Details

analyze650.0ms (13.4%)

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 (29.4%)

Symmetry

(sort V l)

Results

967.0ms	8256×	body	128	valid
416.0ms	3859×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify9.0ms (0.2%)

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

20.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	20.0b	(.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
✓	0.7b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	4.4b	(/.f64 A (*.f64 V l))
✓	18.4b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series86.0ms (1.8%)

Counts

3 → 12

Calls

3 calls:

45.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
24.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
17.0ms	(/.f64 A (*.f64 V l))

rewrite20.0ms (0.4%)

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:

11.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
3.0ms	(/.f64 A (*.f64 V l))
2.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

simplify95.0ms (2%)

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 (1.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	69	17	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	17	87

Error

10.3b

Counts

87 → 17

Alt Table

Status	Error	Program
	50.7b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))
	37.9b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	20.2b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	28.0b	(.f64 c0 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 A (.f64 V l))) 3)))
	39.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	20.8b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	20.3b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	20.6b	(.f64 c0 (.f64 (.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))))))
	42.2b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	20.6b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (.f64 V l)))))
	39.1b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	20.3b	(.f64 c0 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (/.f64 A (.f64 V l))) (cbrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 (/.f64 A (.f64 V l))))))
	38.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	49.9b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 V)) (sqrt.f64 (/.f64 A l))))
▶	20.0b	(pow.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l)))) 1)
	29.1b	(expm1.f64 (log1p.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))))
	50.3b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))

Compiler

Compiled 1776 to 661 computations (62.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.7b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
	4.4b	(/.f64 A (*.f64 V l))
	18.4b	(sqrt.f64 (/.f64 A (*.f64 V l)))

prune98.0ms (2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	86	17	103

Error

10.3b

Counts

103 → 17

Alt Table

Status	Error	Program
	50.7b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))
	37.9b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
▶	20.2b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	28.0b	(.f64 c0 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 A (.f64 V l))) 3)))
	39.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	20.8b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	20.3b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	20.6b	(.f64 c0 (.f64 (.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))))))
	42.2b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	20.6b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (.f64 V l)))))
	39.1b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	20.3b	(.f64 c0 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (/.f64 A (.f64 V l))) (cbrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 (/.f64 A (.f64 V l))))))
	38.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	49.9b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 V)) (sqrt.f64 (/.f64 A l))))
✓	20.0b	(pow.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l)))) 1)
	29.1b	(expm1.f64 (log1p.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))))
	50.3b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))

Compiler

Compiled 1934 to 823 computations (57.4% saved)

localize8.0ms (0.2%)

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)))))
✓	1.6b	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
	4.4b	(/.f64 A (*.f64 V l))
	18.4b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series472.0ms (9.8%)

Counts

2 → 36

Calls

2 calls:

425.0ms	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
46.0ms	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))

rewrite19.0ms (0.4%)

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:

12.0ms	(.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))))

simplify106.0ms (2.2%)

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

prune194.0ms (4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	205	5	210
Fresh	5	10	15
Picked	1	0	1
Done	1	0	1
Total	212	15	227

Error

10.2b

Counts

227 → 15

Alt Table

Status	Error	Program
	50.7b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))
	35.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (exp.f64 (.f64 1/4 (-.f64 (log.f64 (/.f64 A V)) (log.f64 l)))))
	37.9b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
▶	20.0b	(pow.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0) 1)
	38.0b	(.f64 c0 (.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
	39.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	20.8b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	20.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (pow.f64 (/.f64 A (.f64 V l)) 1/4))
	26.3b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))
	42.2b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	20.6b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (.f64 V l)))))
	39.1b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	20.2b	(.f64 (.f64 (sqrt.f64 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l))))))
	49.9b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 V)) (sqrt.f64 (/.f64 A l))))
	50.3b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))

Compiler

Compiled 5270 to 1192 computations (77.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.7b	(.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0)
	4.4b	(/.f64 A (*.f64 V l))
	18.4b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series46.0ms (0.9%)

Counts

1 → 0

Calls

1 calls:

45.0ms

(*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`associate-l_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`sqrt-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

1 → 29

Calls

1 calls:

7.0ms

(*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)

simplify99.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

943×	`fabs-mul_binary64`
723×	`associate-/l*_binary64`
497×	`pow-sqr_binary64`
440×	`times-frac_binary64`
385×	`associate-*l/_binary64`

Counts

29 → 35

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	443
1	96	419
2	213	419
3	442	419
4	1011	419
5	2141	419
6	2219	419
7	2439	419
8	3181	419
9	3744	419
10	4272	419
11	4627	419
12	4969	419

prune84.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	5	9	14
Picked	0	1	1
Done	0	0	0
Total	84	13	97

Error

10.2b

Counts

97 → 13

Alt Table

Status	Error	Program
	50.7b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))
	35.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (exp.f64 (.f64 1/4 (-.f64 (log.f64 (/.f64 A V)) (log.f64 l)))))
	37.9b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	42.2b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	50.2b	(pow.f64 (.f64 (sqrt.f64 (/.f64 1 V)) (.f64 (sqrt.f64 (/.f64 A l)) c0)) 1)
	38.7b	(pow.f64 (.f64 (sqrt.f64 A) (.f64 (sqrt.f64 (/.f64 1 (*.f64 V l))) c0)) 1)
	20.6b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (.f64 V l)))))
	39.1b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	20.2b	(.f64 (.f64 (sqrt.f64 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l))))))
✓	20.0b	(pow.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0) 1)
	49.9b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 V)) (sqrt.f64 (/.f64 A l))))
	22.0b	(pow.f64 (*.f64 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))) c0) 1)
	20.8b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))

Compiler

Compiled 1528 to 619 computations (59.5% saved)

regimes1.1s (23.6%)

Accuracy

Total 5.5b remaining (45%)

Threshold costs 0b (0%)

Counts

83 → 4

Compiler

Compiled 16373 to 9577 computations (41.5% saved)

bsearch4.0ms (0.1%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	95
1	48	95
2	47	95

end164.0ms (3.4%)

Remove: (sort V l)
Compiler: Compiled 491 to 295 computations (39.9% saved)

Details

analyze650.0ms (13.4%)

sample1.4s (29.4%)

simplify9.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series86.0ms (1.8%)

rewrite20.0ms (0.4%)

simplify95.0ms (2%)

prune86.0ms (1.8%)

localize9.0ms (0.2%)

prune98.0ms (2%)

localize8.0ms (0.2%)

series472.0ms (9.8%)

rewrite19.0ms (0.4%)

simplify106.0ms (2.2%)

prune194.0ms (4%)

localize7.0ms (0.1%)

series46.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify99.0ms (2.1%)

prune84.0ms (1.7%)

regimes1.1s (23.6%)

bsearch4.0ms (0.1%)

simplify3.0ms (0.1%)

end164.0ms (3.4%)

Profiling