Details

Time bar (total: 3.1s)

analyze1.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1

sample35.0ms

Algorithm
intervals
Results
17.0ms80×body1280valid
5.0ms132×body80valid
4.0ms25×body640valid
1.0ms10×body320valid
1.0ms9×body160valid

simplify24.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
044212
144212

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 16.6b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))
0.0b
(/.f64 1.0 (hypot.f64 1.0 x))
0.0b
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
2.9b
(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity_binary64
14×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
9×times-frac_binary64
8×add-log-exp_binary64
7×pow1_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
3×associate-/r*_binary64 associate-/l*_binary64
2×flip3-+_binary64 associate-*r/_binary64 sqrt-pow1_binary64 flip-+_binary64 sqrt-div_binary64
1×pow-prod-down_binary64 sub-neg_binary64 pow1/2_binary64 flip3--_binary64 diff-log_binary64 distribute-lft-out_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 flip--_binary64 sqrt-prod_binary64 sum-log_binary64
Counts
4 → 65
Calls
4 calls:
7.0ms
(+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))
3.0ms
(/.f64 1.0 (hypot.f64 1.0 x))
7.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
4.0ms
(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))

series93.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))
6.0ms
(/.f64 1.0 (hypot.f64 1.0 x))
30.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
34.0ms
(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))

simplify73.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
04841870
14841870

prune88.0ms

Filtered
54 candidates to 77 candidates (-42.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New73477
Fresh000
Picked101
Done000
Total74478

Merged error: 16.1b

Counts
78 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (-.f64 (*.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))))
0.0b
(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
0.0b
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
2.4b
(-.f64 (*.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity_binary64
13×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
12×times-frac_binary64
8×add-log-exp_binary64
7×pow1_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
5×distribute-lft-out_binary64
4×associate-/r*_binary64
3×flip3-+_binary64 associate-/l*_binary64 flip-+_binary64
2×associate-/l/_binary64 associate--r+_binary64 flip3--_binary64 associate-*r/_binary64 associate-/r/_binary64 sqrt-pow1_binary64 flip--_binary64 sqrt-div_binary64
1×pow-prod-down_binary64 sub-neg_binary64 pow1/2_binary64 diff-log_binary64 cbrt-undiv_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sqrt-prod_binary64 sum-log_binary64
Counts
4 → 74
Calls
4 calls:
8.0ms
(/.f64 (-.f64 (*.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))))
4.0ms
(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
7.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
4.0ms
(-.f64 (*.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))

series151.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/.f64 (-.f64 (*.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))))
30.0ms
(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
32.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
21.0ms
(-.f64 (*.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
056421860

prune155.0ms

Filtered
63 candidates to 86 candidates (-36.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New81586
Fresh213
Picked101
Done000
Total84690

Merged error: 16.1b

Counts
90 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (-.f64 0.5 (/.f64 0.5 (hypot.f64 1.0 x))) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))))
0.0b
(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
0.0b
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
2.3b
(-.f64 0.5 (/.f64 0.5 (hypot.f64 1.0 x)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt_binary64
44×*-un-lft-identity_binary64
30×times-frac_binary64
16×add-cube-cbrt_binary64
12×difference-of-squares_binary64
8×add-log-exp_binary64 distribute-lft-out_binary64
7×pow1_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64 associate-/l*_binary64 distribute-lft-out--_binary64
4×associate-/r*_binary64
3×flip3-+_binary64 flip-+_binary64
2×associate-/l/_binary64 flip3--_binary64 associate-*r/_binary64 associate-/r/_binary64 sqrt-pow1_binary64 flip--_binary64 sqrt-div_binary64
1×pow-prod-down_binary64 sub-neg_binary64 pow1/2_binary64 diff-log_binary64 cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sqrt-prod_binary64 sum-log_binary64
Counts
4 → 90
Calls
4 calls:
11.0ms
(/.f64 (-.f64 0.5 (/.f64 0.5 (hypot.f64 1.0 x))) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))))
3.0ms
(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
9.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
7.0ms
(-.f64 0.5 (/.f64 0.5 (hypot.f64 1.0 x)))

series151.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/.f64 (-.f64 0.5 (/.f64 0.5 (hypot.f64 1.0 x))) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))))
30.0ms
(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
31.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
20.0ms
(-.f64 0.5 (/.f64 0.5 (hypot.f64 1.0 x)))

simplify58.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049452224
149452224

prune152.0ms

Filtered
68 candidates to 102 candidates (-50.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New966102
Fresh505
Picked101
Done000
Total1026108

Merged error: 16.1b

Counts
108 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
0.0b
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
0.2b
(/.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))))
2.4b
(-.f64 (/.f64 0.5 (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))) (/.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
118×times-frac_binary64
107×*-un-lft-identity_binary64
76×add-sqr-sqrt_binary64
55×add-cube-cbrt_binary64
18×distribute-lft-out_binary64
13×associate-/l*_binary64
10×pow1_binary64
9×add-exp-log_binary64 add-cbrt-cube_binary64
8×div-inv_binary64
7×distribute-lft-out--_binary64
6×add-log-exp_binary64 associate-/r/_binary64 difference-of-squares_binary64
5×flip3-+_binary64 flip-+_binary64
4×associate-/r*_binary64 associate-*r/_binary64 sqrt-pow1_binary64 sqrt-div_binary64
3×distribute-rgt-out--_binary64 cbrt-undiv_binary64 div-exp_binary64
2×pow-prod-down_binary64 pow1/2_binary64 sqrt-prod_binary64
1×associate-/l/_binary64 sub-neg_binary64 flip3--_binary64 diff-log_binary64 clear-num_binary64 frac-2neg_binary64 sub-div_binary64 flip--_binary64 frac-sub_binary64
Counts
4 → 141
Calls
4 calls:
9.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
7.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
9.0ms
(/.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))))
53.0ms
(-.f64 (/.f64 0.5 (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))) (/.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))))

series272.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
29.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
56.0ms
(/.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))))
156.0ms
(-.f64 (/.f64 0.5 (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))) (/.f64 (/.f64 0.5 (hypot.f64 1.0 x)) (+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
050494438

prune350.0ms

Filtered
111 candidates to 153 candidates (-37.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1494153
Fresh415
Picked101
Done000
Total1545159

Merged error: 15.7b

Counts
159 → 5

regimes69.0ms

Accuracy

0% (0.3b remaining)

Error of 14.9b against oracle of 14.7b and baseline of 14.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04551
14551

end0.0ms

sample1.1s

Algorithm
intervals
Results
653.0ms2876×body1280valid
160.0ms4019×body80valid
115.0ms639×body640valid
37.0ms300×body320valid
13.0ms166×body160valid

Profiling

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