Details

Time bar (total: 9.6s)

analyze652.0ms (6.8%)

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)

sample62.0ms (0.6%)

Algorithm
intervals
Symmetry

(sort V l)

Results
24.0ms256×body128valid
4.0ms86×body128nan
1.0ms22×body128invalid
Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify7.0ms (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
18.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
18.7b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
Compiler

Compiled 36 to 24 computations (33.3% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.7b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
5.8b
(/.f64 A (*.f64 V l))
14.5b
(sqrt.f64 (/.f64 A (*.f64 V l)))

series134.0ms (1.4%)

Counts
3 → 12
Calls

3 calls:

77.0ms
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
38.0ms
(sqrt.f64 (/.f64 A (*.f64 V l)))
19.0ms
(/.f64 A (*.f64 V l))

rewrite16.0ms (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)))

simplify109.0ms (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

prune101.0ms (1.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New721486
Fresh000
Picked101
Done000
Total731487
Error
7.9b
Counts
87 → 14
Alt Table
StatusErrorProgram
39.5b
(*.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
19.0b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
19.0b
(*.f64 (*.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (*.f64 V l)))))
50.5b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) V)) (sqrt.f64 (/.f64 (sqrt.f64 A) l))))
43.3b
(*.f64 (sqrt.f64 c0) (*.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
18.8b
(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
19.4b
(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
38.6b
(*.f64 c0 (*.f64 (sqrt.f64 A) (sqrt.f64 (/.f64 1 (*.f64 V l)))))
50.8b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
18.9b
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))
19.4b
(*.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)))))
19.4b
(*.f64 (*.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (*.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
39.3b
(/.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (*.f64 V l)))
18.7b
(*.f64 1 (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l)))))
Compiler

Compiled 1668 to 597 computations (64.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.7b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
5.8b
(/.f64 A (*.f64 V l))
14.5b
(sqrt.f64 (/.f64 A (*.f64 V l)))

prune100.0ms (1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New84286
Fresh31013
Picked011
Done000
Total8713100
Error
7.9b
Counts
100 → 13
Alt Table
StatusErrorProgram
19.0b
(*.f64 (*.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (*.f64 V l)))))
50.5b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) V)) (sqrt.f64 (/.f64 (sqrt.f64 A) l))))
19.1b
(*.f64 1 (*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 (*.f64 V l) (cbrt.f64 A))))))
43.3b
(*.f64 (sqrt.f64 c0) (*.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
18.8b
(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
19.4b
(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
39.5b
(*.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
50.8b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
18.9b
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))
38.4b
(*.f64 1 (*.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (*.f64 V l)))))
19.4b
(*.f64 (*.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (*.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
39.3b
(/.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (*.f64 V l)))
18.7b
(*.f64 1 (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l)))))
Compiler

Compiled 1772 to 741 computations (58.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.7b
(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
5.4b
(/.f64 (/.f64 A V) l)
14.5b
(sqrt.f64 (/.f64 (/.f64 A V) l))

series127.0ms (1.3%)

Counts
3 → 48
Calls

3 calls:

68.0ms
(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
39.0ms
(sqrt.f64 (/.f64 (/.f64 A V) l))
20.0ms
(/.f64 (/.f64 A V) l)

rewrite47.0ms (0.5%)

Algorithm
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:

13.0ms
(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
7.0ms
(sqrt.f64 (/.f64 (/.f64 A V) l))
5.0ms
(/.f64 (/.f64 A V) l)

simplify223.0ms (2.3%)

Algorithm
egg-herbie
Rules
637×fma-neg_binary64
558×fma-def_binary64
379×associate-/l/_binary64
291×div-sub_binary64
290×associate-*l*_binary64
Counts
245 → 280
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03004078
15373931
212973881
325843881
426953881
529143881
634243881
749973881
849493881

prune245.0ms (2.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New26614280
Fresh8311
Picked101
Done101
Total27617293
Error
0.0b
Counts
293 → 17
Alt Table
StatusErrorProgram
14.3b
(*.f64 (*.f64 c0 (fabs.f64 (cbrt.f64 A))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) V) l)))
14.3b
(*.f64 c0 (*.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 V l)))))
39.4b
(*.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 (/.f64 1 V) l)))
25.9b
(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))
48.5b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 A (sqrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 1 V) (sqrt.f64 l))))
14.3b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 A V) (cbrt.f64 l)))))
41.0b
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 A))) (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 A) V) l)))
24.5b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))) (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l))))
37.6b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 A) V) (cbrt.f64 l)))))
19.4b
(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
12.1b
(*.f64 c0 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 (/.f64 A V)) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 (/.f64 A V)) (cbrt.f64 l)))))
19.0b
(*.f64 (*.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (*.f64 V l)))))
12.7b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 V) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (/.f64 A (cbrt.f64 V)) l))))
4.3b
(*.f64 (*.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) l)))
1.3b
(*.f64 (*.f64 c0 (fabs.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))))
39.3b
(/.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (*.f64 V l)))
13.3b
(*.f64 c0 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 A V))) (sqrt.f64 (/.f64 (cbrt.f64 (/.f64 A V)) l))))
Compiler

Compiled 5517 to 1642 computations (70.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))
0.6b
(cbrt.f64 A)
0.6b
(cbrt.f64 l)
0.6b
(cbrt.f64 V)

series908.0ms (9.4%)

Counts
4 → 72
Calls

4 calls:

802.0ms
(/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))
39.0ms
(cbrt.f64 V)
34.0ms
(cbrt.f64 A)
33.0ms
(cbrt.f64 l)

rewrite62.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
492×times-frac_binary64
384×cbrt-prod_binary64
264×*-un-lft-identity_binary64
264×add-sqr-sqrt_binary64
264×add-cube-cbrt_binary64
Counts
4 → 342
Calls

4 calls:

11.0ms
(/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))
1.0ms
(cbrt.f64 V)
1.0ms
(cbrt.f64 A)
1.0ms
(cbrt.f64 l)

simplify311.0ms (3.2%)

Algorithm
egg-herbie
Rules
788×associate-/l*_binary64
457×associate-/l/_binary64
312×associate-/r/_binary64
288×log-div_binary64
276×associate-*l/_binary64
Counts
414 → 505
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040110708
184310107
221749782
343049782
450369782

prune771.0ms (8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New100461010
Fresh21416
Picked101
Done000
Total1007201027
Error
0.0b
Counts
1027 → 20
Alt Table
StatusErrorProgram
19.4b
(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
1.5b
(*.f64 (*.f64 c0 (fabs.f64 (/.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 V)) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))))
39.4b
(*.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 (/.f64 1 V) l)))
25.9b
(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))
48.5b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 A (sqrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 1 V) (sqrt.f64 l))))
14.3b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 A V) (cbrt.f64 l)))))
19.0b
(*.f64 (*.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (*.f64 V l)))))
1.3b
(*.f64 (*.f64 c0 (fabs.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (cbrt.f64 l))))))
41.0b
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 A))) (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 A) V) l)))
24.5b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))) (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l))))
37.6b
(*.f64 c0 (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 A) V) (cbrt.f64 l)))))
1.3b
(*.f64 (*.f64 c0 (fabs.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l)))))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))))
13.3b
(*.f64 c0 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 A V))) (sqrt.f64 (/.f64 (cbrt.f64 (/.f64 A V)) l))))
12.1b
(*.f64 c0 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 (/.f64 A V)) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 (/.f64 A V)) (cbrt.f64 l)))))
1.6b
(*.f64 (*.f64 c0 (fabs.f64 (*.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l)))) (/.f64 (/.f64 1 (cbrt.f64 V)) (cbrt.f64 (cbrt.f64 l)))))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))))
14.3b
(*.f64 (*.f64 c0 (fabs.f64 (cbrt.f64 A))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) V) l)))
1.4b
(*.f64 (*.f64 c0 (fabs.f64 (/.f64 (/.f64 1 (cbrt.f64 (*.f64 (cbrt.f64 V) (cbrt.f64 V)))) (/.f64 (cbrt.f64 l) (/.f64 (cbrt.f64 A) (cbrt.f64 (cbrt.f64 V))))))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))))
4.3b
(*.f64 (*.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) l)))
1.6b
(*.f64 (*.f64 c0 (fabs.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (cbrt.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)))) (/.f64 (cbrt.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (cbrt.f64 l))))) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))))
39.3b
(/.f64 (*.f64 c0 (sqrt.f64 A)) (sqrt.f64 (*.f64 V l)))
Compiler

Compiled 34606 to 7515 computations (78.3% saved)

regimes3.7s (38.3%)

Accuracy

Total 1.0b remaining (92.9%)

Threshold costs 0b (0%)

Counts
254 → 1
Compiler

Compiled 51887 to 31199 computations (39.9% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
fabs-mul_binary64
fabs-div_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01635
12235
22635
32635

end6.0ms (0.1%)

Compiler

Compiled 75 to 45 computations (40% saved)

sample2.0s (21%)

Algorithm
intervals
Results
508.0ms8000×body128valid
166.0ms2926×body128nan
55.0ms894×body128invalid
Compiler

Compiled 516 to 294 computations (43% saved)

Profiling

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