Details

Time bar (total: 8.9s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
01114
11613
22612
33112
done3112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize8.0ms

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)
35.6b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite10.0ms

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

series268.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(fma x x (* y y))
57.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
175.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify851.0ms

Counts
75 → 75
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
01121226
11781167
25111059
318991059
done50001059

prune229.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize12.0ms

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)))
35.5b
(sqrt (fma z z (fma x x (* y y))))

rewrite17.0ms

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))
14.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
1.0ms
(sqrt (fma z z (fma x x (* y y))))

series323.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(fma x x (* y y))
176.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
114.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify1.6s

Counts
81 → 81
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
01121300
11931201
26141115
320191115
done50001115

prune204.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.4b

localize10.0ms

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))
35.5b
(sqrt (fma z z (fma x x (* y y))))

rewrite8.0ms

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 x x (* y y))
4.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
1.0ms
(sqrt (fma z z (fma x x (* y y))))

series382.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(fma x x (* y y))
234.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
115.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify791.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
01171869
11771705
24391629
315381629
done50001629

prune217.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.3b

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ y (sqrt 3.0))

rewrite7.0ms

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:
5.0ms
(/ y (sqrt 3.0))

series53.0ms

Counts
1 → 3
Calls
1 calls:
52.0ms
(/ y (sqrt 3.0))

simplify3.1s

Counts
44 → 44
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
068381
1108352
2268332
3725332
41460332
52739332
done5000332

prune67.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 18.3b

regimes239.0ms

Accuracy

62.5% (7.2b remaining)

Error of 26.2b against oracle of 19.0b and baseline of 38.3b

bsearch63.0ms

Steps
ItersRangePoint
7
1.2661661996649535e+75
4.048855189716541e+76
3.540104367259201e+76
8
-3.4896836630642546e+148
-3.866551906455378e+145
-1.4065040948592316e+146

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02234
12834
done2834

end0.0ms

sample444.0ms

Algorithm
intervals
Results
269.0ms8000×body80valid