Details

Time bar (total: 1.9s)

analyze2.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
50%12.5%37.5%4
50%6.2%43.8%5
50%3.1%46.9%6
50%1.6%48.5%7
50%0.8%49.2%8
50%0.4%49.6%9
50%0.2%49.8%10
50%0.1%49.9%11
50%0%50%12
50%0%50%13
50%0%50%14

sample29.0ms

Algorithm
intervals
Results
7.0ms54×body1280valid
7.0ms22×body320valid
5.0ms47×body640valid
3.0ms118×body80valid
1.0ms15×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0717
1717

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.9b

Counts
2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt.f64 (+.f64 x 1.0))
3.7b
(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64 add-sqr-sqrt_binary64 sqrt-prod_binary64
4×add-log-exp_binary64 difference-of-squares_binary64
3×pow1_binary64 add-cube-cbrt_binary64 distribute-lft-out--_binary64
2×distribute-lft-out_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64
1×flip3-+_binary64 sub-neg_binary64 pow1/2_binary64 flip3--_binary64 diff-log_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip--_binary64 flip-+_binary64
Counts
2 → 34
Calls
2 calls:
3.0ms
(sqrt.f64 (+.f64 x 1.0))
8.0ms
(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

series19.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(sqrt.f64 (+.f64 x 1.0))
14.0ms
(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

simplify55.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
04975520
14975520

prune51.0ms

Filtered
30 candidates to 40 candidates (-33.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New37340
Fresh000
Picked101
Done000
Total38341

Merged error: 0.2b

Counts
41 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt.f64 (+.f64 x 1.0))
0.0b
(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
0.2b
(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity_binary64
24×sqrt-prod_binary64
21×distribute-lft-out_binary64
18×times-frac_binary64
16×add-sqr-sqrt_binary64
15×add-cube-cbrt_binary64
6×associate-/r*_binary64
5×add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
4×pow1_binary64
3×flip3-+_binary64 associate-/l*_binary64 flip-+_binary64
2×associate-/r/_binary64 sqrt-div_binary64
1×pow1/2_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sum-log_binary64
Counts
3 → 71
Calls
3 calls:
3.0ms
(sqrt.f64 (+.f64 x 1.0))
8.0ms
(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
10.0ms
(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))

series26.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(sqrt.f64 (+.f64 x 1.0))
7.0ms
(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
13.0ms
(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))

simplify29.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
050381051

prune100.0ms

Filtered
59 candidates to 80 candidates (-35.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New72880
Fresh202
Picked011
Done000
Total74983

Merged error: 0.0b

Counts
83 → 9

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
0.2b
(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.2b
(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.3b
(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity_binary64
274×sqrt-prod_binary64
157×times-frac_binary64
119×add-sqr-sqrt_binary64
116×distribute-lft-out_binary64
88×add-cube-cbrt_binary64
41×swap-sqr_binary64
27×associate-*r*_binary64 associate-*l*_binary64
20×pow1_binary64
14×associate-/r/_binary64
12×associate-/r*_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64
9×pow1/2_binary64 sqrt-pow1_binary64 unswap-sqr_binary64
7×flip3-+_binary64 div-inv_binary64 flip-+_binary64
6×associate-/l*_binary64
5×pow-prod-up_binary64 sqrt-div_binary64
4×add-log-exp_binary64
3×pow-prod-down_binary64 pow-sqr_binary64
2×cbrt-undiv_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64
1×cbrt-unprod_binary64 rem-square-sqrt_binary64 associate-*r/_binary64 pow-plus_binary64 sqrt-unprod_binary64 prod-exp_binary64 frac-times_binary64 pow2_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 250
Calls
4 calls:
11.0ms
(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
10.0ms
(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
10.0ms
(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
37.0ms
(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

series71.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
12.0ms
(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
12.0ms
(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
21.0ms
(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

simplify87.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049464249
149464249

prune277.0ms

Filtered
142 candidates to 262 candidates (-84.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2584262
Fresh347
Picked101
Done011
Total2629271

Merged error: 0.0b

Counts
271 → 9

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.1b
(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.2b
(/.f64 1.0 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
0.3b
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod_binary64
74×*-un-lft-identity_binary64
32×distribute-lft-out_binary64
30×add-sqr-sqrt_binary64
28×sqrt-div_binary64
21×pow1_binary64
16×add-cube-cbrt_binary64
15×swap-sqr_binary64
14×flip3-+_binary64 flip-+_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
10×pow1/2_binary64 sqrt-pow1_binary64
9×associate-*r*_binary64 associate-*l*_binary64
8×associate-/r/_binary64 frac-times_binary64
5×pow-prod-up_binary64
4×add-log-exp_binary64 associate-*r/_binary64 unswap-sqr_binary64 associate-*l/_binary64
3×pow-prod-down_binary64 associate-/l*_binary64 times-frac_binary64 pow-sqr_binary64
2×cbrt-unprod_binary64 cbrt-undiv_binary64 rem-sqrt-square_binary64 prod-exp_binary64 div-exp_binary64
1×associate-/r*_binary64 rem-square-sqrt_binary64 pow-plus_binary64 sqrt-unprod_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 135
Calls
4 calls:
8.0ms
(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
8.0ms
(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
23.0ms
(/.f64 1.0 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
21.0ms
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))

series52.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
14.0ms
(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
12.0ms
(/.f64 1.0 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
8.0ms
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))

simplify53.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
052542070

prune123.0ms

Filtered
85 candidates to 147 candidates (-72.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1470147
Fresh077
Picked011
Done011
Total1479156

Merged error: 0.0b

Counts
156 → 9

regimes46.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
099
199

end0.0ms

sample650.0ms

Algorithm
intervals
Results
236.0ms1712×body1280valid
139.0ms1278×body640valid
115.0ms4094×body80valid
47.0ms604×body320valid
21.0ms312×body160valid

Profiling

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