Details

Time bar (total: 8.4s)

sample23.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify13.0ms

Counts
1 → 1
Iterations
IterNodes
done31
331
224
114
09

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma z z (fma y y (* x x)))
0.0b
(fma y y (* x x))
36.1b
(sqrt (fma z z (fma y y (* x x))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×pow1 *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u add-cbrt-cube add-exp-log sqrt-prod log1p-expm1-u add-log-exp
2×fma-udef
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
3 → 35
Calls
3 calls:
0.0ms
(fma z z (fma y y (* x x)))
0.0ms
(fma y y (* x x))
2.0ms
(sqrt (fma z z (fma y y (* x x))))

series299.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(fma z z (fma y y (* x x)))
54.0ms
(fma y y (* x x))
166.0ms
(sqrt (fma z z (fma y y (* x x))))

simplify994.0ms

Counts
44 → 44
Iterations
IterNodes
done5000
3828
2202
172
049

prune241.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma y y (* x x))
0.5b
(* (sqrt (sqrt (fma z z (fma y y (* x x))))) (sqrt (sqrt (fma z z (fma y y (* x x))))))
36.1b
(sqrt (fma z z (fma y y (* x x))))
36.1b
(sqrt (fma z z (fma y y (* x x))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
18×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 117
Calls
4 calls:
0.0ms
(fma y y (* x x))
31.0ms
(* (sqrt (sqrt (fma z z (fma y y (* x x))))) (sqrt (sqrt (fma z z (fma y y (* x x))))))
2.0ms
(sqrt (fma z z (fma y y (* x x))))
3.0ms
(sqrt (fma z z (fma y y (* x x))))

series583.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(fma y y (* x x))
164.0ms
(* (sqrt (sqrt (fma z z (fma y y (* x x))))) (sqrt (sqrt (fma z z (fma y y (* x x))))))
147.0ms
(sqrt (fma z z (fma y y (* x x))))
202.0ms
(sqrt (fma z z (fma y y (* x x))))

simplify1.6s

Counts
129 → 129
Iterations
IterNodes
done5001
2951
1189
099

prune529.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 20.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma y y (* x x))
0.1b
(* (sqrt (fma z z (fma y y (* x x)))) (fma z z (fma y y (* x x))))
36.1b
(sqrt (fma z z (fma y y (* x x))))
44.0b
(cbrt (* (sqrt (fma z z (fma y y (* x x)))) (fma z z (fma y y (* x x)))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
8×*-un-lft-identity add-cube-cbrt
7×sqrt-prod
6×add-cbrt-cube associate-*l* add-exp-log
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 associate-*r* fma-udef
2×pow-plus cube-unmult pow-prod-up unswap-sqr
1×cbrt-prod distribute-rgt-in rem-sqrt-square distribute-lft-in pow1/3 pow-prod-down prod-exp *-commutative rem-cbrt-cube cbrt-unprod
Counts
4 → 68
Calls
4 calls:
0.0ms
(fma y y (* x x))
15.0ms
(* (sqrt (fma z z (fma y y (* x x)))) (fma z z (fma y y (* x x))))
2.0ms
(sqrt (fma z z (fma y y (* x x))))
8.0ms
(cbrt (* (sqrt (fma z z (fma y y (* x x)))) (fma z z (fma y y (* x x)))))

series742.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(fma y y (* x x))
342.0ms
(* (sqrt (fma z z (fma y y (* x x)))) (fma z z (fma y y (* x x))))
192.0ms
(sqrt (fma z z (fma y y (* x x))))
161.0ms
(cbrt (* (sqrt (fma z z (fma y y (* x x)))) (fma z z (fma y y (* x x)))))

simplify1.1s

Counts
80 → 80
Iterations
IterNodes
done5000
2748
1166
089

prune708.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 20.4b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune1.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 20.4b

regimes316.0ms

Accuracy

55.3% (8.6b remaining)

Error of 26.5b against oracle of 17.9b and baseline of 37.1b

bsearch244.0ms

Steps
ItersRangePoint
9
3.013358468678059e+131
3.4762415567430176e+137
5.351693709150229e+134
8
2.0486947557873143e-143
1.1606406980354002e-138
3.9603915982691884e-142
9
5.52218963463424e-246
7.727489113673076e-240
7.631866408902893e-240
8
-4.576169969964438e+85
-2.2312565755866114e+81
-2.4101921118306453e+85

simplify3.0ms

Iterations
IterNodes
done20
020

end0.0ms

sample904.0ms

Algorithm
intervals
Results
553.0ms8000×body80valid