Details

Time bar (total: 3.3s)

analyze2.0ms

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

sample45.0ms

Algorithm
intervals
Results
25.0ms89×body1280valid
6.0ms129×body80valid
4.0ms18×body640valid
2.0ms12×body320valid
1.0ms8×body160valid

simplify23.0ms

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: 17.0b

Counts
2 → 1

localize7.0ms

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
(/.f64 1.0 (hypot.f64 1.0 x))
0.0b
(hypot.f64 1.0 x)
2.8b
(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
9×times-frac_binary64
7×pow1_binary64
6×add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
3×associate-/r*_binary64 associate-/l*_binary64
2×associate-*r/_binary64 sqrt-pow1_binary64 sqrt-div_binary64
1×pow-prod-down_binary64 flip3-+_binary64 sub-neg_binary64 pow1/2_binary64 flip3--_binary64 diff-log_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 div-inv_binary64 div-exp_binary64 flip--_binary64 sqrt-prod_binary64 flip-+_binary64
Counts
4 → 60
Calls
4 calls:
11.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
3.0ms
(/.f64 1.0 (hypot.f64 1.0 x))
1.0ms
(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))))))

series40.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
6.0ms
(/.f64 1.0 (hypot.f64 1.0 x))
1.0ms
(hypot.f64 1.0 x)
18.0ms
(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))

simplify56.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
05551757

prune79.0ms

Filtered
51 candidates to 72 candidates (-41.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New69372
Fresh000
Picked101
Done000
Total70373

Merged error: 16.5b

Counts
73 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64 add-log-exp_binary64
9×add-sqr-sqrt_binary64
4×pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
3×diff-log_binary64 distribute-lft-out--_binary64
2×sub-neg_binary64 flip3--_binary64 difference-of-squares_binary64 flip--_binary64 frac-sub_binary64
1×flip3-+_binary64 associate--l-_binary64 distribute-lft-out_binary64 times-frac_binary64 +-commutative_binary64 flip-+_binary64 associate--l+_binary64 sum-log_binary64
Counts
4 → 46
Calls
4 calls:
1.0ms
(hypot.f64 1.0 x)
1.0ms
(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))))))
11.0ms
(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))

series27.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot.f64 1.0 x)
1.0ms
(hypot.f64 1.0 x)
17.0ms
(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
8.0ms
(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
04973647
14973647

prune79.0ms

Filtered
43 candidates to 58 candidates (-34.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New57158
Fresh022
Picked011
Done000
Total57461

Merged error: 16.5b

Counts
61 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))
0.1b
(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))
0.5b
(*.f64 (+.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))) (-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))))
2.3b
(-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt_binary64
52×sqrt-prod_binary64
46×sqrt-div_binary64
41×*-un-lft-identity_binary64
24×times-frac_binary64
20×add-cube-cbrt_binary64
17×flip3--_binary64 flip--_binary64
16×frac-times_binary64
12×associate-*r*_binary64 difference-of-squares_binary64 frac-sub_binary64
10×frac-add_binary64
9×distribute-lft-out--_binary64
8×pow1_binary64
6×add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 associate-*l*_binary64
5×flip3-+_binary64 flip-+_binary64
4×associate-*r/_binary64 rem-sqrt-square_binary64 associate-*l/_binary64
3×sub-neg_binary64 distribute-lft-out_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 div-inv_binary64
1×pow-prod-down_binary64 diff-log_binary64 cbrt-unprod_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 prod-exp_binary64 *-commutative_binary64
Counts
4 → 128
Calls
4 calls:
3.0ms
(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))
3.0ms
(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))
30.0ms
(*.f64 (+.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))) (-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))))
15.0ms
(-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))))

series74.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))
12.0ms
(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))
36.0ms
(*.f64 (+.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))) (-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))))
15.0ms
(-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))))

simplify49.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
051182888

prune343.0ms

Filtered
102 candidates to 140 candidates (-37.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1391140
Fresh022
Picked101
Done011
Total1404144

Merged error: 16.5b

Counts
144 → 4

localize40.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3)
1.0b
(*.f64 (sqrt.f64 (+.f64 (*.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 0.5)))) (sqrt.f64 0.5))
1.0b
(pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3)
2.3b
(-.f64 (pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3) (pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
136×add-sqr-sqrt_binary64
102×sqrt-prod_binary64
70×unpow-prod-down_binary64 cube-prod_binary64
64×*-un-lft-identity_binary64
50×difference-of-squares_binary64
30×add-cube-cbrt_binary64 times-frac_binary64
19×distribute-lft-out--_binary64
16×sqr-pow_binary64
12×pow1_binary64
9×sqrt-div_binary64
8×add-exp-log_binary64 add-cbrt-cube_binary64
7×cube-div_binary64
6×pow-unpow_binary64 add-log-exp_binary64 associate-*r*_binary64 pow-pow_binary64 associate-*l*_binary64
4×pow1/2_binary64 sqrt-pow1_binary64 unswap-sqr_binary64
3×pow-prod-down_binary64 flip3--_binary64 flip--_binary64
2×pow-to-exp_binary64 sqrt-pow2_binary64 rem-cube-cbrt_binary64 div-inv_binary64 frac-sub_binary64 pow-exp_binary64 unpow3_binary64 associate-*l/_binary64 cube-mult_binary64
1×difference-cubes_binary64 flip3-+_binary64 sub-neg_binary64 diff-log_binary64 cbrt-unprod_binary64 sqrt-unprod_binary64 prod-exp_binary64 flip-+_binary64 *-commutative_binary64
Counts
4 → 198
Calls
4 calls:
6.0ms
(pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3)
9.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 0.5)))) (sqrt.f64 0.5))
6.0ms
(pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3)
44.0ms
(-.f64 (pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3) (pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3))

series62.0ms

Counts
4 → 8
Calls
4 calls:
21.0ms
(pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3)
0.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 0.5)))) (sqrt.f64 0.5))
0.0ms
(pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3)
40.0ms
(-.f64 (pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3) (pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3))

simplify51.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
051853816

prune682.0ms

Filtered
86 candidates to 206 candidates (-139.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2033206
Fresh112
Picked101
Done011
Total2055210

Merged error: 16.1b

Counts
210 → 5

regimes272.0ms

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
03724
13724

end0.0ms

sample1.1s

Algorithm
intervals
Results
660.0ms2899×body1280valid
164.0ms4050×body80valid
107.0ms595×body640valid
38.0ms305×body320valid
12.0ms151×body160valid

Profiling

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