Details

analyze557.0ms (2.1%)

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
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.4s (5.4%)

Results

983.0ms	7164×	body	128	valid
137.0ms	431×	body	512	valid
118.0ms	307×	body	1024	valid
68.0ms	309×	body	256	valid
21.0ms	45×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify94.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

930×	`fma-def_binary64`
859×	`div-sub_binary64`
817×	`unsub-neg_binary64`
555×	`neg-mul-1_binary64`
380×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	24	17
2	52	17
3	155	17
4	477	17
5	1268	17
6	3213	17
7	4154	17
8	4434	17
9	4965	17
10	4951	17

prune5.0ms (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

11.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.7b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	11.8b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

Compiler

Compiled 100 to 54 computations (46% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	11.8b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series94.0ms (0.4%)

Counts

2 → 108

Calls

2 calls:

63.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
31.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

simplify140.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

523×	`cancel-sign-sub-inv_binary64`
479×	`sub-neg_binary64`
353×	`associate-+r+_binary64`
286×	`+-commutative_binary64`
272×	`associate-+l+_binary64`

Counts

172 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	6269
1	1045	6192
2	3851	6156
3	5233	6156

prune100.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Error

0.3b

Counts

138 → 6

Alt Table

Status	Error	Program
▶	12.3b	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)
	34.3b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.1b	(-.f64 (+.f64 x (/.f64 (.f64 y t) a)) (/.f64 (.f64 y x) a))
✓	11.7b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	30.4b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	34.6b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))

Compiler

Compiled 4653 to 1420 computations (69.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
✓	0.6b	(cbrt.f64 (-.f64 a z))
✓	11.7b	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)

series175.0ms (0.6%)

Counts

4 → 156

Calls

4 calls:

75.0ms	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)
36.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
32.0ms	(/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z)))
31.0ms	(cbrt.f64 (-.f64 a z))

rewrite77.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`times-frac_binary64`
139×	`add-sqr-sqrt_binary64`
137×	`*-un-lft-identity_binary64`
124×	`cbrt-div_binary64`
123×	`cbrt-prod_binary64`

Counts

4 → 268

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z)))
11.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
2.0ms	(cbrt.f64 (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)

simplify365.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

370×	`associate-/r*_binary64`
343×	`times-frac_binary64`
341×	`associate-/l/_binary64`
322×	`associate-/l*_binary64`
195×	`div-sub_binary64`

Counts

424 → 470

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	738	16952
1	1949	16483
2	4853	16289
3	4962	16289

prune391.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	572	0	572
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	572	6	578

Error

0.3b

Counts

578 → 6

Alt Table

Status	Error	Program
✓	12.3b	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)
	34.3b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.1b	(-.f64 (+.f64 x (/.f64 (.f64 y t) a)) (/.f64 (.f64 y x) a))
✓	11.7b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
▶	30.4b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	34.6b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))

Compiler

Compiled 22795 to 6343 computations (72.2% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a z))
✓	0.0b	(/.f64 z (-.f64 a z))
✓	1.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series76.0ms (0.3%)

Counts

3 → 84

Calls

3 calls:

49.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
18.0ms	(/.f64 y (-.f64 a z))
9.0ms	(/.f64 z (-.f64 a z))

rewrite383.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

1359×	`*-un-lft-identity_binary64`
1351×	`add-sqr-sqrt_binary64`
1338×	`times-frac_binary64`
882×	`prod-diff_binary64`
801×	`add-cube-cbrt_binary64`

Counts

3 → 1043

Calls

3 calls:

52.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
4.0ms	(/.f64 z (-.f64 a z))
4.0ms	(/.f64 y (-.f64 a z))

simplify2.3s (8.4%)

Algorithm

1×	egg-herbie

Rules

421×	`*-commutative_binary64`
356×	`distribute-rgt-in_binary64`
310×	`fma-udef_binary64`
263×	`unsub-neg_binary64`
250×	`distribute-lft-in_binary64`

Counts

1127 → 968

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1367	65557
1	2311	49274
2	3889	40637
3	4669	40637
4	4982	40637
5	4865	40637

prune1.1s (4.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	966	2	968
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	967	7	974

Error

0.3b

Counts

974 → 7

Alt Table

Status	Error	Program
✓	12.3b	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)
	34.3b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.1b	(-.f64 (+.f64 x (/.f64 (.f64 y t) a)) (/.f64 (.f64 y x) a))
✓	11.7b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
▶	30.4b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 1 (/.f64 (-.f64 a z) z))))
	40.2b	(/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z))
	34.6b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))

Compiler

Compiled 52657 to 9004 computations (82.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (-.f64 a z))
✓	0.0b	(/.f64 (-.f64 a z) z)
✓	0.2b	(/.f64 1 (/.f64 (-.f64 a z) z))
✓	1.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 1 (/.f64 (-.f64 a z) z))))

series187.0ms (0.7%)

Counts

3 → 96

Calls

3 calls:

153.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 1 (/.f64 (-.f64 a z) z))))
24.0ms	(/.f64 1 (/.f64 (-.f64 a z) z))
10.0ms	(/.f64 (-.f64 a z) z)

rewrite2.7s (10.1%)

Algorithm

1×	rewrite-expression-head

Rules

6501×	`times-frac_binary64`
4858×	`add-sqr-sqrt_binary64`
4839×	`*-un-lft-identity_binary64`
3255×	`add-cube-cbrt_binary64`
2604×	`prod-diff_binary64`

Counts

3 → 2909

Calls

3 calls:

356.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 1 (/.f64 (-.f64 a z) z))))
12.0ms	(/.f64 1 (/.f64 (-.f64 a z) z))
8.0ms	(/.f64 (-.f64 a z) z)

simplify9.3s (34.5%)

Algorithm

1×	egg-herbie

Rules

429×	`*-commutative_binary64`
324×	`fma-udef_binary64`
313×	`distribute-rgt-in_binary64`
262×	`distribute-lft-in_binary64`
241×	`unsub-neg_binary64`

Counts

3005 → 2501

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1418	274968
1	2225	190984
2	4855	190669
3	5181	190669

prune4.9s (18.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	2559	0	2559
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	2559	7	2566

Error

0.3b

Counts

2566 → 7

Alt Table

Status	Error	Program
✓	12.3b	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)
	34.3b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.1b	(-.f64 (+.f64 x (/.f64 (.f64 y t) a)) (/.f64 (.f64 y x) a))
✓	11.7b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
✓	30.4b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 1 (/.f64 (-.f64 a z) z))))
	40.2b	(/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z))
	34.6b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))

Compiler

Compiled 182895 to 66036 computations (63.9% saved)

regimes2.2s (8.2%)

Accuracy

Total 4.7b remaining (85.8%)

Threshold costs 0b (0%)

Counts

106 → 4

Compiler

Compiled 13200 to 7770 computations (41.1% saved)

bsearch7.0ms (0%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

27×	`+-commutative_binary64`
22×	`*-commutative_binary64`
20×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	192
1	68	192
2	90	192
3	118	192
4	157	192
5	175	192
6	185	192
7	188	192
8	188	192

end173.0ms (0.6%)

Compiler: Compiled 417 to 170 computations (59.2% saved)

Iter	Nodes	Cost
0	45	192
1	68	192
2	90	192
3	118	192
4	157	192
5	175	192
6	185	192
7	188	192
8	188	192

Iter	Nodes	Cost
0	45	192
1	68	192
2	90	192
3	118	192
4	157	192
5	175	192
6	185	192
7	188	192
8	188	192

Details

analyze557.0ms (2.1%)

sample1.4s (5.4%)

simplify94.0ms (0.3%)

prune5.0ms (0%)

localize9.0ms (0%)

series94.0ms (0.4%)

rewrite13.0ms (0%)

simplify140.0ms (0.5%)

prune100.0ms (0.4%)

localize14.0ms (0.1%)

series175.0ms (0.6%)

rewrite77.0ms (0.3%)

simplify365.0ms (1.4%)

prune391.0ms (1.5%)

localize8.0ms (0%)

series76.0ms (0.3%)

rewrite383.0ms (1.4%)

simplify2.3s (8.4%)

prune1.1s (4.2%)

localize15.0ms (0.1%)

series187.0ms (0.7%)

rewrite2.7s (10.1%)

simplify9.3s (34.5%)

prune4.9s (18.2%)

regimes2.2s (8.2%)

bsearch7.0ms (0%)

simplify18.0ms (0.1%)

end173.0ms (0.6%)

Profiling

Iter	Nodes	Cost
0	45	192
1	68	192
2	90	192
3	118	192
4	157	192
5	175	192
6	185	192
7	188	192
8	188	192