Details

Time bar (total: 25.4s)

sample141.0ms

Algorithm
intervals
Results
51.0ms85×body1280valid
26.0ms66×body640valid
25.0ms259×body80valid
12.0ms39×body320valid
2.0ms13×body160valid

simplify330.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01219
12613
25712
38712
411412
513212
615012
717012
817212
done17212

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.5b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* fma-udef log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 61
Calls
3 calls:
0.0ms
(fma a1 a1 (* a2 a2))
23.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
27.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series543.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(fma a1 a1 (* a2 a2))
173.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
322.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify2.9s

Counts
70 → 70
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0103947
1201911
2750777
33465759
done5000758

prune286.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
36×add-exp-log cbrt-prod add-sqr-sqrt
34×add-cube-cbrt *-un-lft-identity
23×add-cbrt-cube
18×sqrt-prod
13×cbrt-undiv div-exp
12×div-inv
10×associate-/r*
9×prod-exp cbrt-unprod
6×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* fma-udef
2×frac-2neg clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
4 → 137
Calls
4 calls:
0.0ms
(fma a1 a1 (* a2 a2))
9.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
25.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
49.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
54.0ms
(fma a1 a1 (* a2 a2))
185.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
966.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
335.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify1.1s

Counts
149 → 149
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02153852
14733510
217603026
done50013009

prune640.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (fma a1 a1 (* a2 a2)) (cos th))
0.3b
(/ (* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th))) (cbrt (sqrt 2.0)))
0.4b
(* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
22×add-sqr-sqrt
20×add-exp-log add-cube-cbrt *-un-lft-identity
19×associate-*l*
18×times-frac
13×add-cbrt-cube
11×pow1
9×associate-/r*
7×prod-exp cbrt-unprod
6×sqrt-prod
4×expm1-log1p-u associate-*r* pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×cbrt-div associate-*l/ *-commutative div-inv
1×frac-2neg clear-num fma-udef associate-/l/ associate-/l* unswap-sqr
Counts
4 → 102
Calls
4 calls:
1.0ms
(fma a1 a1 (* a2 a2))
18.0ms
(* (fma a1 a1 (* a2 a2)) (cos th))
60.0ms
(/ (* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th))) (cbrt (sqrt 2.0)))
49.0ms
(* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th)))

series1.2s

Counts
4 → 12
Calls
4 calls:
65.0ms
(fma a1 a1 (* a2 a2))
140.0ms
(* (fma a1 a1 (* a2 a2)) (cos th))
747.0ms
(/ (* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th))) (cbrt (sqrt 2.0)))
234.0ms
(* (cbrt (/ 1 2.0)) (* (fma a1 a1 (* a2 a2)) (cos th)))

simplify1.5s

Counts
114 → 114
Iterations

Useful iterations: 2 (236.0ms)

IterNodesCost
01771965
13721866
213281608
done50001608

prune619.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (fabs (cbrt 2.0)))
1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
1.0b
(/ (cbrt (/ 1 2.0)) (cbrt (fabs (cbrt 2.0))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
151×cbrt-prod
97×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
8×div-inv
6×add-exp-log associate-/r*
4×pow1 expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×cbrt-undiv cbrt-div frac-2neg div-exp clear-num associate-/l/
Counts
4 → 172
Calls
4 calls:
1.0ms
(cbrt (fabs (cbrt 2.0)))
1.0ms
(cbrt 2.0)
1.0ms
(cbrt 2.0)
13.0ms
(/ (cbrt (/ 1 2.0)) (cbrt (fabs (cbrt 2.0))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(cbrt (fabs (cbrt 2.0)))
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
0.0ms
(/ (cbrt (/ 1 2.0)) (cbrt (fabs (cbrt 2.0))))

simplify6.0s

Counts
176 → 176
Iterations

Useful iterations: 4 (589.0ms)

IterNodesCost
02422967
13162680
24592646
37532636
414342633
527232633
648832633
done50002633

prune998.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes266.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01924
12324
done2324

end0.0ms

sample6.8s

Algorithm
intervals
Results
3.0s2529×body1280valid
1.6s8050×body80valid
1.2s2128×body640valid
403.0ms1047×body320valid
107.0ms487×body160valid