Details

Time bar (total: 1.2m)

sample230.0ms

Algorithm
intervals
Results
72.0ms57×body640valid
64.0ms65×body1280valid
46.0ms262×body80valid
17.0ms35×body320valid
12.0ms17×body160valid

simplify144.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
144.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize46.0ms

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

rewrite125.0ms

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
42.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
41.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
22.0ms
(/ (cos th) (sqrt 2))
17.0ms
(/ (cos th) (sqrt 2))

series445.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
131.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
100.0ms
(/ (cos th) (sqrt 2))
72.0ms
(/ (cos th) (sqrt 2))

simplify8.4s

Counts
180 → 184
Calls
180 calls:
Slowest
686.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
670.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
616.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
572.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
344.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
74×add-sqr-sqrt
61×*-un-lft-identity add-cube-cbrt
44×associate-*l* sqrt-prod
25×add-cbrt-cube add-exp-log
12×associate-/r*
11×pow1
8×prod-exp cbrt-unprod
6×associate-/l* unswap-sqr
5×cbrt-undiv div-exp
4×associate-*r* pow-prod-down insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*l/ *-commutative
Counts
4 → 169
Calls
4 calls:
Slowest
40.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
29.0ms
(* (/ (cos th) (sqrt 2)) a1)
9.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series396.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
122.0ms
(* (/ (cos th) (sqrt 2)) a1)
78.0ms
(/ (cos th) (sqrt 2))
67.0ms
(/ (cos th) (sqrt 2))

simplify6.8s

Counts
177 → 181
Calls
177 calls:
Slowest
559.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
537.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
303.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
302.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
277.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* a1 a1) a1))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

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

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
50×times-frac
41×*-un-lft-identity add-cube-cbrt
31×sqrt-prod
25×add-cbrt-cube associate-*l* add-exp-log
13×associate-*r*
12×associate-/r*
8×pow1
7×prod-exp cbrt-unprod
6×cbrt-undiv div-exp
4×insert-posit16 div-inv associate-/l* add-log-exp unswap-sqr
2×clear-num frac-2neg pow-prod-down *-commutative
1×associate-*l/ associate-*r/
Counts
4 → 142
Calls
4 calls:
Slowest
24.0ms
(/ (* a2 (cos th)) (sqrt 2))
18.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
17.0ms
(/ (cos th) (sqrt 2))
12.0ms
(* (/ (cos th) (sqrt 2)) a1)

series491.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(* (/ (cos th) (sqrt 2)) a1)
140.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
137.0ms
(/ (* a2 (cos th)) (sqrt 2))
66.0ms
(/ (cos th) (sqrt 2))

simplify5.7s

Counts
137 → 154
Calls
137 calls:
Slowest
407.0ms
(/ (* a1 (cos th)) (sqrt 2))
315.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
308.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
304.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* a1 a1) a1))
238.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.3b
(* (/ (cos th) (sqrt 2)) a1)

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
616×sqrt-prod
614×times-frac
349×add-sqr-sqrt
341×*-un-lft-identity add-cube-cbrt
37×associate-/l*
24×associate-/r*
22×associate-*l*
18×add-cbrt-cube add-exp-log
14×div-inv
6×pow1 cbrt-undiv div-exp
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* unswap-sqr
2×prod-exp cbrt-unprod
1×pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 470
Calls
4 calls:
Slowest
32.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
17.0ms
(/ (cos th) (sqrt 2))
12.0ms
(* (/ (cos th) (sqrt 2)) a1)
9.0ms
(/ (cos th) (sqrt (sqrt 2)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(* (/ (cos th) (sqrt 2)) a1)
110.0ms
(/ (cos th) (sqrt (sqrt 2)))
93.0ms
(/ (cos th) (sqrt 2))
73.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify27.1s

Counts
762 → 482
Calls
762 calls:
Slowest
414.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
353.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
316.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* a1 a1) a1))
312.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
300.0ms
(- (/ a1 (sqrt 2)) (* 1/2 (/ (* a1 (pow th 2)) (sqrt 2))))

prune7.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes543.0ms

Accuracy

0% (0.4b remaining)

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

bsearch5.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
3.8s2470×body1280valid
1.9s7994×body80valid
1.9s2140×body640valid
579.0ms1084×body320valid
191.0ms540×body160valid