Details

Time bar (total: 19.0s)

sample47.0ms

Algorithm
intervals
Results
26.0ms256×body80valid

simplify20.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
36.3b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite14.0ms

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:
6.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
4.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series350.0ms

Counts
2 → 6
Calls
2 calls:
103.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
247.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify3.0s

Counts
62 → 62
Iterations

Useful iterations: 3 (293.0ms)

IterNodesCost
01011118
11641062
2362977
3933974
43336974
done5000974

prune336.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.8b

localize24.0ms

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))))))
36.2b
(sqrt (fma z z (fma x x (* y y))))
36.2b
(sqrt (fma z z (fma x x (* y y))))
36.3b
(sqrt (/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y)))))))

rewrite119.0ms

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:
34.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y))))))
3.0ms
(sqrt (fma z z (fma x x (* y y))))
3.0ms
(sqrt (fma z z (fma x x (* y y))))
39.0ms
(sqrt (/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y)))))))

series631.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y))))))
127.0ms
(sqrt (fma z z (fma x x (* y y))))
164.0ms
(sqrt (fma z z (fma x x (* y y))))
267.0ms
(sqrt (/ (sqrt (fma z z (fma x x (* y y)))) (/ 3.0 (sqrt (fma z z (fma x x (* y y)))))))

simplify2.4s

Counts
375 → 375
Iterations

Useful iterations: done (2.3s)

IterNodesCost
043516247
172214618
2195112955
done500012090

prune973.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))
0.1b
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
36.3b
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
51×times-frac
50×add-exp-log
36×*-un-lft-identity
33×add-cube-cbrt
24×cbrt-prod
22×associate-*r*
20×prod-exp
18×add-cbrt-cube
16×div-exp
9×unswap-sqr
8×pow1 cbrt-undiv cbrt-unprod
7×associate-*l*
6×associate-/r*
4×rec-exp 1-exp
3×expm1-log1p-u sqrt-div log1p-expm1-u div-inv associate-/l* add-log-exp
2×frac-times sqrt-pow1 associate-*r/ pow-prod-down associate-*l/
1×frac-2neg pow1/2 clear-num sqrt-prod *-commutative
Counts
3 → 129
Calls
3 calls:
101.0ms
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))
6.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
59.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))

series863.0ms

Counts
3 → 9
Calls
3 calls:
206.0ms
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))
182.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
475.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))

simplify3.0s

Counts
138 → 138
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02053314
14813069
216392566
done50012414

prune590.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
0.2b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))
0.2b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
36.3b
(sqrt (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))))

rewrite751.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
56×times-frac
41×*-un-lft-identity
38×add-cube-cbrt
25×cbrt-prod sqrt-div
24×sqrt-prod
23×associate-*r*
20×add-exp-log associate-*l*
17×pow1 add-cbrt-cube
12×unswap-sqr
11×frac-times associate-*r/
7×pow-prod-down associate-*l/ prod-exp cbrt-unprod
6×associate-/r*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv sqrt-pow1 div-exp associate-/l*
2×*-commutative
1×frac-2neg pow1/2 clear-num
Counts
4 → 160
Calls
4 calls:
6.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
97.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))
345.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
297.0ms
(sqrt (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
321.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))
254.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
523.0ms
(sqrt (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))))

simplify2.1s

Counts
172 → 172
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02234786
14714006
214733613
done50003581

prune905.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 18.8b

regimes224.0ms

Accuracy

62.8% (7.3b remaining)

Error of 26.1b against oracle of 18.8b and baseline of 38.5b

bsearch107.0ms

Steps
ItersRangePoint
9
2.2645982852769956e+107
1.5814905187816295e+112
7.196367607327084e+111
9
-1.3235433073311637e+70
-1.7135815393373675e+64
-1.3103221636513423e+70

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02141
12641
22841
done2841

end0.0ms

sample1.0s

Algorithm
intervals
Results
639.0ms8000×body80valid