Details

Time bar (total: 29.1s)

sample200.0ms

Algorithm
intervals
Results
71.0ms76×body1280valid
58.0ms61×body640valid
35.0ms257×body80valid
14.0ms30×body320valid
3.0ms12×body160valid

simplify86.0ms

Counts
1 → 1
Iterations
IterNodes
done113
7113
6101
591
479
370
248
125
012

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×*-un-lft-identity add-cube-cbrt
44×associate-*l* sqrt-prod
32×add-cbrt-cube add-exp-log
14×pow1
12×associate-/r* prod-exp cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r* associate-*l/ *-commutative
Counts
4 → 172
Calls
4 calls:
20.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
31.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
22.0ms
(/ (cos th) (sqrt 2))
18.0ms
(/ (cos th) (sqrt 2))

series470.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
149.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
74.0ms
(/ (cos th) (sqrt 2))
88.0ms
(/ (cos th) (sqrt 2))

simplify1.5s

Counts
184 → 184
Iterations
IterNodes
done5001
21563
1533
0183

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (* a1 a1))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b
(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
44×times-frac
43×add-sqr-sqrt
37×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
28×sqrt-prod
25×associate-*l*
14×pow1
12×associate-/r* prod-exp cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down
4×insert-posit16 associate-/l* add-log-exp unswap-sqr
3×div-inv
2×clear-num frac-2neg associate-*r* *-commutative
1×associate-*l/
Counts
4 → 136
Calls
4 calls:
23.0ms
(* (cos th) (* a1 a1))
22.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
33.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series460.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (cos th) (* a1 a1))
142.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
158.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
84.0ms
(/ (cos th) (sqrt 2))

simplify1.6s

Counts
148 → 148
Iterations
IterNodes
done5001
21570
1536
0194

prune762.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
0.3b
(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.7b
(/ (cos th) (sqrt (sqrt 2)))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
1143×sqrt-prod
1125×times-frac
615×add-sqr-sqrt
581×*-un-lft-identity add-cube-cbrt
283×associate-*l*
41×add-cbrt-cube add-exp-log
35×associate-/l*
24×associate-/r*
23×div-inv
13×cbrt-undiv div-exp unswap-sqr
12×prod-exp cbrt-unprod
9×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 738
Calls
4 calls:
72.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
20.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
14.0ms
(/ (cos th) (sqrt (sqrt 2)))
25.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series1.0s

Counts
4 → 12
Calls
4 calls:
189.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
544.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
165.0ms
(/ (cos th) (sqrt (sqrt 2)))
118.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify3.1s

Counts
750 → 750
Iterations
IterNodes
done5000
24846
11741
0587

prune3.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (/ (cos th) (fabs (cbrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))) (* a2 a2))
0.3b
(/ (* (cos th) (* a1 a1)) (sqrt 2))
1.0b
(/ 1 (sqrt (sqrt 2)))
1.0b
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
777×sqrt-prod
756×times-frac
405×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
192×cbrt-prod
131×add-exp-log
85×add-cbrt-cube
56×prod-exp
45×div-exp
36×cbrt-unprod
35×associate-/l*
27×associate-/r*
25×cbrt-undiv
20×pow1
16×div-inv
8×pow-prod-down
7×sqrt-pow1 pow-flip
6×rec-exp 1-exp
4×associate-*l/ insert-posit16 add-log-exp
3×clear-num frac-2neg pow1/2
2×pow1/3 pow-div
1×frac-times associate-*r* associate-*l* associate-*r/ *-commutative inv-pow associate-/l/
Counts
4 → 579
Calls
4 calls:
76.0ms
(* (* (/ (cos th) (fabs (cbrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))) (* a2 a2))
39.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
22.0ms
(/ 1 (sqrt (sqrt 2)))
24.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))

series954.0ms

Counts
4 → 8
Calls
4 calls:
806.0ms
(* (* (/ (cos th) (fabs (cbrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))) (* a2 a2))
147.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.0ms
(/ 1 (sqrt (sqrt 2)))
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))

simplify3.0s

Counts
587 → 587
Iterations
IterNodes
done5001
24601
11653
0664

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes562.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done27
127
021

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.5s2449×body1280valid
2.1s2010×body640valid
1.5s7946×body80valid
658.0ms980×body320valid
219.0ms521×body160valid