Details

Time bar (total: 3.6s)

sample15.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
074
174

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.7b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
28.6b
(sqrt (+ (* x x) (* y y)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
3.0ms
(+ (* x x) (* y y))
3.0ms
(sqrt (+ (* x x) (* y y)))

series66.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(+ (* x x) (* y y))
40.0ms
(sqrt (+ (* x x) (* y y)))

simplify49.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
0125177
1530163
21540163
35001162

prune62.0ms

Filtered
32 candidates to 25 candidates (78.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New27532
Fresh000
Picked011
Done000
Total27633

Merged error: 7.9b

Counts
33 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (cbrt (+ (* x x) (* y y))))
0.3b
(* (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (cbrt (+ (* x x) (* y y)))))
29.6b
(cbrt (+ (* x x) (* y y)))
29.6b
(cbrt (+ (* x x) (* y y)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×cbrt-prod sqrt-prod
12×add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×cbrt-div
7×pow1
6×add-exp-log add-cbrt-cube
4×flip3-+ sqrt-div flip-+ add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×rem-sqrt-square sqrt-pow1 associate-*r/
1×pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 74
Calls
4 calls:
4.0ms
(sqrt (cbrt (+ (* x x) (* y y))))
7.0ms
(* (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (cbrt (+ (* x x) (* y y)))))
3.0ms
(cbrt (+ (* x x) (* y y)))
3.0ms
(cbrt (+ (* x x) (* y y)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(sqrt (cbrt (+ (* x x) (* y y))))
113.0ms
(* (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (cbrt (+ (* x x) (* y y)))))
92.0ms
(cbrt (+ (* x x) (* y y)))
92.0ms
(cbrt (+ (* x x) (* y y)))

simplify125.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (116.0ms)

IterNodesCost
0278853
11080799
24410792
35002785

prune220.0ms

Filtered
86 candidates to 73 candidates (84.9%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New84286
Fresh134
Picked011
Done011
Total85792

Merged error: 7.9b

Counts
92 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (exp (log (cbrt (+ (* x x) (* y y)))))))
5.3b
(exp (log (cbrt (+ (* x x) (* y y)))))
29.6b
(cbrt (+ (* x x) (* y y)))
29.6b
(cbrt (+ (* x x) (* y y)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
14×add-cube-cbrt log-prod *-un-lft-identity exp-sum
13×cbrt-prod
12×associate-*r* sqrt-prod
8×cbrt-div
7×pow1
6×add-exp-log add-cbrt-cube
5×exp-prod
4×log-div flip3-+ exp-diff flip-+ add-log-exp unswap-sqr
3×pow1/3 associate-*l*
2×sqrt-div associate-*r/ log-pow
1×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log
Counts
4 → 79
Calls
4 calls:
19.0ms
(* (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (exp (log (cbrt (+ (* x x) (* y y)))))))
9.0ms
(exp (log (cbrt (+ (* x x) (* y y)))))
3.0ms
(cbrt (+ (* x x) (* y y)))
3.0ms
(cbrt (+ (* x x) (* y y)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (exp (log (cbrt (+ (* x x) (* y y)))))))
98.0ms
(exp (log (cbrt (+ (* x x) (* y y)))))
132.0ms
(cbrt (+ (* x x) (* y y)))
121.0ms
(cbrt (+ (* x x) (* y y)))

simplify124.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (114.0ms)

IterNodesCost
0313987
11103912
24342886
35001870

prune349.0ms

Filtered
91 candidates to 76 candidates (83.5%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New90191
Fresh134
Picked011
Done022
Total91798

Merged error: 7.9b

Counts
98 → 7

localize37.0ms

Local error

Found 4 expressions with local error:

29.6b
(cbrt (+ (* x x) (* y y)))
29.6b
(cbrt (+ (* x x) (* y y)))
29.6b
(cbrt (+ (* x x) (* y y)))
29.6b
(cbrt (+ (* x x) (* y y)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
5.0ms
(cbrt (+ (* x x) (* y y)))
6.0ms
(cbrt (+ (* x x) (* y y)))
7.0ms
(cbrt (+ (* x x) (* y y)))
7.0ms
(cbrt (+ (* x x) (* y y)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(cbrt (+ (* x x) (* y y)))
99.0ms
(cbrt (+ (* x x) (* y y)))
93.0ms
(cbrt (+ (* x x) (* y y)))
104.0ms
(cbrt (+ (* x x) (* y y)))

simplify51.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0123488
1408452
21387444
35001444

prune302.0ms

Filtered
64 candidates to 60 candidates (93.8%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New63164
Fresh033
Picked101
Done033
Total64771

Merged error: 7.9b

Counts
71 → 7

regimes426.0ms

Accuracy

59% (9.8b remaining)

Error of 17.9b against oracle of 8.1b and baseline of 32.0b

bsearch44.0ms

Steps
ItersRangePoint
7
3.3840843726061656e+70
7.402926812642739e+71
6.097588289625691e+71
8
-9.551618771889815e+129
-1.155698580497464e+126
-1.3830219520310334e+128

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0175
1175

end0.0ms

sample369.0ms

Algorithm
intervals
Results
238.0ms8000×body80valid