Details

Time bar (total: 12.1s)

sample20.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify15.0ms

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: 36.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
33.9b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×expm1-log1p-u rem-sqrt-square log1p-expm1-u div-inv add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
2 → 56
Calls
2 calls:
5.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
5.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series287.0ms

Counts
2 → 6
Calls
2 calls:
75.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
212.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify1.9s

Counts
62 → 62
Iterations

Useful iterations: 3 (201.0ms)

IterNodesCost
01011118
11641062
2362977
3933974
43336974
done5000974

prune227.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.9b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y y (pow z 2))
0.1b
(* 0.3333333333333333 (fma x x (fma y y (pow z 2))))
33.9b
(sqrt (* 0.3333333333333333 (fma x x (fma y y (pow z 2)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1
7×add-sqr-sqrt
5×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×expm1-log1p-u associate-*r* associate-*l* fma-udef log1p-expm1-u add-log-exp
2×sqrt-pow1 pow-prod-down
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
3 → 45
Calls
3 calls:
0.0ms
(fma y y (pow z 2))
8.0ms
(* 0.3333333333333333 (fma x x (fma y y (pow z 2))))
6.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (pow z 2)))))

series324.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(fma y y (pow z 2))
69.0ms
(* 0.3333333333333333 (fma x x (fma y y (pow z 2))))
211.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (pow z 2)))))

simplify781.0ms

Counts
54 → 54
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
075675
1136638
2346558
31431558
done5002558

prune180.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y y (pow z 2))
0.1b
(* (sqrt 0.3333333333333333) (sqrt (fma x x (fma y y (pow z 2)))))
33.8b
(sqrt (fma x x (fma y y (pow z 2))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity
6×associate-*r* associate-*l*
5×add-exp-log add-cbrt-cube
4×unswap-sqr
3×expm1-log1p-u sqrt-pow1 pow1/2 pow-prod-down log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-unprod prod-exp *-commutative cbrt-unprod fma-udef
Counts
3 → 57
Calls
3 calls:
0.0ms
(fma y y (pow z 2))
14.0ms
(* (sqrt 0.3333333333333333) (sqrt (fma x x (fma y y (pow z 2)))))
2.0ms
(sqrt (fma x x (fma y y (pow z 2))))

series381.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(fma y y (pow z 2))
202.0ms
(* (sqrt 0.3333333333333333) (sqrt (fma x x (fma y y (pow z 2)))))
135.0ms
(sqrt (fma x x (fma y y (pow z 2))))

simplify2.4s

Counts
66 → 66
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
072889
1124809
2316761
3826761
42463761
done5000761

prune206.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
33.8b
(sqrt (fma z z (fma x x (* y y))))
33.8b
(sqrt (fma z z (fma x x (* y y))))
33.9b
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0)) (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
49×sqrt-prod
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
14×pow1
8×sqrt-pow1
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square pow1/2 sqrt-div
1×cbrt-undiv pow2 frac-times sqrt-undiv frac-2neg pow-plus associate-*r/ div-exp pow-prod-down associate-*l/ clear-num pow-sqr pow-prod-up div-inv
Counts
4 → 114
Calls
4 calls:
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))))
2.0ms
(sqrt (fma z z (fma x x (* y y))))
22.0ms
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0)) (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))

series800.0ms

Counts
4 → 12
Calls
4 calls:
266.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
129.0ms
(sqrt (fma z z (fma x x (* y y))))
131.0ms
(sqrt (fma z z (fma x x (* y y))))
274.0ms
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0)) (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))

simplify3.2s

Counts
126 → 126
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
01252466
11822013
23141939
35561939
411231939
518231939
635491939
done50001939

prune382.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.8b

regimes231.0ms

Accuracy

39.6% (18.8b remaining)

Error of 25.1b against oracle of 6.3b and baseline of 37.5b

bsearch78.0ms

Steps
ItersRangePoint
8
5.2211603344189125e+47
1.338752107099957e+51
1.3221493030139048e+51
10
-1.1996080839781489e+124
-1.8713537616617044e+109
-3.655717002048407e+123

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02029
12429
22729
done2729

end0.0ms

sample509.0ms

Algorithm
intervals
Results
269.0ms8000×body80valid