Details

Time bar (total: 13.0s)

sample20.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
11613
22612
33012
done3012

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (* y y))
0.2b
(/ (fma z z (fma x x (* y y))) 3.0)
35.2b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite7.0ms

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))

series313.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(fma x x (* y y))
64.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
209.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify2.4s

Counts
75 → 75
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
01121226
11751167
24141059
312091059
447421059
done50001059

prune262.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y))))))
35.2b
(sqrt (fma z z (fma x x (* y y))))
35.2b
(sqrt (fma z z (fma x x (* y y))))
35.2b
(sqrt (/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y)))))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
508×times-frac
400×sqrt-prod
285×add-sqr-sqrt
266×add-cube-cbrt *-un-lft-identity
22×associate-/r*
15×div-inv
9×add-exp-log rem-sqrt-square add-cbrt-cube
7×pow1
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp
2×associate-/r/
1×frac-2neg sqrt-div clear-num
Counts
4 → 363
Calls
4 calls:
9.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y))))))
1.0ms
(sqrt (fma z z (fma x x (* y y))))
1.0ms
(sqrt (fma z z (fma x x (* y y))))
23.0ms
(sqrt (/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y)))))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y))))))
117.0ms
(sqrt (fma z z (fma x x (* y y))))
117.0ms
(sqrt (fma z z (fma x x (* y y))))
195.0ms
(sqrt (/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y)))))))

simplify1.2s

Counts
375 → 375
Iterations

Useful iterations: 2 (597.0ms)

IterNodesCost
043516247
174314709
2212512979
done500112979

prune706.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow x 2) (fma y y (pow z 2)))
0.1b
(* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2))))
35.2b
(sqrt (* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2)))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
9×add-sqr-sqrt
8×pow1 fma-def
7×add-cube-cbrt
5×add-exp-log add-cbrt-cube add-log-exp
4×associate-*r/ associate-*r*
3×expm1-log1p-u unpow-prod-down flip3-+ associate-*l* flip-+ log1p-expm1-u
2×sqrt-pow1 sqrt-div pow-prod-down distribute-lft-out
1×+-commutative distribute-rgt-in associate-+r+ distribute-lft-in pow1/2 prod-exp sum-log sqrt-prod *-commutative cbrt-unprod fma-udef unpow2 unswap-sqr sqr-pow
Counts
3 → 63
Calls
3 calls:
7.0ms
(+ (pow x 2) (fma y y (pow z 2)))
24.0ms
(* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2))))
7.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2)))))

series273.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(+ (pow x 2) (fma y y (pow z 2)))
52.0ms
(* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2))))
179.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2)))))

simplify2.0s

Counts
72 → 72
Iterations

Useful iterations: 3 (701.0ms)

IterNodesCost
0891003
1214925
2761793
33797787
done5000787

prune248.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
35.2b
(sqrt (fma z z (fma x x (* y y))))
35.2b
(sqrt (fma z z (fma x x (* y y))))
35.2b
(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))))

rewrite21.0ms

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:
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))))
1.0ms
(sqrt (fma z z (fma x x (* y y))))
11.0ms
(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))))

series746.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
123.0ms
(sqrt (fma z z (fma x x (* y y))))
121.0ms
(sqrt (fma z z (fma x x (* y y))))
252.0ms
(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))))

simplify3.1s

Counts
126 → 126
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
01252466
11822025
23121941
36351941
413121941
520391941
637761941
done50001941

prune378.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.1b

regimes212.0ms

Accuracy

38.9% (19.3b remaining)

Error of 25.8b against oracle of 6.6b and baseline of 38.1b

bsearch79.0ms

Steps
ItersRangePoint
9
6.367322558950871e+56
2.9131270869485945e+65
2.8539710068846394e+65
8
-6.818135621868607e+134
-9.818251175618728e+131
-2.2291282360035104e+133

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02341
12641
done2641

end0.0ms

sample452.0ms

Algorithm
intervals
Results
282.0ms8000×body80valid