3.0ms	(fma.f64 1/2 (/.f64 (+.f64 x y) t) (neg.f64 (*.f64 1/2 (/.f64 z t))))	y	-inf
3.0ms	(/.f64 (+.f64 x y) t)	x	inf
2.0ms	(fma.f64 1/2 (/.f64 (+.f64 x y) t) (neg.f64 (*.f64 1/2 (/.f64 z t))))	x	-inf
2.0ms	(fma.f64 1/2 (/.f64 (+.f64 x y) t) (neg.f64 (*.f64 1/2 (/.f64 z t))))	y	inf
2.0ms	(fma.f64 1/2 (/.f64 (+.f64 x y) t) (neg.f64 (*.f64 1/2 (/.f64 z t))))	x	0

rewrite106.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`prod-diff_binary64`
299×	`egg-rr`
138×	`add-sqr-sqrt_binary64`
130×	`log1p-expm1-u_binary64`
130×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	269	24
2	3774	24

Stop Event

1×	node limit

Counts

2 → 299

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-neg_binary64`
385×	`fma-def_binary64`
248×	`div-sub_binary64`
242×	`distribute-rgt-in_binary64`
207×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	34	1263
1	91	1146
2	226	912
3	493	903
4	1288	903
5	2941	813

Stop Event

1×	node limit

Counts

383 → 321

prune230.0ms (4.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	320	1	321
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	321	3	324

Error

Counts

324 → 3

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 1/2 (pow.f64 (/.f64 t (+.f64 x y)) -1) (neg.f64 (*.f64 1/2 (/.f64 z t))))
	0.4b	(pow.f64 (/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t)) -1)
✓	0.0b	(fma.f64 1/2 (/.f64 (+.f64 x y) t) (neg.f64 (*.f64 1/2 (/.f64 z t))))

Compiler

Compiled 11641 to 5449 computations (53.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (pow.f64 (/.f64 t (+.f64 x y)) -1) (neg.f64 (*.f64 1/2 (/.f64 z t))))
✓	0.0b	(/.f64 t (+.f64 x y))
✓	0.3b	(pow.f64 (/.f64 t (+.f64 x y)) -1)

series168.0ms (3%)

Counts

3 → 120

Calls

30 calls:

14.0ms	(fma.f64 1/2 (pow.f64 (/.f64 t (+.f64 x y)) -1) (neg.f64 (*.f64 1/2 (/.f64 z t))))	x	inf
13.0ms	(fma.f64 1/2 (pow.f64 (/.f64 t (+.f64 x y)) -1) (neg.f64 (*.f64 1/2 (/.f64 z t))))	x	-inf
12.0ms	(fma.f64 1/2 (pow.f64 (/.f64 t (+.f64 x y)) -1) (neg.f64 (*.f64 1/2 (/.f64 z t))))	y	-inf
11.0ms	(pow.f64 (/.f64 t (+.f64 x y)) -1)	y	0
9.0ms	(fma.f64 1/2 (pow.f64 (/.f64 t (+.f64 x y)) -1) (neg.f64 (*.f64 1/2 (/.f64 z t))))	y	0

rewrite140.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

739×	`prod-diff_binary64`
316×	`egg-rr`
156×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	310	31
2	4213	31

Stop Event

1×	node limit

Counts

3 → 316

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-def_binary64`
399×	`fma-neg_binary64`
390×	`associate-/r/_binary64`
338×	`associate-/l/_binary64`
213×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	1659
1	189	1542
2	534	1482
3	2053	1416

Stop Event

1×	node limit

Counts

436 → 353

prune254.0ms (4.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	353	0	353
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	353	3	356

Error

Counts

356 → 3

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 1/2 (pow.f64 (/.f64 t (+.f64 x y)) -1) (neg.f64 (*.f64 1/2 (/.f64 z t))))
▶	0.4b	(pow.f64 (/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t)) -1)
✓	0.0b	(fma.f64 1/2 (/.f64 (+.f64 x y) t) (neg.f64 (*.f64 1/2 (/.f64 z t))))

Compiler

Compiled 11825 to 5551 computations (53.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x (-.f64 y z)) t)
✓	0.3b	(/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t))
✓	0.6b	(pow.f64 (/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t)) -1)

series1.2s (21.8%)

Counts

3 → 144

Calls

36 calls:

226.0ms	(pow.f64 (/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t)) -1)	z	inf
211.0ms	(pow.f64 (/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t)) -1)	z	-inf
170.0ms	(pow.f64 (/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t)) -1)	y	inf
170.0ms	(pow.f64 (/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t)) -1)	x	inf
169.0ms	(pow.f64 (/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t)) -1)	x	-inf

rewrite69.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

382×	`fma-def_binary64`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
210×	`fma-neg_binary64`
141×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	277	36
2	3926	36

Stop Event

1×	node limit

Counts

3 → 96

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

264×	`cancel-sign-sub-inv_binary64`
261×	`times-frac_binary64`
219×	`fma-def_binary64`
209×	`associate-/l*_binary64`
203×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	3592
1	821	3396
2	3390	3310

Stop Event

1×	node limit

Counts

240 → 172

prune142.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	172	3	175

Error

Counts

175 → 3

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 1/2 (pow.f64 (/.f64 t (+.f64 x y)) -1) (neg.f64 (*.f64 1/2 (/.f64 z t))))
✓	0.4b	(pow.f64 (/.f64 2 (/.f64 (+.f64 x (-.f64 y z)) t)) -1)
✓	0.0b	(fma.f64 1/2 (/.f64 (+.f64 x y) t) (neg.f64 (*.f64 1/2 (/.f64 z t))))

Compiler

Compiled 3622 to 1853 computations (48.8% saved)

regimes837.0ms (14.7%)

Accuracy

Total 0.0b remaining (16.4%)

Threshold costs 0.0b (16.4%)

Counts

105 → 1

Compiler

Compiled 12046 to 8921 computations (25.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`
7×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	23	15
2	41	15
3	63	13
4	85	13
5	92	13

Stop Event

1×

saturated

end58.0ms (1%)

Stop Event

1×

done

Remove

(sort x y)

Compiler

Compiled 103 to 73 computations (29.1% saved)

Details

analyze661.0ms (11.6%)

sample1.3s (22.3%)

preprocess43.0ms (0.8%)

simplify28.0ms (0.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series21.0ms (0.4%)

rewrite50.0ms (0.9%)

simplify42.0ms (0.7%)

prune57.0ms (1%)

localize8.0ms (0.1%)

series36.0ms (0.6%)

rewrite106.0ms (1.9%)

simplify58.0ms (1%)

prune230.0ms (4.1%)

localize10.0ms (0.2%)

series168.0ms (3%)

rewrite140.0ms (2.5%)

simplify65.0ms (1.1%)

prune254.0ms (4.5%)

localize7.0ms (0.1%)

series1.2s (21.8%)

rewrite69.0ms (1.2%)

simplify71.0ms (1.3%)

prune142.0ms (2.5%)

regimes837.0ms (14.7%)

simplify2.0ms (0%)

end58.0ms (1%)

Profiling