Details

Time bar (total: 7.3s)

analyze2.0ms

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

sample46.0ms

Algorithm
intervals
Results
25.0ms97×body1280valid
5.0ms129×body80valid
3.0ms19×body640valid
1.0ms9×body320valid
0.0ms2×body160valid

simplify141.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
04515
14515

prune17.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 15.1b

Counts
2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.9b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64_574 add-sqr-sqrt_binary64_559
8×sqrt-prod_binary64_553
4×difference-of-squares_binary64_603 add-log-exp_binary64_539
3×add-cube-cbrt_binary64_545 pow1_binary64_520 distribute-lft-out--_binary64_619
2×add-cbrt-cube_binary64_546 sqrt-div_binary64_554 distribute-lft-out_binary64_618 add-exp-log_binary64_538
1×rem-sqrt-square_binary64_562 flip3--_binary64_573 sqrt-pow1_binary64_555 flip3-+_binary64_572 flip-+_binary64_599 diff-log_binary64_490 sub-neg_binary64_578 pow1/2_binary64_510 flip--_binary64_600
Counts
2 → 34
Calls
2 calls:
6.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
9.0ms
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series107.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
58.0ms
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify87.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
05044763

prune115.0ms

Filtered
24 candidates to 40 candidates (-66.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New38240
Fresh000
Picked011
Done000
Total38341

Merged error: 14.6b

Counts
41 → 3

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.4b
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt_binary64_559
71×*-un-lft-identity_binary64_574
44×times-frac_binary64_569
29×distribute-lft-out_binary64_618
18×add-cube-cbrt_binary64_545 sqrt-prod_binary64_553
16×difference-of-squares_binary64_603
8×distribute-lft-out--_binary64_619
6×associate-/l*_binary64_638 associate-/r*_binary64_637
5×add-cbrt-cube_binary64_546 add-exp-log_binary64_538 add-log-exp_binary64_539
4×pow1_binary64_520
2×flip3--_binary64_573 associate-/r/_binary64_639 sqrt-div_binary64_554 associate-/l/_binary64_640 flip3-+_binary64_572 flip-+_binary64_599 flip--_binary64_600
1×rem-sqrt-square_binary64_562 div-inv_binary64_575 sqrt-pow1_binary64_555 div-exp_binary64_527 frac-2neg_binary64_567 diff-log_binary64_490 clear-num_binary64_577 sub-neg_binary64_578 pow1/2_binary64_510 div-sub_binary64_568 cbrt-undiv_binary64_544
Counts
3 → 95
Calls
3 calls:
24.0ms
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
6.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
6.0ms
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series244.0ms

Counts
3 → 9
Calls
3 calls:
149.0ms
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
55.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
40.0ms
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify90.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
050643292

prune322.0ms

Filtered
60 candidates to 104 candidates (-73.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1022104
Fresh101
Picked101
Done011
Total1043107

Merged error: 14.5b

Counts
107 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b
(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.2b
(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.5b
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
217×*-un-lft-identity_binary64_574
188×times-frac_binary64_569
147×add-sqr-sqrt_binary64_559
89×distribute-lft-out_binary64_618
81×add-cube-cbrt_binary64_545
48×sqrt-prod_binary64_553
16×associate-/l*_binary64_638
12×associate-/r*_binary64_637
11×add-cbrt-cube_binary64_546 div-inv_binary64_575 distribute-lft-out--_binary64_619 add-exp-log_binary64_538
8×associate-/r/_binary64_639
6×difference-of-squares_binary64_603 add-log-exp_binary64_539
5×pow1_binary64_520 flip3-+_binary64_572 flip-+_binary64_599
4×div-exp_binary64_527 cbrt-undiv_binary64_544
3×distribute-rgt-out--_binary64_621
2×sqrt-div_binary64_554 frac-2neg_binary64_567 clear-num_binary64_577
1×rem-sqrt-square_binary64_562 flip3--_binary64_573 frac-sub_binary64_565 associate-/l/_binary64_640 sqrt-pow1_binary64_555 diff-log_binary64_490 sub-neg_binary64_578 pow1/2_binary64_510 sub-div_binary64_563 flip--_binary64_600
Counts
4 → 204
Calls
4 calls:
6.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
10.0ms
(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
14.0ms
(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
97.0ms
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

series547.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
97.0ms
(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
131.0ms
(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
263.0ms
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

simplify123.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049628119
149628119

prune1.1s

Filtered
124 candidates to 216 candidates (-74.2%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2142216
Fresh011
Picked101
Done011
Total2154219

Merged error: 14.3b

Counts
219 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(-.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
0.5b
(/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
0.5b
(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
0.6b
(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
319×times-frac_binary64_569
306×*-un-lft-identity_binary64_574
256×add-sqr-sqrt_binary64_559
217×sqrt-prod_binary64_553
142×add-cube-cbrt_binary64_545
104×distribute-lft-out_binary64_618
27×associate-/r*_binary64_637
19×associate-/l*_binary64_638
16×distribute-lft-out--_binary64_619
15×div-inv_binary64_575 difference-of-squares_binary64_603
14×add-exp-log_binary64_538
13×add-cbrt-cube_binary64_546
10×associate-/r/_binary64_639 sqrt-div_binary64_554
6×pow1_binary64_520 add-log-exp_binary64_539
5×div-exp_binary64_527 flip3-+_binary64_572 flip-+_binary64_599 cbrt-undiv_binary64_544
3×distribute-rgt-out--_binary64_621 pow-flip_binary64_504 frac-2neg_binary64_567 clear-num_binary64_577
1×flip3--_binary64_573 frac-sub_binary64_565 inv-pow_binary64_496 associate-/l/_binary64_640 sqrt-pow1_binary64_555 rec-exp_binary64_526 diff-log_binary64_490 sub-neg_binary64_578 pow1/2_binary64_510 sub-div_binary64_563 flip--_binary64_600
Counts
4 → 314
Calls
4 calls:
164.0ms
(-.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
18.0ms
(/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
12.0ms
(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
17.0ms
(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

series758.0ms

Counts
4 → 12
Calls
4 calls:
321.0ms
(-.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
131.0ms
(/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
125.0ms
(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
181.0ms
(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

simplify162.0ms

Algorithm
egg-herbie
Counts
326 → 326
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
0536413365

prune1.7s

Filtered
162 candidates to 326 candidates (-101.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3242326
Fresh022
Picked101
Done011
Total3255330

Merged error: 14.3b

Counts
330 → 5

regimes150.0ms

Accuracy

0% (0.7b remaining)

Error of 15.4b against oracle of 14.7b and baseline of 15.4b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04698
14698

end0.0ms

sample1.1s

Algorithm
intervals
Results
626.0ms2910×body1280valid
163.0ms4021×body80valid
109.0ms609×body640valid
36.0ms299×body320valid
18.0ms161×body160valid

Profiling

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