Details

Time bar (total: 17.2s)

sample40.0ms

Algorithm
intervals
Results
22.0ms256×body80valid

simplify28.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
35.5b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite11.0ms

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

series380.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
295.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify2.5s

Counts
62 → 62
Iterations

Useful iterations: 3 (261.0ms)

IterNodesCost
01011118
11641062
2362977
3933974
43336974
done5000974

prune315.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))
35.4b
(sqrt (fma z z (fma x x (* y y))))
35.4b
(sqrt (fma z z (fma x x (* y y))))
35.5b
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
21×cbrt-prod
9×pow1
6×add-exp-log associate-/r* associate-/l*
5×add-cbrt-cube
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×pow1/2 sqrt-div
2×rem-sqrt-square
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv
Counts
4 → 108
Calls
4 calls:
15.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))
3.0ms
(sqrt (fma z z (fma x x (* y y))))
3.0ms
(sqrt (fma z z (fma x x (* y y))))
58.0ms
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
410.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))
175.0ms
(sqrt (fma z z (fma x x (* y y))))
190.0ms
(sqrt (fma z z (fma x x (* y y))))
522.0ms
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))))

simplify5.4s

Counts
120 → 120
Iterations

Useful iterations: 3 (252.0ms)

IterNodesCost
01322478
11952082
23411983
36191947
412241947
520231947
635301947
done50001947

prune531.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.8b

localize29.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (fma x x (fma y y (pow z 2))))
35.5b
(sqrt (* 0.3333333333333333 (fma x x (fma y y (pow z 2)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt
4×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×associate-*r* associate-*l*
2×expm1-log1p-u sqrt-pow1 pow-prod-down fma-udef log1p-expm1-u add-log-exp
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
2 → 35
Calls
2 calls:
7.0ms
(* 0.3333333333333333 (fma x x (fma y y (pow z 2))))
7.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (pow z 2)))))

series341.0ms

Counts
2 → 6
Calls
2 calls:
78.0ms
(* 0.3333333333333333 (fma x x (fma y y (pow z 2))))
264.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (pow z 2)))))

simplify884.0ms

Counts
41 → 41
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
064567
1124533
2303473
31210473
done5000473

prune202.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.5b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
35.4b
(sqrt (fma z z (fma x x (* y y))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
32×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
3×pow1
2×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 div-inv
Counts
2 → 78
Calls
2 calls:
9.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series479.0ms

Counts
2 → 6
Calls
2 calls:
321.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
158.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify2.9s

Counts
84 → 84
Iterations

Useful iterations: 3 (202.0ms)

IterNodesCost
01041761
11551588
22791546
34871544
49101544
514001544
628941544
done50001544

prune304.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.4b

regimes452.0ms

Accuracy

37.7% (19.3b remaining)

Error of 26.1b against oracle of 6.8b and baseline of 37.8b

bsearch68.0ms

Steps
ItersRangePoint
8
5.294198543636e+57
5.840439438579558e+61
5.165075679522047e+61
6
-1.2093633317186018e+82
-1.201978405841871e+81
-1.1896418808192102e+82

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02648
13248
23448
done3448

end0.0ms

sample854.0ms

Algorithm
intervals
Results
614.0ms8000×body80valid