Details

Time bar (total: 3.7s)

analyze835.0ms (22.9%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%48.6%51.4%0
0%48.6%51.4%1
24.3%24.3%51.4%2
24.3%24.3%51.4%3
30.4%18.2%51.4%4
30.4%18.2%51.4%5
33.4%15.2%51.4%6
33.4%15.2%51.4%7
34.6%14.1%51.4%8
34.8%13.9%51.4%9
35.4%13.2%51.4%10
35.6%13.1%51.4%11
35.9%12.7%51.4%12
36%12.6%51.4%13
36.2%12.4%51.4%14

sample38.0ms (1%)

Algorithm
1×intervals
Results
10.0ms198×body80valid
9.0ms27×body2560valid
4.0ms256×pre80true
4.0ms16×body1280valid
1.0ms7×body640valid
1.0ms5×body320valid
0.0ms3×body160valid

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
03817
13817

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 11.9b

Counts
2 → 1

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x))))
0.0b
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))))))
1.2b
(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))))
15.9b
(sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))

rewrite49.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Rules
22×*-un-lft-identity_binary64
21×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
18×times-frac_binary64
16×sqrt-prod_binary64
8×pow1_binary64
6×associate-/r*_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64
4×flip3-+_binary64 flip-+_binary64
3×sqrt-pow1_binary64 associate-/l*_binary64
2×pow1/2_binary64 associate-*r/_binary64 associate-/r/_binary64
1×pow-prod-down_binary64 distribute-lft-out_binary64 cbrt-undiv_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 81
Calls

4 calls:

19.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))))))
13.0ms
(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))))
9.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x))))
6.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))

series81.0ms (2.2%)

Counts
4 → 12
Calls

4 calls:

41.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))))))
15.0ms
(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))))
14.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x))))
10.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))

simplify75.0ms (2.1%)

Algorithm
1×egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
055761479

prune170.0ms (4.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New821193
Fresh000
Picked101
Done000
Total831194

Merged error: 11.6b

Counts
94 → 11

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (*.f64 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) 0.5))
0.9b
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) 0.5))))
1.2b
(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))
15.9b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))

rewrite36.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
9×*-un-lft-identity_binary64 pow1_binary64
8×add-sqr-sqrt_binary64
7×add-cube-cbrt_binary64
6×add-log-exp_binary64
5×log-pow_binary64 sqrt-prod_binary64
4×add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64 exp-prod_binary64
3×flip3-+_binary64 log-prod_binary64 sqrt-pow1_binary64 flip-+_binary64
2×pow1/2_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 distribute-lft-out_binary64 rem-log-exp_binary64 rem-sqrt-square_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 56
Calls

4 calls:

14.0ms
(sqrt.f64 (*.f64 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) 0.5))
13.0ms
(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))
6.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))
2.0ms
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) 0.5))))

series104.0ms (2.8%)

Counts
4 → 12
Calls

4 calls:

42.0ms
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) 0.5))))
38.0ms
(sqrt.f64 (*.f64 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) 0.5))
14.0ms
(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))
9.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))

simplify49.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049931054
149931054

prune127.0ms (3.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New62668
Fresh4610
Picked101
Done000
Total671279

Merged error: 11.6b

Counts
79 → 12

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))
7.1b
(+.f64 1.0 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))))
15.9b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))
15.9b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))

rewrite30.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
42×sqrt-prod_binary64
30×add-sqr-sqrt_binary64
28×*-un-lft-identity_binary64 add-cube-cbrt_binary64
27×times-frac_binary64
9×associate-/r*_binary64
8×sqrt-div_binary64
6×add-log-exp_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
4×flip3-+_binary64 flip-+_binary64
3×associate-/l*_binary64
2×pow1/2_binary64 associate-/r/_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
1×cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 94
Calls

4 calls:

12.0ms
(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))
6.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))
6.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))
4.0ms
(+.f64 1.0 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))))

series62.0ms (1.7%)

Counts
4 → 12
Calls

4 calls:

28.0ms
(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))
15.0ms
(+.f64 1.0 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))))
9.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))
9.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))

simplify63.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
050611775

prune223.0ms (6.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1033106
Fresh2911
Picked011
Done000
Total10513118

Merged error: 11.6b

Counts
118 → 13

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))
7.5b
(+.f64 1.0 (/.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x))))))
15.9b
(sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))
15.9b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))

rewrite100.0ms (2.7%)

Algorithm
1×rewrite-expression-head
Rules
42×sqrt-prod_binary64
30×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
28×add-cube-cbrt_binary64
27×times-frac_binary64
9×associate-/r*_binary64
8×sqrt-div_binary64
6×add-log-exp_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
4×flip3-+_binary64 flip-+_binary64
3×associate-/l*_binary64
2×pow1/2_binary64 associate-/r/_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
1×distribute-lft-out_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 95
Calls

4 calls:

75.0ms
(+.f64 1.0 (/.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x))))))
10.0ms
(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))
6.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))
6.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))

series61.0ms (1.7%)

Counts
4 → 12
Calls

4 calls:

27.0ms
(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))))
15.0ms
(+.f64 1.0 (/.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x))))))
10.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4.0 p)) (*.f64 x x)))
9.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 4.0 p) p) (*.f64 x x)))

simplify42.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
050531770

prune176.0ms (4.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1061107
Fresh11011
Picked011
Done011
Total10713120

Merged error: 11.6b

Counts
120 → 13

regimes144.0ms (3.9%)

Accuracy

Total 1.2b remaining (9%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02532
12532

end0.0ms (0%)

sample1.1s (30.4%)

Algorithm
1×intervals
Results
317.0ms6125×body80valid
257.0ms792×body2560valid
146.0ms555×body1280valid
138.0ms8000×pre80true
62.0ms295×body640valid
23.0ms155×body320valid
8.0ms78×body160valid

Profiling

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