Details

Time bar (total: 11.2s)

analyze1.4s (12.1%)

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)

sample87.0ms (0.8%)

Algorithm
intervals
Results
21.0ms256×body128valid
17.0ms116×body128nan
2.0ms28×body128invalid
Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify13.0ms (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

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
18.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
18.9b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
Compiler

Compiled 36 to 24 computations (33.3% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
1.9b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
3.8b
(/.f64 A (*.f64 V l))
16.7b
(sqrt.f64 (/.f64 A (*.f64 V l)))

series227.0ms (2%)

Counts
3 → 12
Calls

3 calls:

123.0ms
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
70.0ms
(sqrt.f64 (/.f64 A (*.f64 V l)))
35.0ms
(/.f64 A (*.f64 V l))

rewrite29.0ms (0.3%)

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:

12.0ms
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
6.0ms
(/.f64 A (*.f64 V l))
5.0ms
(sqrt.f64 (/.f64 A (*.f64 V l)))

simplify147.0ms (1.3%)

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

prune156.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New731386
Fresh000
Picked101
Done000
Total741387
Error
9.6b
Counts
87 → 13
Alt Table
StatusErrorProgram
19.5b
(*.f64 c0 (sqrt.f64 (*.f64 A (/.f64 1 (*.f64 V l)))))
50.2b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))
19.2b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
19.3b
(*.f64 c0 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 A (*.f64 V l)))) (sqrt.f64 (cbrt.f64 (/.f64 A (*.f64 V l))))))
19.1b
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))
35.7b
(*.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (*.f64 V 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)))))
50.3b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
51.6b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
43.1b
(*.f64 (sqrt.f64 c0) (*.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
19.6b
(*.f64 (*.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (*.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
18.9b
(*.f64 (*.f64 c0 1) (sqrt.f64 (/.f64 A (*.f64 V l))))
Compiler

Compiled 1620 to 581 computations (64.1% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
1.9b
(*.f64 (*.f64 c0 1) (sqrt.f64 (/.f64 A (*.f64 V l))))
3.8b
(/.f64 A (*.f64 V l))
16.7b
(sqrt.f64 (/.f64 A (*.f64 V l)))

series123.0ms (1.1%)

Counts
1 → 12
Calls

1 calls:

122.0ms
(*.f64 (*.f64 c0 1) (sqrt.f64 (/.f64 A (*.f64 V l))))

rewrite17.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×associate-*r*_binary64
add-exp-log_binary64
sqrt-prod_binary64
add-cbrt-cube_binary64
pow1_binary64
Counts
1 → 29
Calls

1 calls:

13.0ms
(*.f64 (*.f64 c0 1) (sqrt.f64 (/.f64 A (*.f64 V l))))

simplify126.0ms (1.1%)

Algorithm
egg-herbie
Rules
585×associate-/l*_binary64
401×associate-*l/_binary64
374×unswap-sqr_binary64
370×times-frac_binary64
365×associate-*r/_binary64
Counts
41 → 44
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
064547
1115511
2229511
3454511
4965511
52059511
62161511
72492511
83497511
94838511
105063511

prune155.0ms (1.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New91091
Fresh01212
Picked011
Done000
Total9113104
Error
9.6b
Counts
104 → 13
Alt Table
StatusErrorProgram
19.5b
(*.f64 c0 (sqrt.f64 (*.f64 A (/.f64 1 (*.f64 V l)))))
50.2b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))
19.2b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
19.3b
(*.f64 c0 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 A (*.f64 V l)))) (sqrt.f64 (cbrt.f64 (/.f64 A (*.f64 V l))))))
19.1b
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))
35.7b
(*.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (*.f64 V 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)))))
50.3b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
51.6b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
43.1b
(*.f64 (sqrt.f64 c0) (*.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
19.6b
(*.f64 (*.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (*.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
18.9b
(*.f64 (*.f64 c0 1) (sqrt.f64 (/.f64 A (*.f64 V l))))
Compiler

Compiled 1832 to 767 computations (58.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))
2.3b
(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
3.8b
(/.f64 A (*.f64 V l))
16.7b
(sqrt.f64 (/.f64 A (*.f64 V l)))

series1.2s (10.4%)

Counts
2 → 36
Calls

2 calls:

1.0s
(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
133.0ms
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))

rewrite41.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
35×sqrt-prod_binary64
13×associate-*r*_binary64
11×add-sqr-sqrt_binary64
10×sqrt-div_binary64
*-un-lft-identity_binary64
Counts
2 → 59
Calls

2 calls:

25.0ms
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))
6.0ms
(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))

simplify168.0ms (1.5%)

Algorithm
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)

IterNodesCost
01291643
12541503
25861503
39111359
414141359
526511359
645751359
749921359

prune331.0ms (3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New2091210
Fresh01111
Picked011
Done011
Total20914223
Error
9.6b
Counts
223 → 14
Alt Table
StatusErrorProgram
37.2b
(/.f64 (*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 A))) (sqrt.f64 (sqrt.f64 A))) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 V l))) (sqrt.f64 (sqrt.f64 (*.f64 V l)))))
51.6b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
19.5b
(*.f64 c0 (sqrt.f64 (*.f64 A (/.f64 1 (*.f64 V l)))))
50.2b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))
19.2b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
19.3b
(*.f64 c0 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 A (*.f64 V l)))) (sqrt.f64 (cbrt.f64 (/.f64 A (*.f64 V l))))))
19.1b
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))
35.7b
(*.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (*.f64 V 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)))))
50.3b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
43.1b
(*.f64 (sqrt.f64 c0) (*.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
19.6b
(*.f64 (*.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (*.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
18.9b
(*.f64 (*.f64 c0 1) (sqrt.f64 (/.f64 A (*.f64 V l))))
Compiler

Compiled 5185 to 1124 computations (78.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 A)
1.9b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
4.1b
(*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
16.7b
(sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

series341.0ms (3%)

Counts
4 → 60
Calls

4 calls:

139.0ms
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
83.0ms
(sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
61.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
58.0ms
(cbrt.f64 A)

rewrite75.0ms (0.7%)

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:

23.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
19.0ms
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
12.0ms
(sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
1.0ms
(cbrt.f64 A)

simplify215.0ms (1.9%)

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

prune363.0ms (3.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New2167223
Fresh4711
Picked101
Done112
Total22215237
Error
7.1b
Counts
237 → 15
Alt Table
StatusErrorProgram
37.2b
(/.f64 (*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 A))) (sqrt.f64 (sqrt.f64 A))) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 V l))) (sqrt.f64 (sqrt.f64 (*.f64 V l)))))
28.5b
(/.f64 (*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (cbrt.f64 A)))) (sqrt.f64 l))
51.6b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
49.8b
(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A l))) (sqrt.f64 V))
50.2b
(*.f64 (*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))
19.5b
(*.f64 (*.f64 (cbrt.f64 (*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))) (cbrt.f64 (*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))))) (cbrt.f64 (*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))))
19.1b
(*.f64 (*.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))
54.5b
(*.f64 c0 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (log.f64 (exp.f64 (cbrt.f64 A))) l))))
27.5b
(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 A V)) (sqrt.f64 l)))
35.7b
(*.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (*.f64 V l))))
19.3b
(*.f64 c0 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) 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)))))
19.2b
(*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (cbrt.f64 A)) (*.f64 V l))))
43.1b
(*.f64 (sqrt.f64 c0) (*.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
Compiler

Compiled 4868 to 1299 computations (73.3% saved)

regimes3.3s (29.5%)

Accuracy

Total 3.2b remaining (37.2%)

Threshold costs 0b (0%)

Counts
118 → 5
Compiler

Compiled 21379 to 12459 computations (41.7% saved)

bsearch9.0ms (0.1%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
*-rgt-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042118
151118
250118

end16.0ms (0.1%)

Compiler

Compiled 243 to 117 computations (51.9% saved)

sample2.7s (23.8%)

Algorithm
intervals
Results
699.0ms8000×body128valid
264.0ms2938×body128nan
68.0ms831×body128invalid
Compiler

Compiled 414 to 219 computations (47.1% saved)

Profiling

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