Details

Time bar (total: 24.2s)

sample137.0ms

Algorithm
intervals
Results
41.0ms264×body80valid
40.0ms86×body1280valid
24.0ms78×body640valid
7.0ms36×body320valid
3.0ms23×body160valid

simplify250.0ms

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×*-un-lft-identity add-cube-cbrt
22×associate-*r* sqrt-prod
9×add-cbrt-cube add-exp-log
6×associate-/r*
4×pow1
3×associate-*l* associate-/l* unswap-sqr
2×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
1×clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
2 → 85
Calls
2 calls:
18.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
5.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series380.0ms

Counts
2 → 6
Calls
2 calls:
255.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
125.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify1.6s

Counts
91 → 91
Iterations
IterNodes
done5001
22100
1272
0126

prune456.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
195×times-frac
110×add-sqr-sqrt
94×cbrt-prod
90×*-un-lft-identity add-cube-cbrt
67×associate-*r*
47×sqrt-prod
31×add-exp-log
22×div-inv
19×add-cbrt-cube
12×cbrt-undiv div-exp
10×associate-/r* associate-/l*
7×prod-exp cbrt-unprod unswap-sqr
5×pow1
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×pow-prod-down associate-*r/ *-commutative associate-/l/
Counts
3 → 218
Calls
3 calls:
60.0ms
(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
12.0ms
(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
18.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series963.0ms

Counts
3 → 9
Calls
3 calls:
317.0ms
(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
518.0ms
(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
127.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify1.1s

Counts
227 → 227
Iterations
IterNodes
done5001
1734
0289

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite449.0ms

Algorithm
rewrite-expression-head
Rules
258×times-frac
235×cbrt-prod
143×add-sqr-sqrt
117×*-un-lft-identity add-cube-cbrt
88×associate-*r*
79×add-exp-log
47×sqrt-prod
43×add-cbrt-cube
31×prod-exp cbrt-unprod
28×div-inv
27×cbrt-undiv div-exp
13×associate-/r*
10×associate-/l*
9×unswap-sqr
5×pow1
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×pow-prod-down associate-*r/ *-commutative associate-/l/
Counts
3 → 283
Calls
3 calls:
272.0ms
(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
79.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
69.0ms
(/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0)))))

series1.3s

Counts
3 → 9
Calls
3 calls:
366.0ms
(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
158.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
733.0ms
(/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0)))))

simplify1.7s

Counts
292 → 292
Iterations
IterNodes
done5000
11040
0384

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 3 expressions with local error:

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

rewrite855.0ms

Algorithm
rewrite-expression-head
Rules
185×add-exp-log
106×prod-exp
80×add-cbrt-cube
64×cbrt-unprod
47×associate-*r*
45×cbrt-prod
44×div-exp
43×times-frac
37×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
27×cbrt-undiv
10×pow1
9×sqrt-prod
7×rec-exp 1-exp
4×associate-*l* pow-prod-down associate-*r/
3×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
2×*-commutative unswap-sqr
1×frac-times clear-num associate-/r* frac-2neg associate-*l/ un-div-inv
Counts
3 → 164
Calls
3 calls:
167.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))))))
592.0ms
(* (* (cos th) (/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0)))))) (/ 1 (cbrt (cbrt (sqrt 2.0)))))
86.0ms
(/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0)))))

series2.2s

Counts
3 → 9
Calls
3 calls:
1.1s
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))))))
325.0ms
(* (* (cos th) (/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0)))))) (/ 1 (cbrt (cbrt (sqrt 2.0)))))
754.0ms
(/ (fma a1 a1 (* a2 a2)) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0)))))

simplify1.8s

Counts
173 → 173
Iterations
IterNodes
done5001
1933
0291

prune999.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes480.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done22
122
017

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.3s2543×body1280valid
1.6s2145×body640valid
825.0ms8005×body80valid
350.0ms1061×body320valid
192.0ms522×body160valid