Details

Time bar (total: 20.5s)

sample55.0ms

Algorithm
intervals
Results
32.0ms256×body80valid

simplify31.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (* y y))
0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
35.2b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×rem-sqrt-square div-inv
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num fma-udef
Counts
3 → 66
Calls
3 calls:
1.0ms
(fma x x (* y y))
10.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
8.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series376.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(fma x x (* y y))
77.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
251.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify3.1s

Counts
75 → 75
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
01121226
11761167
24051059
311111059
443451059
done50001059

prune356.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (* y y))
0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
35.1b
(sqrt (fma z z (fma x x (* y y))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num fma-udef div-inv
Counts
3 → 88
Calls
3 calls:
1.0ms
(fma x x (* y y))
17.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
4.0ms
(sqrt (fma z z (fma x x (* y y))))

series578.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(fma x x (* y y))
374.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
162.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify3.7s

Counts
97 → 97
Iterations

Useful iterations: 3 (237.0ms)

IterNodesCost
01171869
11741693
23351631
36481629
413571629
530951629
done50001629

prune381.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.3b

localize5.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ y (sqrt 3.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
6×associate-/r*
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 41
Calls
1 calls:
7.0ms
(/ y (sqrt 3.0))

series82.0ms

Counts
1 → 3
Calls
1 calls:
82.0ms
(/ y (sqrt 3.0))

simplify6.2s

Counts
44 → 44
Iterations

Useful iterations: 3 (125.0ms)

IterNodesCost
068381
1105344
2190334
3301332
4504332
5763332
61424332
74858332
done5002332

prune128.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 14.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (* y y))
0.4b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
35.1b
(sqrt (fma z z (fma x x (* y y))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×sqrt-prod
16×*-un-lft-identity associate-*r*
14×add-cube-cbrt
13×times-frac
8×pow1 unswap-sqr
6×associate-*l*
5×add-exp-log add-cbrt-cube
3×expm1-log1p-u sqrt-pow1 pow1/2 pow-prod-down log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod fma-udef div-inv
Counts
3 → 72
Calls
3 calls:
0.0ms
(fma x x (* y y))
22.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series402.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(fma x x (* y y))
232.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
133.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify3.1s

Counts
81 → 81
Iterations

Useful iterations: 2 (122.0ms)

IterNodesCost
01121300
11891182
23881115
38881115
427161115
done50011115

prune275.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 14.2b

regimes433.0ms

Accuracy

48.2% (13.1b remaining)

Error of 25.5b against oracle of 12.4b and baseline of 37.7b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01625
done1625

end0.0ms

sample1.1s

Algorithm
intervals
Results
669.0ms8000×body80valid