Details

Time bar (total: 8.3s)

analyze586.0ms (7%)

Algorithm
search
Search
TrueOtherFalseIter
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)

sample56.0ms (0.7%)

Algorithm
intervals
Symmetry

(sort V l)

Results
15.0ms256×body128valid
4.0ms95×body128nan
2.0ms37×body128invalid
Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-/r*_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11312
21512
31512

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
20.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
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:

NewErrorProgram
2.4b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
4.4b
(/.f64 A (*.f64 V l))
15.6b
(sqrt.f64 (/.f64 A (*.f64 V l)))

series119.0ms (1.4%)

Counts
3 → 12
Calls

3 calls:

64.0ms
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
38.0ms
(sqrt.f64 (/.f64 A (*.f64 V l)))
17.0ms
(/.f64 A (*.f64 V l))

rewrite15.0ms (0.2%)

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

simplify95.0ms (1.1%)

Algorithm
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)

IterNodesCost
01031084
11941009
25611009
316311009
421871009
524461009
631961009
743401009
846981009

prune90.0ms (1.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New711586
Fresh000
Picked011
Done000
Total711687
Error
9.6b
Counts
87 → 16
Alt Table
StatusErrorProgram
37.3b
(*.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
19.8b
(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
40.5b
(*.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))))
20.0b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
37.2b
(/.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (*.f64 V l)))
19.4b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
20.6b
(*.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))))))
36.5b
(*.f64 c0 (*.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
42.8b
(cbrt.f64 (*.f64 (*.f64 (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l)))) (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))) (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))))
49.7b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) V)) (sqrt.f64 (/.f64 (sqrt.f64 A) l))))
36.5b
(*.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (*.f64 V l))))
20.2b
(*.f64 c0 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))))
29.2b
(*.f64 c0 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) 3)))
50.5b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V)) (sqrt.f64 (/.f64 (cbrt.f64 A) l))))
20.4b
(*.f64 c0 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 A (*.f64 V l)))) (sqrt.f64 (cbrt.f64 (/.f64 A (*.f64 V l))))))
Compiler

Compiled 1750 to 631 computations (63.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 A)
2.4b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
4.0b
(*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
15.6b
(sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

series172.0ms (2.1%)

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))))
40.0ms
(sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
36.0ms
(cbrt.f64 A)
29.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))

rewrite35.0ms (0.4%)

Algorithm
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 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
10.0ms
(*.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 (1.5%)

Algorithm
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)

IterNodesCost
01812248
14291954
215681941
337491927
447291927
549451927
649631927

prune150.0ms (1.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New2203223
Fresh5914
Picked011
Done011
Total22514239
Error
5.6b
Counts
239 → 14
Alt Table
StatusErrorProgram
37.3b
(*.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
19.8b
(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
26.0b
(*.f64 c0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (cbrt.f64 A))) (sqrt.f64 l)))
40.5b
(*.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))))
20.0b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
37.2b
(/.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (*.f64 V l)))
19.4b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
20.6b
(*.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))))))
36.5b
(*.f64 c0 (*.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
36.5b
(*.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (*.f64 V l))))
49.7b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) V)) (sqrt.f64 (/.f64 (sqrt.f64 A) l))))
25.8b
(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
38.5b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)))
Compiler

Compiled 4995 to 1397 computations (72% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
2.4b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l))))
4.4b
(*.f64 (/.f64 1 V) (/.f64 A l))
15.6b
(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))

series118.0ms (1.4%)

Counts
3 → 48
Calls

3 calls:

64.0ms
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l))))
38.0ms
(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))
17.0ms
(*.f64 (/.f64 1 V) (/.f64 A l))

rewrite26.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64
27×add-exp-log_binary64
25×times-frac_binary64
21×*-un-lft-identity_binary64
19×add-cube-cbrt_binary64
Counts
3 → 98
Calls

3 calls:

9.0ms
(*.f64 (/.f64 1 V) (/.f64 A l))
7.0ms
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l))))
4.0ms
(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))

simplify147.0ms (1.8%)

Algorithm
egg-herbie
Rules
474×sqr-pow_binary64
426×associate-*l/_binary64
402×fabs-mul_binary64
354×associate-/l*_binary64
346×associate-*r/_binary64
Counts
146 → 159
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01461670
13211517
29621517
325491517
426651517
530411517
634151517
740321517
848251517
951831517

prune116.0ms (1.4%)

Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New1581159
Fresh01111
Picked011
Done022
Total15815173
Error
5.6b
Counts
173 → 15
Alt Table
StatusErrorProgram
36.5b
(*.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (*.f64 V l))))
27.0b
(/.f64 (*.f64 c0 (sqrt.f64 (*.f64 (/.f64 1 V) A))) (sqrt.f64 l))
37.3b
(*.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
19.8b
(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
26.0b
(*.f64 c0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (cbrt.f64 A))) (sqrt.f64 l)))
40.5b
(*.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))))
20.0b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
37.2b
(/.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (*.f64 V l)))
19.4b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
20.6b
(*.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))))))
36.5b
(*.f64 c0 (*.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
49.7b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) V)) (sqrt.f64 (/.f64 (sqrt.f64 A) l))))
25.8b
(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
38.5b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)))
Compiler

Compiled 2987 to 1415 computations (52.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (/.f64 V (/.f64 A l)))
2.4b
(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
4.6b
(/.f64 V (/.f64 A l))
15.6b
(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))

series130.0ms (1.6%)

Counts
4 → 84
Calls

4 calls:

64.0ms
(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
37.0ms
(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))
17.0ms
(/.f64 1 (/.f64 V (/.f64 A l)))
12.0ms
(/.f64 V (/.f64 A l))

rewrite150.0ms (1.8%)

Algorithm
rewrite-expression-head
Rules
1155×times-frac_binary64
574×add-sqr-sqrt_binary64
539×*-un-lft-identity_binary64
533×add-cube-cbrt_binary64
281×sqrt-prod_binary64
Counts
4 → 601
Calls

4 calls:

34.0ms
(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
15.0ms
(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))
10.0ms
(/.f64 1 (/.f64 V (/.f64 A l)))
4.0ms
(/.f64 V (/.f64 A l))

simplify658.0ms (7.9%)

Algorithm
egg-herbie
Rules
741×fma-neg_binary64
709×fma-def_binary64
332×sqr-pow_binary64
286×associate-/r/_binary64
204×*-commutative_binary64
Counts
685 → 911
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041213768
172712311
2218711996
3226311786
4271111786
5301411786
6373411786
7454611786
8489911786
9506011786

prune772.0ms (9.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New89714911
Fresh8311
Picked101
Done303
Total90917926
Error
0.0b
Counts
926 → 17
Alt Table
StatusErrorProgram
30.1b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 1 (sqrt.f64 l)))) (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A (sqrt.f64 l))))))
9.6b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 1 (*.f64 (*.f64 (cbrt.f64 V) (cbrt.f64 V)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))) (sqrt.f64 (/.f64 1 (/.f64 (cbrt.f64 V) (/.f64 A (cbrt.f64 l))))))
37.2b
(/.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (*.f64 V l)))
8.6b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 (*.f64 (cbrt.f64 V) (cbrt.f64 V)) (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) 1))))) (sqrt.f64 (/.f64 1 (/.f64 (cbrt.f64 V) (/.f64 (cbrt.f64 A) l)))))
25.8b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 (/.f64 1 l))))
1.1b
(*.f64 (*.f64 c0 (fabs.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 l)) (cbrt.f64 V)))) (sqrt.f64 (/.f64 1 (/.f64 (cbrt.f64 V) (/.f64 (cbrt.f64 A) (cbrt.f64 l))))))
11.9b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 1 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 A l)) (cbrt.f64 (/.f64 A l)))))) (sqrt.f64 (/.f64 1 (/.f64 V (cbrt.f64 (/.f64 A l)))))))
23.4b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (sqrt.f64 l)))) (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 (cbrt.f64 A) (sqrt.f64 l))))))
3.4b
(*.f64 c0 (*.f64 (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)))))
27.2b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V A)))) (sqrt.f64 (/.f64 1 l)))
19.5b
(/.f64 c0 (sqrt.f64 (/.f64 V (/.f64 A l))))
27.0b
(/.f64 (*.f64 c0 (sqrt.f64 (*.f64 (/.f64 1 V) A))) (sqrt.f64 l))
7.2b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 1 (/.f64 1 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))) (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 (cbrt.f64 A) (cbrt.f64 l)))))))
20.0b
(*.f64 c0 (sqrt.f64 (*.f64 1 (/.f64 A (*.f64 V l)))))
22.2b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (*.f64 (cbrt.f64 V) (cbrt.f64 V)) (sqrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 A (sqrt.f64 l)) (cbrt.f64 V)))))
36.5b
(*.f64 c0 (*.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
7.0b
(*.f64 (*.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 l)))) (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 (cbrt.f64 A) (cbrt.f64 l))))))
Compiler

Compiled 20536 to 8134 computations (60.4% saved)

regimes3.2s (38.4%)

Accuracy

Total 1.1b remaining (93.1%)

Threshold costs 0b (0%)

Counts
285 → 1
Compiler

Compiled 53369 to 35591 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
fabs-div_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01838
12538
22838
32638

end8.0ms (0.1%)

Compiler

Compiled 81 to 48 computations (40.7% saved)

sample1.5s (18.3%)

Algorithm
intervals
Results
390.0ms8000×body128valid
145.0ms2982×body128nan
41.0ms939×body128invalid
Compiler

Compiled 420 to 271 computations (35.5% saved)

Profiling

Loading profile data...