Details

Time bar (total: 14.1s)

sample190.0ms

Algorithm
intervals
Results
65.0ms250×body80valid
56.0ms85×body1280valid
27.0ms55×body640valid
12.0ms35×body320valid
5.0ms21×body160valid

simplify145.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01219
12513
24913
37613
49513
511113
612513
713913
done13913

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.4b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*l* sqrt-prod
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 add-log-exp
3×flip3-+ associate-*r* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod div-inv
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num sum-log *-commutative
Counts
3 → 98
Calls
3 calls:
8.0ms
(+ (* a1 a1) (* a2 a2))
69.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
21.0ms
(/ (cos th) (sqrt 2.0))

series411.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* a1 a1) (* a2 a2))
299.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
83.0ms
(/ (cos th) (sqrt 2.0))

simplify1.7s

Counts
107 → 107
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01581536
14801469
215991325
done50001322

prune418.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (pow a2 2))
0.1b
(* (pow a1 2) (cos th))
0.3b
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
0.3b
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
30×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity add-cbrt-cube
12×times-frac prod-exp associate-/r* sqrt-prod
11×associate-*r* associate-*l*
8×unpow-prod-down div-exp unswap-sqr
4×pow1 cbrt-undiv pow-to-exp pow-exp cbrt-unprod unpow2 add-log-exp sqr-pow
2×frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 112
Calls
4 calls:
22.0ms
(* (cos th) (pow a2 2))
30.0ms
(* (pow a1 2) (cos th))
30.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
40.0ms
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))

series409.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (cos th) (pow a2 2))
85.0ms
(* (pow a1 2) (cos th))
138.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
119.0ms
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))

simplify1.7s

Counts
124 → 124
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01801380
14001260
214991116
done50001114

prune555.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow a1 2) (sqrt (sqrt 2.0)))
0.2b
(* (/ (pow a1 2) (sqrt (sqrt 2.0))) (/ (cos th) (sqrt (sqrt 2.0))))
0.3b
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
309×sqrt-prod
306×add-sqr-sqrt
291×times-frac
139×add-cube-cbrt *-un-lft-identity
76×associate-*l*
69×unpow-prod-down
52×unswap-sqr
45×add-exp-log
31×associate-*r* unpow2 sqr-pow
25×add-cbrt-cube
24×associate-/r*
18×div-exp
12×associate-/l*
11×prod-exp
8×cbrt-undiv
6×pow1
5×cbrt-unprod div-inv
4×pow-to-exp pow-exp add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 366
Calls
4 calls:
26.0ms
(/ (pow a1 2) (sqrt (sqrt 2.0)))
158.0ms
(* (/ (pow a1 2) (sqrt (sqrt 2.0))) (/ (cos th) (sqrt (sqrt 2.0))))
15.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
18.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series668.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(/ (pow a1 2) (sqrt (sqrt 2.0)))
161.0ms
(* (/ (pow a1 2) (sqrt (sqrt 2.0))) (/ (cos th) (sqrt (sqrt 2.0))))
145.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
171.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify2.0s

Counts
378 → 378
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03726743
19076228
226665421
done50015417

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 add-log-exp
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv associate-/l/
1×+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
3 → 94
Calls
3 calls:
17.0ms
(+ (* a2 a2) (* a1 a1))
40.0ms
(* (cos th) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2.0)))
39.0ms
(/ (+ (* a2 a2) (* a1 a1)) (sqrt 2.0))

series488.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(+ (* a2 a2) (* a1 a1))
318.0ms
(* (cos th) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2.0)))
127.0ms
(/ (+ (* a2 a2) (* a1 a1)) (sqrt 2.0))

simplify3.1s

Counts
103 → 103
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01411776
13371685
211441547
336681541
done50001541

prune368.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes2.0ms