Details

Time bar (total: 29.2s)

sample140.0ms

Algorithm
intervals
Results
52.0ms77×body1280valid
25.0ms56×body640valid
24.0ms227×body80valid
8.0ms25×body320valid
3.0ms14×body160valid

simplify255.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01219
12613
25712
38712
411412
513212
615012
717012
817212
done17212

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite39.0ms

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))
14.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
23.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series569.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(fma a1 a1 (* a2 a2))
176.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
322.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.5s

Counts
70 → 70
Iterations

Useful iterations: done (3.5s)

IterNodesCost
0103947
1201911
2750777
33465759
done5000758

prune313.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
234×sqrt-prod
216×times-frac
96×add-sqr-sqrt
94×add-cube-cbrt *-un-lft-identity
20×add-exp-log add-cbrt-cube
18×associate-/r*
14×associate-/l*
12×div-inv
7×cbrt-undiv div-exp
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* prod-exp cbrt-unprod fma-udef
2×frac-2neg clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
4 → 225
Calls
4 calls:
1.0ms
(fma a1 a1 (* a2 a2))
13.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
15.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
40.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series980.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(fma a1 a1 (* a2 a2))
145.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
507.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
283.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.3s

Counts
237 → 237
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02695586
16164970
217424533
done50014463

prune836.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
867×sqrt-prod
750×times-frac
403×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
102×cbrt-prod
34×associate-/l*
21×associate-/r*
17×add-exp-log
15×div-inv
11×sqrt-pow1 add-cbrt-cube
8×pow1 div-exp
7×pow-flip
4×cbrt-undiv expm1-log1p-u pow1/3 log1p-expm1-u add-log-exp
3×pow1/2
2×rec-exp frac-2neg 1-exp clear-num pow-div
1×associate-/l/ inv-pow
Counts
4 → 523
Calls
4 calls:
41.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))
2.0ms
(cbrt 2.0)
2.0ms
(cbrt 2.0)
18.0ms
(/ 1 (sqrt (sqrt 2.0)))

series0.0ms

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

simplify4.8s

Counts
527 → 527
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
050811469
110859099
215068950
327338944
449318944
done50008944

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (fabs (cbrt 2.0)))) (sqrt (sqrt (cbrt 2.0))))
0.3b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
2709×times-frac
2472×sqrt-prod
1007×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
255×cbrt-prod
93×div-inv
83×associate-/l*
23×add-exp-log add-cbrt-cube
21×associate-/r*
11×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg pow1/3 prod-exp clear-num cbrt-unprod
1×associate-/l/
Counts
4 → 1160
Calls
4 calls:
101.0ms
(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (fabs (cbrt 2.0)))) (sqrt (sqrt (cbrt 2.0))))
30.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
2.0ms
(cbrt 2.0)
2.0ms
(cbrt 2.0)

series1.9s

Counts
4 → 8
Calls
4 calls:
1.5s
(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (fabs (cbrt 2.0)))) (sqrt (sqrt (cbrt 2.0))))
395.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)

simplify1.8s

Counts
1168 → 1168
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0113548078
1252143324
done500142993

prune4.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes350.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02025
12425
done2425

end0.0ms

sample6.5s

Algorithm
intervals
Results
2.6s2525×body1280valid
1.7s7986×body80valid
947.0ms2049×body640valid
382.0ms1057×body320valid
153.0ms503×body160valid