Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.8s (18.1%)

Results

706.0ms	2038×	body	1024	valid
486.0ms	4417×	body	128	valid
286.0ms	1081×	body	512	valid
100.0ms	528×	body	256	valid
83.0ms	192×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

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

28.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	2.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

rewrite236.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

1304×	`*-un-lft-identity_binary64`
1000×	`times-frac_binary64`
859×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
523×	`add-cube-cbrt_binary64`

Counts

2 → 748

Calls

2 calls:

46.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
7.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify819.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

552×	`fma-neg_binary64`
418×	`distribute-rgt-in_binary64`
361×	`unsub-neg_binary64`
255×	`fma-udef_binary64`
202×	`associate-+r-_binary64`

Counts

772 → 551

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	521	54026
1	1234	30580
2	2848	22272
3	4495	22270
4	4718	22270

prune777.0ms (7.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	547	4	551
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	548	4	552

Error

0.0b

Counts

552 → 4

Alt Table

Status	Error	Program
	33.0b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	30.9b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
	45.0b	(+.f64 (fma.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 x 1)) (neg.f64 (.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x 1))) (+.f64 x 1) (.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1))))
▶	28.9b	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

Compiler

Compiled 29160 to 21556 computations (26.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	0.0b	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
	2.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series13.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

10.0ms

(sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

3.0ms

(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

rewrite344.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

863×	`*-un-lft-identity_binary64`
324×	`times-frac_binary64`
235×	`distribute-lft-out--_binary64`
202×	`sqrt-prod_binary64`
152×	`distribute-lft-out_binary64`

Counts

2 → 196

Calls

2 calls:

110.0ms

(sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

77.0ms

(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

simplify443.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

543×	`distribute-rgt-in_binary64`
532×	`fma-neg_binary64`
297×	`associate-l_binary64`
273×	`associate-r_binary64`
246×	`fma-def_binary64`

Counts

212 → 173

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	177	6292
1	351	5987
2	990	5837
3	2758	5696
4	4973	5688
5	5174	5688

prune3.7s (37.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1317	2	1319
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	1320	3	1323

Error

Counts

1323 → 3

Alt Table

Status	Error	Program
	30.9b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
▶	25.9b	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))
	33.0b	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))

Compiler

Compiled 84539 to 62680 computations (25.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 x) (-.f64 x 1))
✓	0.0b	(-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x)
✓	1.7b	(+.f64 (-.f64 x 1) (-.f64 -1 x))
✓	13.8b	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))

series16.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))
5.0ms	(*.f64 (+.f64 1 x) (-.f64 x 1))
4.0ms	(-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x)
2.0ms	(+.f64 (-.f64 x 1) (-.f64 -1 x))

rewrite96.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
61×	`add-sqr-sqrt_binary64`
45×	`prod-diff_binary64`
45×	`add-cube-cbrt_binary64`
18×	`add-log-exp_binary64`

Counts

4 → 187

Calls

4 calls:

23.0ms	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))
22.0ms	(+.f64 (-.f64 x 1) (-.f64 -1 x))
18.0ms	(*.f64 (+.f64 1 x) (-.f64 x 1))
7.0ms	(-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x)

simplify209.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-neg_binary64`
299×	`distribute-rgt-in_binary64`
280×	`cancel-sign-sub-inv_binary64`
277×	`distribute-lft-in_binary64`
184×	`associate-l_binary64`

Counts

235 → 297

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	290	3681
1	701	2973
2	3052	2946
3	4665	2943
4	4967	2943

prune577.0ms (5.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	297	3	300

Error

Counts

300 → 3

Alt Table

Status	Error	Program
▶	30.9b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
✓	25.9b	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))
	33.0b	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))

Compiler

Compiled 9228 to 6373 computations (30.9% saved)

localize13.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.1b	(fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x))

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x))

simplify163.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

906×	`distribute-rgt-in_binary64`
886×	`distribute-lft-in_binary64`
524×	`fma-def_binary64`
431×	`*-commutative_binary64`
292×	`associate-+r+_binary64`

Counts

22 → 26

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	340
1	48	304
2	142	304
3	614	304
4	3296	304
5	3922	304
6	4952	304
7	4998	304
8	4801	304

prune24.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	26	3	29

Error

Counts

29 → 3

Alt Table

Status	Error	Program
✓	30.9b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
✓	25.9b	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))
	33.0b	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))

Compiler

Compiled 474 to 334 computations (29.5% saved)

regimes387.0ms (3.9%)

Accuracy

Total 0.0b remaining (56.6%)

Threshold costs 0.0b (56.6%)

Counts

61 → 3

Compiler

Compiled 2697 to 1983 computations (26.5% saved)

bsearch12.0ms (0.1%)

Steps

Iters	Range		Point
2	1327.2471198748406	55628.15765906012	22073.547601646904
1	-7.1546292106118625e+22	-214747898527.92075	-124526734327407820.0

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	62
1	43	62
2	55	62
3	68	62
4	74	62
5	76	62
6	73	62

end162.0ms (1.6%)

Compiler: Compiled 141 to 106 computations (24.8% saved)

Details

analyze5.0ms (0.1%)

sample1.8s (18.1%)

simplify88.0ms (0.9%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite236.0ms (2.4%)

simplify819.0ms (8.2%)

prune777.0ms (7.8%)

localize8.0ms (0.1%)

series13.0ms (0.1%)

rewrite344.0ms (3.5%)

simplify443.0ms (4.4%)

prune3.7s (37.3%)

localize22.0ms (0.2%)

series16.0ms (0.2%)

rewrite96.0ms (1%)

simplify209.0ms (2.1%)

prune577.0ms (5.8%)

localize13.0ms (0.1%)

series6.0ms (0.1%)

rewrite2.0ms (0%)

simplify163.0ms (1.6%)

prune24.0ms (0.2%)

regimes387.0ms (3.9%)

bsearch12.0ms (0.1%)

simplify5.0ms (0%)

end162.0ms (1.6%)

Profiling