Details

Time bar (total: 13.7s)

sample34.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify23.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
0912
11411
22410
33110
done3110

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
37.8b
(sqrt (fma z z (fma x x (* y y))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
2 → 25
Calls
2 calls:
1.0ms
(fma z z (fma x x (* y y)))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series292.0ms

Counts
2 → 6
Calls
2 calls:
79.0ms
(fma z z (fma x x (* y y)))
213.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify3.4s

Counts
31 → 31
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
038363
160333
2151304
3588304
44299304
done5000304

prune157.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (fma z z (fma x x (* y y)))))
0.5b
(* (sqrt (sqrt (fma z z (fma x x (* y y))))) (sqrt (sqrt (fma z z (fma x x (* y y))))))
37.8b
(sqrt (fma z z (fma x x (* y y))))
37.8b
(sqrt (fma z z (fma x x (* y y))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u rem-sqrt-square log1p-expm1-u add-log-exp
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 128
Calls
4 calls:
3.0ms
(sqrt (sqrt (fma z z (fma x x (* y y)))))
24.0ms
(* (sqrt (sqrt (fma z z (fma x x (* y y))))) (sqrt (sqrt (fma z z (fma x x (* y y))))))
2.0ms
(sqrt (fma z z (fma x x (* y y))))
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series848.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(sqrt (sqrt (fma z z (fma x x (* y y)))))
213.0ms
(* (sqrt (sqrt (fma z z (fma x x (* y y))))) (sqrt (sqrt (fma z z (fma x x (* y y))))))
210.0ms
(sqrt (fma z z (fma x x (* y y))))
223.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify1.9s

Counts
140 → 140
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01032980
12131821
210171681
done50011644

prune491.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 20.3b

localize42.0ms

Local error

Found 4 expressions with local error:

37.8b
(sqrt (* (* (cbrt (fma z z (fma x x (* y y)))) (cbrt (fma z z (fma x x (* y y))))) (cbrt (fma z z (fma x x (* y y))))))
38.9b
(cbrt (fma z z (fma x x (* y y))))
38.9b
(cbrt (fma z z (fma x x (* y y))))
38.9b
(cbrt (fma z z (fma x x (* y y))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
15×sqrt-pow1
12×pow1/3
9×cbrt-prod pow-prod-up
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 65
Calls
4 calls:
40.0ms
(sqrt (* (* (cbrt (fma z z (fma x x (* y y)))) (cbrt (fma z z (fma x x (* y y))))) (cbrt (fma z z (fma x x (* y y))))))
2.0ms
(cbrt (fma z z (fma x x (* y y))))
2.0ms
(cbrt (fma z z (fma x x (* y y))))
3.0ms
(cbrt (fma z z (fma x x (* y y))))

series854.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(sqrt (* (* (cbrt (fma z z (fma x x (* y y)))) (cbrt (fma z z (fma x x (* y y))))) (cbrt (fma z z (fma x x (* y y))))))
219.0ms
(cbrt (fma z z (fma x x (* y y))))
210.0ms
(cbrt (fma z z (fma x x (* y y))))
213.0ms
(cbrt (fma z z (fma x x (* y y))))

simplify3.2s

Counts
77 → 77
Iterations

Useful iterations: 4 (1.6s)

IterNodesCost
0731247
11381122
2310828
3965765
44414762
done5000762

prune374.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 20.3b

localize1.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 20.3b

regimes274.0ms

Accuracy

60.1% (8.0b remaining)

Error of 26.0b against oracle of 18.0b and baseline of 38.0b

bsearch212.0ms

Steps
ItersRangePoint
8
2.076897170420828e+65
8.513147127683243e+68
1.3138979852720737e+67
9
-2.154144417514084e-248
-4.713895385524712e-257
-2.0033564760002915e-248
10
-2.004514806375514e-194
-4.7948385983044623e-206
-2.6727131427269115e-197
9
-1.593392701854085e+123
-2.829049393529762e+117
-2.6686434086554147e+122

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02040
done2040

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s8000×body80valid