Details

Time bar (total: 23.5s)

sample183.0ms

Algorithm
intervals
Results
56.0ms78×body1280valid
49.0ms68×body640valid
28.0ms242×body80valid
16.0ms39×body320valid
3.0ms12×body160valid

simplify236.0ms

Counts
1 → 1
Iterations
IterNodes
done175
8175
7173
6151
5132
4114
387
257
126
012

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.1b
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
0.4b
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×*-un-lft-identity add-cube-cbrt
22×associate-*r* sqrt-prod
10×add-cbrt-cube add-exp-log
6×associate-/r*
5×pow1
3×expm1-log1p-u associate-*l* log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×clear-num frac-2neg pow-prod-down associate-*r/ *-commutative fma-udef
Counts
3 → 95
Calls
3 calls:
0.0ms
(fma a1 a1 (* a2 a2))
18.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
9.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series560.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(fma a1 a1 (* a2 a2))
346.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
150.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify2.1s

Counts
104 → 104
Iterations
IterNodes
done5000
22126
1276
0131

prune717.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ (* a2 a2) (sqrt 2.0)) (/ (* a1 a1) (sqrt 2.0)))
0.1b
(* (cos th) (+ (/ (* a2 a2) (sqrt 2.0)) (/ (* a1 a1) (sqrt 2.0))))
0.3b
(/ (* a2 a2) (sqrt 2.0))
0.3b
(/ (* a1 a1) (sqrt 2.0))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
19×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt
16×add-cbrt-cube add-exp-log
15×sqrt-prod
12×associate-/r*
10×fma-def
7×div-inv
6×pow1 add-log-exp
5×associate-*r*
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u
3×associate-*l* prod-exp associate-*r/ cbrt-unprod
2×clear-num frac-2neg flip3-+ distribute-rgt-out frac-add flip-+ distribute-lft-out associate-/l*
1×distribute-rgt-in +-commutative sum-log distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 111
Calls
4 calls:
30.0ms
(+ (/ (* a2 a2) (sqrt 2.0)) (/ (* a1 a1) (sqrt 2.0)))
139.0ms
(* (cos th) (+ (/ (* a2 a2) (sqrt 2.0)) (/ (* a1 a1) (sqrt 2.0))))
18.0ms
(/ (* a2 a2) (sqrt 2.0))
18.0ms
(/ (* a1 a1) (sqrt 2.0))

series778.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(+ (/ (* a2 a2) (sqrt 2.0)) (/ (* a1 a1) (sqrt 2.0)))
397.0ms
(* (cos th) (+ (/ (* a2 a2) (sqrt 2.0)) (/ (* a1 a1) (sqrt 2.0))))
88.0ms
(/ (* a2 a2) (sqrt 2.0))
109.0ms
(/ (* a1 a1) (sqrt 2.0))

simplify2.2s

Counts
123 → 123
Iterations
IterNodes
done5001
23383
1499
0162

prune760.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (+ (/ a2 (/ (sqrt 2.0) a2)) (/ (* a1 a1) (sqrt 2.0))))
0.2b
(/ a2 (/ (sqrt 2.0) a2))
0.3b
(/ (* a1 a1) (sqrt 2.0))
0.4b
(/ (sqrt 2.0) a2)

rewrite323.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
102×add-sqr-sqrt *-un-lft-identity
100×add-cube-cbrt
54×sqrt-prod
31×associate-/r*
18×add-cbrt-cube add-exp-log
10×associate-/l*
7×div-inv
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l* associate-*r/
2×prod-exp cbrt-unprod
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down frac-add associate-/r/ *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 204
Calls
4 calls:
282.0ms
(* (cos th) (+ (/ a2 (/ (sqrt 2.0) a2)) (/ (* a1 a1) (sqrt 2.0))))
9.0ms
(/ a2 (/ (sqrt 2.0) a2))
14.0ms
(/ (* a1 a1) (sqrt 2.0))
10.0ms
(/ (sqrt 2.0) a2)

series700.0ms

Counts
4 → 12
Calls
4 calls:
427.0ms
(* (cos th) (+ (/ a2 (/ (sqrt 2.0) a2)) (/ (* a1 a1) (sqrt 2.0))))
106.0ms
(/ a2 (/ (sqrt 2.0) a2))
85.0ms
(/ (* a1 a1) (sqrt 2.0))
80.0ms
(/ (sqrt 2.0) a2)

simplify810.0ms

Counts
216 → 216
Iterations
IterNodes
done5000
1819
0297

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (hypot a1 a2))
0.3b
(* (* (cos th) (hypot a1 a2)) (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0)))
0.4b
(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0))
7.2b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
81×sqrt-prod
72×times-frac
63×add-sqr-sqrt
60×*-un-lft-identity add-cube-cbrt
43×associate-*r*
20×add-cbrt-cube add-exp-log
12×pow1
7×prod-exp cbrt-unprod
6×associate-/r* associate-/l*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×*-commutative div-inv
1×rem-sqrt-square sqrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r/ fma-udef hypot-def unswap-sqr
Counts
4 → 161
Calls
4 calls:
14.0ms
(* (cos th) (hypot a1 a2))
50.0ms
(* (* (cos th) (hypot a1 a2)) (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0)))
6.0ms
(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series899.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (cos th) (hypot a1 a2))
468.0ms
(* (* (cos th) (hypot a1 a2)) (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0)))
186.0ms
(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0))
70.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify3.6s

Counts
173 → 173
Iterations
IterNodes
done5000
23565
1486
0194

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes652.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done14
114
012

end0.0ms

sample5.7s

Algorithm
intervals
Results
1.9s2077×body640valid
1.8s2508×body1280valid
988.0ms7978×body80valid
363.0ms1041×body320valid
157.0ms518×body160valid