Details

analyze751.0ms (11.5%)

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%	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)

sample1.4s (21.8%)

Symmetry

(sort V l)

Results

955.0ms	8256×	body	128	valid
421.0ms	3817×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify8.0ms (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

18.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	18.3b	(.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
✓	0.5b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	5.4b	(/.f64 A (*.f64 V l))
✓	15.7b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series114.0ms (1.7%)

Counts

3 → 12

Calls

3 calls:

61.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
35.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
17.0ms	(/.f64 A (*.f64 V l))

rewrite57.0ms (0.9%)

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:

44.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
6.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
3.0ms	(/.f64 A (*.f64 V l))

simplify94.0ms (1.4%)

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

prune87.0ms (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

7.0b

Counts

87 → 14

Alt Table

Status	Error	Program
	36.6b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	18.7b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	19.7b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
▶	16.7b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
	18.5b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	50.9b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))
	51.4b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 V)) (sqrt.f64 (/.f64 A l))))
	38.3b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	19.6b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	38.2b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	26.1b	(.f64 c0 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) (sqrt.f64 (/.f64 A (.f64 V l)))) (sqrt.f64 (/.f64 A (.f64 V l))))))
	36.8b	(exp.f64 (log.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)))
	18.3b	(pow.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l)))) 1)
	50.8b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))

Compiler

Compiled 1664 to 601 computations (63.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
✓	0.6b	(cbrt.f64 A)
✓	3.3b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
✓	15.7b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

series171.0ms (2.6%)

Counts

4 → 60

Calls

4 calls:

67.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
39.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
36.0ms	(cbrt.f64 A)
28.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))

rewrite36.0ms (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:

11.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
10.0ms	(.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)

simplify131.0ms (2%)

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

prune159.0ms (2.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	215	8	223
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	222	15	237

Error

3.8b

Counts

237 → 15

Alt Table

Status	Error	Program
	18.3b	(.f64 1 (.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0))
	19.3b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
	50.8b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	38.3b	(/.f64 (.f64 c0 (sqrt.f64 (.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (cbrt.f64 A)))) (sqrt.f64 (.f64 V l)))
	24.8b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	36.6b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	51.4b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 V)) (sqrt.f64 (/.f64 A l))))
	18.5b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	38.3b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	19.6b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	38.2b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	18.7b	(.f64 c0 (sqrt.f64 (.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 (cbrt.f64 A) (.f64 V l)))))
▶	17.0b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))))
	26.6b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))
	26.8b	(/.f64 (.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (cbrt.f64 A)))) (sqrt.f64 l))

Compiler

Compiled 5048 to 1446 computations (71.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 A)
✓	0.6b	(cbrt.f64 c0)
	3.3b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
	15.7b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

series32.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

32.0ms

(cbrt.f64 c0)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(cbrt.f64 c0)

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l/_binary64`
374×	`log-prod_binary64`
316×	`distribute-rgt-neg-in_binary64`
314×	`distribute-lft-neg-in_binary64`
287×	`*-commutative_binary64`

Counts

25 → 18

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	141
1	38	137
2	86	137
3	208	137
4	626	133
5	1904	133
6	2565	133
7	3552	133
8	4861	133

prune157.0ms (2.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	233	2	235
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	235	15	250

Error

3.8b

Counts

250 → 15

Alt Table

Status	Error	Program
	50.8b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	38.3b	(/.f64 (.f64 c0 (sqrt.f64 (.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (cbrt.f64 A)))) (sqrt.f64 (.f64 V l)))
	24.8b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	36.6b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	51.4b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 V)) (sqrt.f64 (/.f64 A l))))
	18.5b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	38.3b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	19.6b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	38.2b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	18.7b	(.f64 c0 (sqrt.f64 (.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 (cbrt.f64 A) (.f64 V l)))))
	25.3b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (/.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (cbrt.f64 A))) (sqrt.f64 l))))
	18.3b	(.f64 1 (.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0))
▶	17.3b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 c0)) (cbrt.f64 (cbrt.f64 c0))) (cbrt.f64 (cbrt.f64 c0))) (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))))
	26.6b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))
	26.8b	(/.f64 (.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (cbrt.f64 A)))) (sqrt.f64 l))

Compiler

Compiled 6929 to 1760 computations (74.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 c0)
✓	0.6b	(cbrt.f64 (cbrt.f64 c0))
	3.3b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
	15.7b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

series256.0ms (3.9%)

Counts

1 → 12

Calls

1 calls:

256.0ms

(cbrt.f64 (cbrt.f64 c0))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 16

Calls

1 calls:

1.0ms

(cbrt.f64 (cbrt.f64 c0))

simplify105.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

952×	`unswap-sqr_binary64`
687×	`sqr-pow_binary64`
466×	`*-commutative_binary64`
325×	`cube-prod_binary64`
311×	`associate-/l/_binary64`

Counts

28 → 21

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	234
1	51	234
2	89	234
3	160	230
4	410	226
5	652	226
6	1364	226
7	1508	226
8	1713	226
9	1972	226
10	2408	226
11	3558	226
12	3799	226
13	4679	226
14	4777	226

prune224.0ms (3.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	278	2	280
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	280	15	295

Error

3.8b

Counts

295 → 15

Alt Table

Status	Error	Program
	37.0b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 c0)) (cbrt.f64 (cbrt.f64 c0))) (cbrt.f64 (cbrt.f64 c0))) (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l)))))
	26.6b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))
	17.4b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 c0)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 c0))) (cbrt.f64 (cbrt.f64 (cbrt.f64 c0)))) (cbrt.f64 (cbrt.f64 (cbrt.f64 c0))))) (cbrt.f64 (cbrt.f64 c0))) (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))))
	50.8b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	38.3b	(/.f64 (.f64 c0 (sqrt.f64 (.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (cbrt.f64 A)))) (sqrt.f64 (.f64 V l)))
	24.8b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
	36.6b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	51.4b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 V)) (sqrt.f64 (/.f64 A l))))
	18.5b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	38.3b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	19.6b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	38.2b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	25.3b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (/.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (cbrt.f64 A))) (sqrt.f64 l))))
	18.3b	(.f64 1 (.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0))
	26.8b	(/.f64 (.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (cbrt.f64 A)))) (sqrt.f64 l))

Compiler

Compiled 10408 to 1787 computations (82.8% saved)

regimes2.3s (34.8%)

Accuracy

Total 2.7b remaining (33.9%)

Threshold costs 0b (0%)

Counts

147 → 5

Compiler

Compiled 36488 to 19328 computations (47% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	105
1	45	105
2	44	105

end319.0ms (4.9%)

Compiler: Compiled 585 to 314 computations (46.3% saved)

Details

analyze751.0ms (11.5%)

sample1.4s (21.8%)

simplify8.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series114.0ms (1.7%)

rewrite57.0ms (0.9%)

simplify94.0ms (1.4%)

prune87.0ms (1.3%)

localize9.0ms (0.1%)

series171.0ms (2.6%)

rewrite36.0ms (0.6%)

simplify131.0ms (2%)

prune159.0ms (2.4%)

localize14.0ms (0.2%)

series32.0ms (0.5%)

rewrite1.0ms (0%)

simplify74.0ms (1.1%)

prune157.0ms (2.4%)

localize16.0ms (0.3%)

series256.0ms (3.9%)

rewrite2.0ms (0%)

simplify105.0ms (1.6%)

prune224.0ms (3.4%)

regimes2.3s (34.8%)

bsearch6.0ms (0.1%)

simplify3.0ms (0.1%)

end319.0ms (4.9%)

Profiling