Details

analyze599.0ms (10.8%)

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
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
41.7%	58.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.0s (18.9%)

Symmetry

(sort y t)

Results

916.0ms	8256×	body	128	valid
54.0ms	403×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-neg_binary64`
750×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
204×	`unsub-neg_binary64`
135×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	35	13
3	88	13
4	231	13
5	568	13
6	1029	13
7	1474	13
8	1787	13
9	1744	13
10	1744	13
11	1905	13
12	1905	13
13	1862	13

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

7.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.1b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 t z))
✓	7.1b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

series140.0ms (2.5%)

Counts

2 → 84

Calls

2 calls:

128.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
12.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

10.0ms	(*.f64 (-.f64 y z) (-.f64 t z))
7.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

simplify162.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
452×	`associate-/l*_binary64`
442×	`associate-/r*_binary64`
280×	`associate-l_binary64`
188×	`fma-def_binary64`

Counts

173 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	5441
1	1244	5124
2	4955	5124
3	5000	5124

prune175.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	186	7	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	7	194

Error

0.0b

Counts

194 → 7

Alt Table

Status	Error	Program
	2.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	7.6b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (cbrt.f64 (-.f64 y z)) (-.f64 t z))))
	2.5b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	7.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	1.6b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
▶	0.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	31.1b	(*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 t z)))

Compiler

Compiled 5720 to 2111 computations (63.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 t z))
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	0.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))

series168.0ms (3%)

Counts

3 → 96

Calls

3 calls:

140.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
19.0ms	(/.f64 x (-.f64 t z))
9.0ms	(/.f64 1 (-.f64 y z))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
67×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 156

Calls

3 calls:

15.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
4.0ms	(/.f64 1 (-.f64 y z))
4.0ms	(/.f64 x (-.f64 t z))

simplify107.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

719×	`times-frac_binary64`
570×	`associate-/l*_binary64`
453×	`associate-/r*_binary64`
186×	`associate-*l/_binary64`
181×	`associate-*r/_binary64`

Counts

252 → 278

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	457	6865
1	1402	6443
2	5057	6443

prune219.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	276	2	278
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	278	7	285

Error

Counts

285 → 7

Alt Table

Status	Error	Program
▶	0.7b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	7.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	2.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	2.5b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	1.6b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
	28.8b	(.f64 (-.f64 (/.f64 -1 z) (/.f64 y (.f64 z z))) (/.f64 x (-.f64 t z)))
	31.1b	(*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 t z)))

Compiler

Compiled 7444 to 2930 computations (60.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 t z))
✓	0.7b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

series173.0ms (3.1%)

Counts

1 → 48

Calls

1 calls:

173.0ms

(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
157×	`*-un-lft-identity_binary64`
157×	`add-sqr-sqrt_binary64`
77×	`add-cube-cbrt_binary64`
40×	`distribute-lft-out--_binary64`

Counts

1 → 150

Calls

1 calls:

10.0ms

(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

simplify228.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
530×	`times-frac_binary64`
481×	`associate-/r*_binary64`
452×	`associate-/l*_binary64`
309×	`associate-/l/_binary64`

Counts

198 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	495	7582
1	1498	7346
2	4934	7270
3	5647	7270

prune169.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	270	7	277

Error

Counts

277 → 7

Alt Table

Status	Error	Program
✓	0.7b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	7.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	2.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	2.5b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
▶	1.6b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
	28.8b	(.f64 (-.f64 (/.f64 -1 z) (/.f64 y (.f64 z z))) (/.f64 x (-.f64 t z)))
	31.1b	(*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 t z)))

Compiler

Compiled 7646 to 2337 computations (69.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 t z))
✓	0.7b	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))
✓	1.0b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))

series157.0ms (2.8%)

Counts

2 → 96

Calls

2 calls:

121.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
36.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

rewrite157.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

1245×	`times-frac_binary64`
825×	`*-un-lft-identity_binary64`
825×	`add-sqr-sqrt_binary64`
457×	`add-cube-cbrt_binary64`
184×	`distribute-lft-out--_binary64`

Counts

2 → 621

Calls

2 calls:

22.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
11.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

simplify378.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

681×	`associate-/r/_binary64`
654×	`times-frac_binary64`
231×	`associate-/l/_binary64`
167×	`fma-def_binary64`
144×	`distribute-rgt-in_binary64`

Counts

717 → 720

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	681	23881
1	1959	23320
2	5004	23320

prune464.0ms (8.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	775	2	777
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	779	5	784

Error

Counts

784 → 5

Alt Table

Status	Error	Program
✓	0.7b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	7.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	2.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	1.8b	(/.f64 1 (.f64 (-.f64 y z) (.f64 (/.f64 1 x) (-.f64 t z))))
	2.9b	(*.f64 (/.f64 1 (/.f64 (-.f64 y z) x)) (/.f64 1 (-.f64 t z)))

Compiler

Compiled 21943 to 6100 computations (72.2% saved)

regimes797.0ms (14.4%)

Accuracy

Total 2.1b remaining (98.9%)

Threshold costs 0b (0%)

Counts

132 → 1

Compiler

Compiled 14446 to 9197 computations (36.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	18	13
3	20	13
4	21	13
5	21	13

end215.0ms (3.9%)

Compiler: Compiled 134 to 85 computations (36.6% saved)

Details

analyze599.0ms (10.8%)

sample1.0s (18.9%)

simplify76.0ms (1.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series140.0ms (2.5%)

rewrite23.0ms (0.4%)

simplify162.0ms (2.9%)

prune175.0ms (3.1%)

localize7.0ms (0.1%)

series168.0ms (3%)

rewrite35.0ms (0.6%)

simplify107.0ms (1.9%)

prune219.0ms (3.9%)

localize6.0ms (0.1%)

series173.0ms (3.1%)

rewrite29.0ms (0.5%)

simplify228.0ms (4.1%)

prune169.0ms (3%)

localize9.0ms (0.2%)

series157.0ms (2.8%)

rewrite157.0ms (2.8%)

simplify378.0ms (6.8%)

prune464.0ms (8.4%)

regimes797.0ms (14.4%)

simplify3.0ms (0%)

end215.0ms (3.9%)

Profiling