Details

analyze653.0ms (6.5%)

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 (10.1%)

Symmetry

(sort y t)

Results

894.0ms	8256×	body	128	valid
43.0ms	405×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify80.0ms (0.8%)

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

7.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.0b	(/.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))
✓	7.0b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

series127.0ms (1.3%)

Counts

2 → 84

Calls

2 calls:

114.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
12.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite23.0ms (0.2%)

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:

8.0ms	(*.f64 (-.f64 y z) (-.f64 t z))
7.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

simplify119.0ms (1.2%)

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

prune154.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	188	6	194

Error

0.0b

Counts

194 → 6

Alt Table

Status	Error	Program
	7.2b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	2.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
▶	1.9b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
✓	7.0b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	25.2b	(.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t z))) (+.f64 y z))

Compiler

Compiled 5663 to 2081 computations (63.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))

series296.0ms (2.9%)

Counts

4 → 108

Calls

4 calls:

142.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
79.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
38.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
37.0ms	(cbrt.f64 x)

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
42×	`associate-r_binary64`
36×	`cbrt-prod_binary64`

Counts

4 → 163

Calls

4 calls:

21.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
6.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
5.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify115.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
678×	`associate-/l*_binary64`
491×	`associate-/r*_binary64`
190×	`fma-def_binary64`
138×	`*-commutative_binary64`

Counts

271 → 313

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	494	7735
1	1554	6690
2	5178	6690

prune268.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	345	2	347
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	346	7	353

Error

Counts

353 → 7

Alt Table

Status	Error	Program
	2.1b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))) (cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z))))) (cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))))
	7.2b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
▶	2.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
	2.1b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x)))) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
✓	1.9b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
✓	7.0b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 9962 to 2974 computations (70.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 t z))
✓	0.6b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	1.6b	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

series157.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

111.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
30.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))
15.0ms	(/.f64 x (-.f64 t z))

rewrite160.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

1260×	`times-frac_binary64`
844×	`*-un-lft-identity_binary64`
844×	`add-sqr-sqrt_binary64`
468×	`add-cube-cbrt_binary64`
188×	`distribute-lft-out--_binary64`

Counts

3 → 660

Calls

3 calls:

21.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
10.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))
4.0ms	(/.f64 x (-.f64 t z))

simplify428.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

753×	`associate-/r/_binary64`
672×	`times-frac_binary64`
271×	`associate-/l/_binary64`
167×	`fma-def_binary64`
153×	`distribute-rgt-in_binary64`

Counts

780 → 773

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	715	24963
1	2044	24462
2	5306	24462

prune572.0ms (5.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	772	1	773
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	773	7	780

Error

Counts

780 → 7

Alt Table

Status	Error	Program
▶	2.1b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))) (cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z))))) (cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))))
	7.2b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
✓	2.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
	3.5b	(/.f64 1 (*.f64 (/.f64 (-.f64 y z) x) (-.f64 t z)))
✓	1.9b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
✓	7.0b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 22014 to 6132 computations (72.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
	0.6b	(cbrt.f64 x)
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
✓	24.2b	(cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z))))

series1.5s (15.1%)

Counts

1 → 48

Calls

1 calls:

1.5s	(cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-div_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`cbrt-prod_binary64`
1×	`associate-*r/_binary64`

Counts

1 → 14

Calls

1 calls:

9.0ms

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

simplify179.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

901×	`fma-def_binary64`
451×	`*-commutative_binary64`
233×	`+-commutative_binary64`
192×	`associate-+r+_binary64`
175×	`associate-r_binary64`

Counts

62 → 102

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1017	12127
1	3988	11857
2	5144	11857

prune1.7s (16.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1158	0	1158
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	1158	7	1165

Error

Counts

1165 → 7

Alt Table

Status	Error	Program
✓	2.1b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))) (cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z))))) (cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))))
	7.2b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
✓	2.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
	3.5b	(/.f64 1 (*.f64 (/.f64 (-.f64 y z) x) (-.f64 t z)))
✓	1.9b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
✓	7.0b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 114464 to 35543 computations (68.9% saved)

regimes2.2s (21.9%)

Accuracy

Total 1.2b remaining (98.6%)

Threshold costs 0b (0%)

Counts

278 → 1

Compiler

Compiled 54382 to 26664 computations (51% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	20	43
2	26	43
3	28	43
4	29	43
5	29	43

end235.0ms (2.3%)

Compiler: Compiled 272 to 127 computations (53.3% saved)

Details

analyze653.0ms (6.5%)

sample1.0s (10.1%)

simplify80.0ms (0.8%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series127.0ms (1.3%)

rewrite23.0ms (0.2%)

simplify119.0ms (1.2%)

prune154.0ms (1.5%)

localize9.0ms (0.1%)

series296.0ms (2.9%)

rewrite48.0ms (0.5%)

simplify115.0ms (1.1%)

prune268.0ms (2.7%)

localize7.0ms (0.1%)

series157.0ms (1.6%)

rewrite160.0ms (1.6%)

simplify428.0ms (4.2%)

prune572.0ms (5.7%)

localize17.0ms (0.2%)

series1.5s (15.1%)

rewrite10.0ms (0.1%)

simplify179.0ms (1.8%)

prune1.7s (16.6%)

regimes2.2s (21.9%)

simplify3.0ms (0%)

end235.0ms (2.3%)

Profiling