Details

Time bar (total: 16.2s)

sample33.0ms

Algorithm
intervals
Results
17.0ms256×body80valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
011284
116259
226234
332234
done32234

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x x (* y y))
0.0b
(fma z z (fma x x (* y y)))
0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
32.8b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×sqrt-prod
6×add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×rem-sqrt-square fma-udef div-inv
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp
Counts
4 → 76
Calls
4 calls:
0.0ms
(fma x x (* y y))
0.0ms
(fma z z (fma x x (* y y)))
7.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
6.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series504.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(fma x x (* y y))
68.0ms
(fma z z (fma x x (* y y)))
73.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
300.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify2.5s

Counts
88 → 88
Iterations

Useful iterations: 2 (128.0ms)

IterNodesCost
011829941
118624870
257324280
3329824280
done500024280

prune553.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x x (* y y))
0.0b
(fma z z (fma x x (* y y)))
0.1b
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
32.8b
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt
6×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×sqrt-pow1 pow-prod-down
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp *-commutative sqrt-prod cbrt-unprod unswap-sqr
Counts
4 → 55
Calls
4 calls:
0.0ms
(fma x x (* y y))
0.0ms
(fma z z (fma x x (* y y)))
11.0ms
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
6.0ms
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

series512.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(fma x x (* y y))
73.0ms
(fma z z (fma x x (* y y)))
95.0ms
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
293.0ms
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

simplify3.7s

Counts
67 → 67
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
08118627
115613959
264913649
3475013449
done500013449

prune389.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x x (* y y))
0.0b
(fma z z (fma x x (* y y)))
0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
32.7b
(sqrt (fma z z (fma x x (* y y))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
34×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
6×associate-/r* add-cbrt-cube add-exp-log associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×fma-udef
1×cbrt-undiv rem-sqrt-square sqrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 98
Calls
4 calls:
0.0ms
(fma x x (* y y))
0.0ms
(fma z z (fma x x (* y y)))
7.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
1.0ms
(sqrt (fma z z (fma x x (* y y))))

series612.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(fma x x (* y y))
74.0ms
(fma z z (fma x x (* y y)))
335.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
146.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify4.3s

Counts
110 → 110
Iterations

Useful iterations: 2 (181.0ms)

IterNodesCost
012743985
119439356
266639121
3406439121
done500139121

prune571.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 14.7b

localize10.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ (- z) (sqrt 3.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
44×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
33×sqrt-prod
21×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/l*
7×neg-mul-1
6×associate-/r*
3×add-cbrt-cube add-exp-log
1×neg-sub0 expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-sub div-exp distribute-frac-neg log1p-expm1-u div-inv add-log-exp
Counts
1 → 92
Calls
1 calls:
8.0ms
(/ (- z) (sqrt 3.0))

series67.0ms

Counts
1 → 3
Calls
1 calls:
67.0ms
(/ (- z) (sqrt 3.0))

simplify614.0ms

Counts
95 → 95
Iterations

Useful iterations: 2 (123.0ms)

IterNodesCost
013328429
126026100
281326019
done500026019

prune242.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 14.7b

regimes598.0ms

Accuracy

62.5% (7.5b remaining)

Error of 25.8b against oracle of 18.3b and baseline of 38.3b

bsearch88.0ms

Steps
ItersRangePoint
9
2.699479943071983e+113
1.2388519257666938e+120
9.721182782519792e+117
6
-4.389998254864137e+150
-9.036506680703694e+149
-1.0323608071043042e+150

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
020657
122657
done22657

end0.0ms

sample732.0ms

Algorithm
intervals
Results
525.0ms8000×body80valid