Details

analyze805.0ms (12.6%)

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)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
4.0ms	81×	body	128	nan
1.0ms	16×	body	128	invalid

Compiler

Compiled 29 to 21 computations (27.6% 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

16.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.9b	(.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
✓	1.0b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	4.2b	(/.f64 A (*.f64 V l))
✓	14.3b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series135.0ms (2.1%)

Counts

3 → 12

Calls

3 calls:

75.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
41.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
18.0ms	(/.f64 A (*.f64 V l))

rewrite16.0ms (0.2%)

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))))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
3.0ms	(/.f64 A (*.f64 V l))

simplify103.0ms (1.6%)

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

prune89.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	73	13	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	13	87

Error

7.1b

Counts

87 → 13

Alt Table

Status	Error	Program
	41.0b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	17.2b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	35.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	17.6b	(.f64 (.f64 (cbrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) (cbrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l)))))) (cbrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))))
	34.2b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	47.7b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	17.5b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	26.0b	(.f64 c0 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 A (.f64 V l))) 3)))
	35.0b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
▶	15.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
	46.5b	(cbrt.f64 (.f64 (.f64 (.f64 c0 c0) c0) (.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) (sqrt.f64 (/.f64 A (.f64 V l)))) (sqrt.f64 (/.f64 A (.f64 V l))))))
	16.8b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
	17.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))

Compiler

Compiled 1664 to 581 computations (65.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(cbrt.f64 A)
✓	1.0b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
✓	3.4b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
✓	14.3b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

series187.0ms (2.9%)

Counts

4 → 60

Calls

4 calls:

75.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
43.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
37.0ms	(cbrt.f64 A)
31.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))

rewrite63.0ms (1%)

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:

31.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
11.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
11.0ms	(.f64 c0 (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

prune176.0ms (2.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	218	5	223
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	222	14	236

Error

4.0b

Counts

236 → 14

Alt Table

Status	Error	Program
	41.0b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	17.2b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	35.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	17.6b	(.f64 (.f64 (cbrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) (cbrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l)))))) (cbrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))))
	34.2b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	17.2b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
	47.7b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	17.5b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
▶	17.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	24.9b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))
	36.9b	(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)))
	35.0b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	17.6b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 (cbrt.f64 A) l)) V)))
	19.6b	(.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 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))))

Compiler

Compiled 5052 to 1426 computations (71.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
✓	2.1b	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
	4.2b	(/.f64 A (*.f64 V l))
	14.3b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series668.0ms (10.5%)

Counts

2 → 36

Calls

2 calls:

596.0ms	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
72.0ms	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`sqrt-prod_binary64`
13×	`associate-r_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`sqrt-div_binary64`
9×	`*-un-lft-identity_binary64`

Counts

2 → 59

Calls

2 calls:

13.0ms	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
3.0ms	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))

simplify107.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

510×	`fma-neg_binary64`
461×	`unswap-sqr_binary64`
396×	`fma-def_binary64`
254×	`sqr-pow_binary64`
246×	`div-sub_binary64`

Counts

95 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1643
1	254	1503
2	586	1503
3	911	1359
4	1414	1359
5	2651	1359
6	4575	1359
7	4992	1359

prune167.0ms (2.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	212	12	224

Error

4.0b

Counts

224 → 12

Alt Table

Status	Error	Program
	35.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	34.2b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
▶	17.2b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
	17.3b	(.f64 (.f64 c0 (.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	47.7b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	17.5b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	17.6b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 (cbrt.f64 A) l)) V)))
	17.3b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))))
	17.2b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	35.0b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	17.8b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 1 (/.f64 (.f64 V l) A)))))
	24.9b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))

Compiler

Compiled 5164 to 1106 computations (78.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.0b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
✓	4.3b	(/.f64 (/.f64 A l) V)
✓	14.3b	(sqrt.f64 (/.f64 (/.f64 A l) V))

series132.0ms (2.1%)

Counts

3 → 48

Calls

3 calls:

72.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
40.0ms	(sqrt.f64 (/.f64 (/.f64 A l) V))
21.0ms	(/.f64 (/.f64 A l) V)

rewrite46.0ms (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)))
6.0ms	(sqrt.f64 (/.f64 (/.f64 A l) V))
5.0ms	(/.f64 (/.f64 A l) V)

simplify203.0ms (3.2%)

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

prune226.0ms (3.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	270	9	279
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	278	13	291

Error

0.0b

Counts

291 → 13

Alt Table

Status	Error	Program
	11.4b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 (/.f64 A l)) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 (/.f64 A l)) (cbrt.f64 V)))))
	8.2b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (.f64 (cbrt.f64 V) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (/.f64 A (cbrt.f64 l)) (cbrt.f64 V)))))
	35.0b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	23.6b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 l))) (sqrt.f64 (/.f64 (/.f64 A (sqrt.f64 l)) V))))
	35.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	5.3b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) l) (cbrt.f64 V)))))
	17.5b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	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))))
	12.9b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A l)))) (sqrt.f64 (/.f64 (cbrt.f64 (/.f64 A l)) V)))
	17.5b	(.f64 (.f64 c0 (sqrt.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 A l) V)) (cbrt.f64 (/.f64 (/.f64 A l) V))))) (sqrt.f64 (cbrt.f64 (/.f64 (/.f64 A l) V))))
	24.9b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))
	17.2b	(*.f64 (sqrt.f64 (/.f64 (/.f64 A l) V)) c0)
	4.4b	(.f64 (.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 l)) V)))

Compiler

Compiled 5109 to 1392 computations (72.8% saved)

regimes1.5s (23.4%)

Accuracy

Total 1.0b remaining (89.9%)

Threshold costs 0b (0%)

Counts

172 → 1

Compiler

Compiled 31733 to 18363 computations (42.1% saved)

simplify3.0ms (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

end7.0ms (0.1%)

Compiler: Compiled 75 to 39 computations (48% saved)

sample1.5s (23.9%)

Algorithm

1×

intervals

Results

390.0ms	8000×	body	128	valid
147.0ms	2994×	body	128	nan
46.0ms	880×	body	128	invalid

Compiler

Compiled 292 to 174 computations (40.4% saved)

Details

analyze805.0ms (12.6%)

sample42.0ms (0.7%)

simplify8.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series135.0ms (2.1%)

rewrite16.0ms (0.2%)

simplify103.0ms (1.6%)

prune89.0ms (1.4%)

localize10.0ms (0.2%)

series187.0ms (2.9%)

rewrite63.0ms (1%)

simplify131.0ms (2%)

prune176.0ms (2.8%)

localize8.0ms (0.1%)

series668.0ms (10.5%)

rewrite21.0ms (0.3%)

simplify107.0ms (1.7%)

prune167.0ms (2.6%)

localize6.0ms (0.1%)

series132.0ms (2.1%)

rewrite46.0ms (0.7%)

simplify203.0ms (3.2%)

prune226.0ms (3.5%)

regimes1.5s (23.4%)

simplify3.0ms (0%)

end7.0ms (0.1%)

sample1.5s (23.9%)

Profiling