Details

Time bar (total: 16.9s)

sample24.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
30.4b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite12.0ms

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:
0.0ms
(fma z z (fma x x (* y y)))
5.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
4.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series410.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(fma z z (fma x x (* y y)))
80.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
273.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify3.3s

Counts
75 → 75
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
01071274
11711215
23761106
310901106
443691106
done50001106

prune356.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
30.3b
(sqrt (fma z z (fma x x (* y y))))

rewrite15.0ms

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:
0.0ms
(fma z z (fma x x (* y y)))
8.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series589.0ms

Counts
3 → 9
Calls
3 calls:
85.0ms
(fma z z (fma x x (* y y)))
318.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
186.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify2.7s

Counts
97 → 97
Iterations

Useful iterations: 3 (276.0ms)

IterNodesCost
01161917
11771741
23441678
38111676
429651676
done50001676

prune339.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 17.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.4b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
30.3b
(sqrt (fma z z (fma x x (* y y))))

rewrite42.0ms

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 z z (fma x x (* y y)))
37.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series505.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(fma z z (fma x x (* y y)))
267.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
166.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify3.5s

Counts
81 → 81
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
01111348
11921230
23981162
311101162
447081162
done50001162

prune261.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 17.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.4b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
5.9b
(exp (log (* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))))
30.3b
(sqrt (fma z z (fma x x (* y y))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
29×sqrt-prod
18×*-un-lft-identity
16×add-cube-cbrt associate-*r*
14×pow1
13×times-frac
8×unswap-sqr
7×exp-prod
6×add-exp-log associate-*l* pow-prod-down add-cbrt-cube
5×sqrt-pow1 pow1/2
4×expm1-log1p-u log-pow log1p-expm1-u add-log-exp
2×sqrt-div associate-*r/
1×rem-sqrt-square log-div log-prod exp-diff sqrt-unprod exp-sum prod-exp *-commutative cbrt-unprod fma-udef div-inv rem-exp-log
Counts
4 → 91
Calls
4 calls:
0.0ms
(fma z z (fma x x (* y y)))
35.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
47.0ms
(exp (log (* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))))
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series730.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(fma z z (fma x x (* y y)))
262.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
253.0ms
(exp (log (* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))))
143.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify2.2s

Counts
103 → 103
Iterations

Useful iterations: 2 (165.0ms)

IterNodesCost
01361681
12241504
24561424
312651424
done50011424

prune374.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 17.0b

regimes344.0ms

Accuracy

61.9% (7.3b remaining)

Error of 25.9b against oracle of 18.6b and baseline of 37.8b

bsearch151.0ms

Steps
ItersRangePoint
7
1.2097950679130598e+120
2.8096875911191325e+121
2.7010859166721207e+121
8
1.0246055850432579e-284
4.6961454093349e-282
1.0826621875915e-284
6
-2.6483090030731803e-308
3.263116816351477e-308
3.2169338021372217e-308
8
-2.9247701996111134e+154
-1.9690694688920877e+151
-1.919949817214074e+152

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03054
13654
23854
done3854

end0.0ms

sample820.0ms

Algorithm
intervals
Results
520.0ms8000×body80valid