Details

analyze664.0ms (10.1%)

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
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.6s (24.5%)

Symmetry

(sort V l)

Results

1.0s	8256×	body	128	valid
547.0ms	4151×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	15	12
3	15	12

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

18.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	18.2b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.6b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	6.6b	(/.f64 A (*.f64 V l))
✓	14.8b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series123.0ms (1.9%)

Counts

3 → 12

Calls

3 calls:

65.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
41.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
16.0ms	(/.f64 A (*.f64 V l))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`

Counts

3 → 72

Calls

3 calls:

6.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
6.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
3.0ms	(/.f64 A (*.f64 V l))

simplify98.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-neg_binary64`
679×	`associate-/r/_binary64`
449×	`div-sub_binary64`
262×	`times-frac_binary64`
261×	`sub-neg_binary64`

Counts

84 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	1084
1	194	1009
2	561	1009
3	1631	1009
4	2187	1009
5	2446	1009
6	3196	1009
7	4340	1009
8	4698	1009

prune86.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	72	14	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	14	87

Error

8.3b

Counts

87 → 14

Alt Table

Status	Error	Program
	18.4b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
▶	15.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
	17.3b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	37.5b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	38.8b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	18.5b	(.f64 c0 (sqrt.f64 (.f64 A (/.f64 1 (*.f64 V l)))))
	49.8b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	18.2b	(.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 (.f64 V l) A))))
	18.9b	(.f64 (.f64 c0 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	42.3b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	51.2b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 V)) (sqrt.f64 (/.f64 A l))))
	48.8b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) V)) (sqrt.f64 (/.f64 (sqrt.f64 A) l))))
	17.2b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
	18.6b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))

Compiler

Compiled 1658 to 595 computations (64.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 A)
✓	1.6b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
✓	3.5b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
✓	14.8b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

series172.0ms (2.6%)

Counts

4 → 60

Calls

4 calls:

68.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
41.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
34.0ms	(cbrt.f64 A)
29.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
27×	`add-exp-log_binary64`
26×	`associate-r_binary64`
22×	`*-un-lft-identity_binary64`

Counts

4 → 114

Calls

4 calls:

14.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
9.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
6.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
1.0ms	(cbrt.f64 A)

simplify126.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

589×	`times-frac_binary64`
401×	`*-commutative_binary64`
383×	`associate-/l/_binary64`
276×	`unswap-sqr_binary64`
275×	`associate-/r*_binary64`

Counts

174 → 187

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	2248
1	429	1954
2	1568	1941
3	3749	1927
4	4729	1927
5	4945	1927
6	4963	1927

prune176.0ms (2.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	216	7	223
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	223	14	237

Error

3.5b

Counts

237 → 14

Alt Table

Status	Error	Program
	18.9b	(.f64 (.f64 c0 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	37.7b	(.f64 c0 (/.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (cbrt.f64 A))) (sqrt.f64 (.f64 V l))))
	17.3b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	17.2b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
	37.5b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	38.8b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	22.7b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	24.8b	(/.f64 (.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (cbrt.f64 A)))) (sqrt.f64 l))
	18.6b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	18.4b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	42.3b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
▶	15.9b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))))
	24.5b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))
	51.5b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A l))) (sqrt.f64 V))

Compiler

Compiled 5058 to 1416 computations (72% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 A)
✓	1.9b	(sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
	3.5b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
	14.8b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

series666.0ms (10.1%)

Counts

1 → 28

Calls

1 calls:

666.0ms

(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`sqrt-div_binary64`
6×	`sqrt-pow1_binary64`
5×	`sqrt-prod_binary64`
5×	`pow1_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 22

Calls

1 calls:

7.0ms

(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Rules

944×	`div-sub_binary64`
702×	`fma-def_binary64`
690×	`fma-neg_binary64`
680×	`exp-sum_binary64`
418×	`exp-diff_binary64`

Counts

50 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	777
1	157	713
2	290	713
3	859	545
4	2180	545
5	4188	545
6	5436	545

prune298.0ms (4.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	444	0	444
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	444	14	458

Error

3.5b

Counts

458 → 14

Alt Table

Status	Error	Program
	18.9b	(.f64 (.f64 c0 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	37.7b	(.f64 c0 (/.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (cbrt.f64 A))) (sqrt.f64 (.f64 V l))))
	17.3b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
▶	17.2b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
	37.5b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	38.8b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	22.7b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	24.8b	(/.f64 (.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (cbrt.f64 A)))) (sqrt.f64 l))
	18.6b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	18.4b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	42.3b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
✓	15.9b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))))
	24.5b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))
	51.5b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A l))) (sqrt.f64 V))

Compiler

Compiled 16435 to 2698 computations (83.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.6b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
✓	4.8b	(/.f64 (/.f64 A l) V)
✓	14.8b	(sqrt.f64 (/.f64 (/.f64 A l) V))

series120.0ms (1.8%)

Counts

3 → 48

Calls

3 calls:

65.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
38.0ms	(sqrt.f64 (/.f64 (/.f64 A l) V))
17.0ms	(/.f64 (/.f64 A l) V)

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

213×	`times-frac_binary64`
134×	`add-sqr-sqrt_binary64`
117×	`*-un-lft-identity_binary64`
117×	`add-cube-cbrt_binary64`
89×	`sqrt-prod_binary64`

Counts

3 → 197

Calls

3 calls:

14.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
5.0ms	(sqrt.f64 (/.f64 (/.f64 A l) V))
4.0ms	(/.f64 (/.f64 A l) V)

simplify184.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-neg_binary64`
565×	`fma-def_binary64`
384×	`associate-/l/_binary64`
301×	`associate-l_binary64`
291×	`div-sub_binary64`

Counts

245 → 279

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	4078
1	539	3931
2	1320	3881
3	2679	3881
4	2781	3881
5	3004	3881
6	3520	3881
7	5052	3881

prune265.0ms (4%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	269	10	279
Fresh	8	4	12
Picked	0	1	1
Done	0	1	1
Total	277	16	293

Error

0.1b

Counts

293 → 16

Alt Table

Status	Error	Program
	14.3b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 A))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) l) V)))
	13.8b	(.f64 c0 (.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 V l)))))
	42.3b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	25.3b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 (sqrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 A (sqrt.f64 l)) V)))
	7.9b	(.f64 (.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) l) (cbrt.f64 V))))
	37.8b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 A 1)) (sqrt.f64 (/.f64 (/.f64 1 l) V))))
✓	15.9b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))))
	5.3b	(.f64 (.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 l)) V)))
	3.7b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 l))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 l)) V))))
	17.3b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
✓	17.2b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
	22.1b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (/.f64 1 (sqrt.f64 l)) (*.f64 (cbrt.f64 V) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (/.f64 A (sqrt.f64 l)) (cbrt.f64 V)))))
	1.1b	(.f64 (.f64 c0 (fabs.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 l)) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 l)) (cbrt.f64 V))))
	11.7b	(.f64 (.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 (/.f64 A l)) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (cbrt.f64 (/.f64 A l)) (cbrt.f64 V))))
	22.7b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	24.5b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))

Compiler

Compiled 5167 to 1427 computations (72.4% saved)

regimes1.4s (22%)

Accuracy

Total 1.1b remaining (91.4%)

Threshold costs 0b (0%)

Counts

169 → 1

Compiler

Compiled 30765 to 17969 computations (41.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`fabs-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	19	35
2	22	35
3	22	35

end333.0ms (5%)

Compiler: Compiled 408 to 235 computations (42.4% saved)

Details

analyze664.0ms (10.1%)

sample1.6s (24.5%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series123.0ms (1.9%)

rewrite18.0ms (0.3%)

simplify98.0ms (1.5%)

prune86.0ms (1.3%)

localize10.0ms (0.1%)

series172.0ms (2.6%)

rewrite38.0ms (0.6%)

simplify126.0ms (1.9%)

prune176.0ms (2.7%)

localize12.0ms (0.2%)

series666.0ms (10.1%)

rewrite8.0ms (0.1%)

simplify69.0ms (1%)

prune298.0ms (4.5%)

localize6.0ms (0.1%)

series120.0ms (1.8%)

rewrite44.0ms (0.7%)

simplify184.0ms (2.8%)

prune265.0ms (4%)

regimes1.4s (22%)

simplify2.0ms (0%)

end333.0ms (5%)

Profiling