Details

Time bar (total: 58.2s)

sample295.0ms

Algorithm
intervals
Results
118.0ms75×body1280valid
72.0ms77×body640valid
50.0ms248×body80valid
20.0ms31×body320valid
8.0ms19×body160valid

simplify159.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
159.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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:
Slowest
45.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
40.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
8.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series440.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
133.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
91.0ms
(/ (cos th) (sqrt 2))
77.0ms
(/ (cos th) (sqrt 2))

simplify8.2s

Counts
180 → 184
Calls
180 calls:
Slowest
697.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
635.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
572.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
536.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
278.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.5b
(/ (* a2 (cos th)) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.2b
(* a2 (/ (* a2 (cos th)) (sqrt 2)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
50×times-frac
47×add-sqr-sqrt
40×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
31×sqrt-prod
25×associate-*l*
12×associate-/r*
11×pow1 associate-*r* prod-exp cbrt-unprod
7×cbrt-undiv div-exp
4×pow-prod-down insert-posit16 div-inv associate-/l* add-log-exp unswap-sqr
2×clear-num frac-2neg *-commutative
1×associate-*l/ associate-*r/
Counts
4 → 145
Calls
4 calls:
Slowest
21.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
20.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
13.0ms
(/ (cos th) (sqrt 2))
13.0ms
(/ (* a2 (cos th)) (sqrt 2))

series545.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
171.0ms
(/ (* a2 (cos th)) (sqrt 2))
154.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
153.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
67.0ms
(/ (cos th) (sqrt 2))

simplify6.7s

Counts
140 → 157
Calls
140 calls:
Slowest
649.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
545.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
330.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
319.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
271.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt 2) a1)
0.5b
(/ (* a2 (cos th)) (sqrt 2))
0.2b
(/ (* (cos th) a1) (/ (sqrt 2) a1))
0.2b
(* a2 (/ (* a2 (cos th)) (sqrt 2)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
55×add-sqr-sqrt
53×*-un-lft-identity add-cube-cbrt
39×sqrt-prod
32×add-cbrt-cube add-exp-log
31×associate-/r*
11×cbrt-undiv div-exp
10×associate-*r*
8×associate-/l*
7×prod-exp cbrt-unprod
6×pow1 div-inv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*l*
1×pow-prod-down associate-*r/ associate-/r/ *-commutative unswap-sqr
Counts
4 → 164
Calls
4 calls:
Slowest
28.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
14.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
10.0ms
(/ (* a2 (cos th)) (sqrt 2))
5.0ms
(/ (sqrt 2) a1)

series523.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(/ (* a2 (cos th)) (sqrt 2))
155.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
144.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
62.0ms
(/ (sqrt 2) a1)

simplify6.8s

Counts
176 → 176
Calls
176 calls:
Slowest
354.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
320.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
296.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
288.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (sqrt 2) a1) (/ (sqrt 2) a1)) (/ (sqrt 2) a1)))
286.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt 2) a1)
0.2b
(/ (* (cos th) a1) (/ (sqrt 2) a1))
0.2b
(* (* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (cbrt (sqrt 2))))
0.2b
(* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
107×times-frac
71×add-sqr-sqrt
67×*-un-lft-identity add-cube-cbrt
59×add-exp-log
49×add-cbrt-cube
39×sqrt-prod
38×associate-*r*
25×associate-/r*
22×prod-exp cbrt-unprod
18×cbrt-prod
17×cbrt-undiv div-exp
11×pow1
7×associate-/l*
6×div-inv
4×associate-*l* pow-prod-down associate-*r/ insert-posit16 add-log-exp
2×clear-num frac-2neg *-commutative unswap-sqr
1×frac-times associate-*l/ associate-/r/
Counts
4 → 196
Calls
4 calls:
Slowest
94.0ms
(* (* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (cbrt (sqrt 2))))
47.0ms
(* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
20.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
10.0ms
(/ (sqrt 2) a1)

series869.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
492.0ms
(* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
161.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
160.0ms
(* (* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (cbrt (sqrt 2))))
55.0ms
(/ (sqrt 2) a1)

simplify14.0s

Counts
206 → 208
Calls
206 calls:
Slowest
638.0ms
(* (* (* a2 a2) a2) (* (* (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))))
606.0ms
(* (* (* (* a2 a2) a2) (/ (* (* a2 a2) a2) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (* (* (/ (cos th) (cbrt (sqrt 2))) (/ (cos th) (cbrt (sqrt 2)))) (/ (cos th) (cbrt (sqrt 2)))))
476.0ms
(* (* (* a2 a2) a2) (/ (* (* a2 a2) a2) (* (sqrt 2) (sqrt 2))))
466.0ms
(* (* (* (* a2 a2) a2) (/ (* (* a2 a2) a2) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (/ (* (* (cos th) (cos th)) (cos th)) (sqrt 2)))
442.0ms
(* (* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (cbrt (sqrt 2))))

prune3.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes481.0ms

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample8.9s

Algorithm
intervals
Results
3.2s2478×body1280valid
2.0s2142×body640valid
1.9s7953×body80valid
1.1s1042×body320valid
271.0ms561×body160valid