Details

Time bar (total: 19.1s)

sample25.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify22.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.0b
(fma x x (* y y))
0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
34.1b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
6×add-exp-log add-cbrt-cube
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 frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 76
Calls
4 calls:
0.0ms
(fma z z (fma x x (* y y)))
0.0ms
(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))

series483.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(fma z z (fma x x (* y y)))
63.0ms
(fma x x (* y y))
97.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
236.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify3.5s

Counts
88 → 88
Iterations

Useful iterations: 2 (121.0ms)

IterNodesCost
01181382
11831320
24201191
312401191
448221191
done50001191

prune446.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.0b
(fma x x (* y y))
0.3b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
34.0b
(sqrt (fma z z (fma x x (* y y))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×sqrt-prod
17×*-un-lft-identity
16×associate-*r*
15×add-cube-cbrt
13×times-frac
9×pow1
8×unswap-sqr
6×add-exp-log associate-*l* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 pow-prod-down
2×fma-udef
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 82
Calls
4 calls:
0.0ms
(fma z z (fma x x (* y y)))
0.0ms
(fma x x (* y y))
34.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series598.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(fma z z (fma x x (* y y)))
65.0ms
(fma x x (* y y))
262.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
203.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify2.2s

Counts
94 → 94
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
01221456
12041335
24371247
312571247
done50001247

prune389.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.0b
(fma x x (* y y))
0.3b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
34.0b
(sqrt (fma z z (fma x x (* y y))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
6×add-exp-log associate-/r* add-cbrt-cube 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 frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 98
Calls
4 calls:
0.0ms
(fma z z (fma x x (* y y)))
0.0ms
(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))))

series626.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(fma z z (fma x x (* y y)))
63.0ms
(fma x x (* y y))
357.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
138.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify2.7s

Counts
110 → 110
Iterations

Useful iterations: 3 (226.0ms)

IterNodesCost
01272025
11891846
23851763
39511761
434141761
done50001761

prune365.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.2b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
44×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
33×sqrt-prod
21×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/l*
7×neg-mul-1
6×associate-/r*
3×add-exp-log add-cbrt-cube
1×pow1 cbrt-undiv neg-sub0 expm1-log1p-u frac-2neg div-sub distribute-frac-neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 92
Calls
1 calls:
10.0ms
(/ (- z) (sqrt 3.0))

series98.0ms

Counts
1 → 3
Calls
1 calls:
98.0ms
(/ (- z) (sqrt 3.0))

simplify5.4s

Counts
95 → 95
Iterations

Useful iterations: 3 (435.0ms)

IterNodesCost
01331051
1233942
2494930
31208928
43263928
done5000928

prune223.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 16.2b

regimes350.0ms

Accuracy

63.8% (7.2b remaining)

Error of 25.6b against oracle of 18.4b and baseline of 38.2b

bsearch125.0ms

Steps
ItersRangePoint
9
3.3911511265698697e+126
1.3870714403563658e+135
4.171828716999667e+130
10
-3.7885935661345695e+111
-7.715368434473106e+100
-3.746938595761261e+111

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02637
13137
23337
done3337

end0.0ms

sample1.3s

Algorithm
intervals
Results
931.0ms8000×body80valid