Details

Time bar (total: 4.0m)

sample223.0ms

Algorithm
intervals
Results
72.0ms83×body1280valid
71.0ms222×body80valid
42.0ms60×body640valid
12.0ms24×body320valid
5.0ms16×body160valid

simplify132.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
132.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

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))

rewrite115.0ms

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
38.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
28.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
24.0ms
(/ (cos th) (sqrt 2))
18.0ms
(/ (cos th) (sqrt 2))

series465.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
139.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
95.0ms
(/ (cos th) (sqrt 2))
74.0ms
(/ (cos th) (sqrt 2))

simplify8.4s

Counts
180 → 184
Calls
180 calls:
Slowest
655.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
633.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
631.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
625.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
316.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
616×sqrt-prod
614×times-frac
345×add-sqr-sqrt
340×*-un-lft-identity add-cube-cbrt
37×associate-/l*
25×add-cbrt-cube add-exp-log
24×associate-/r*
22×associate-*l*
14×div-inv
9×pow1
7×cbrt-undiv div-exp
6×prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 473
Calls
4 calls:
Slowest
37.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
31.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
26.0ms
(/ (cos th) (sqrt (sqrt 2)))
15.0ms
(/ (cos th) (sqrt 2))

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
120.0ms
(/ (cos th) (sqrt (sqrt 2)))
86.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
71.0ms
(/ (cos th) (sqrt 2))

simplify28.1s

Counts
765 → 485
Calls
765 calls:
Slowest
986.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
664.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
384.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
330.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
317.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))

prune6.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.4b
(/ (* a2 (cos th)) (sqrt 2))
0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
1143×sqrt-prod
1125×times-frac
615×add-sqr-sqrt
581×*-un-lft-identity add-cube-cbrt
283×associate-*l*
37×add-cbrt-cube add-exp-log
35×associate-/l*
24×associate-/r*
23×div-inv
13×unswap-sqr
12×cbrt-undiv div-exp
10×prod-exp cbrt-unprod
9×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 736
Calls
4 calls:
Slowest
50.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
21.0ms
(/ (* a2 (cos th)) (sqrt 2))
21.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
16.0ms
(/ (cos th) (sqrt (sqrt 2)))

series571.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(/ (cos th) (sqrt (sqrt 2)))
160.0ms
(/ (* a2 (cos th)) (sqrt 2))
145.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
104.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify45.3s

Counts
1026 → 748
Calls
1026 calls:
Slowest
458.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (+ (log a1) (log a1)))
449.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (log (* a1 a1)))
425.0ms
(/ (/ (sqrt (cos th)) 1) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2)))))
418.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
410.0ms
(+ (- (log (/ (cos th) (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (+ (log a1) (log a1)))

prune11.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (sqrt (sqrt 2)))
0.7b
(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
0.4b
(/ (* a2 (cos th)) (sqrt 2))
0.3b
(* (* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2))))) (* a1 a1))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
1482×sqrt-prod
1141×times-frac
1014×add-sqr-sqrt
468×*-un-lft-identity
408×add-cube-cbrt
377×associate-*r*
153×add-exp-log
145×unswap-sqr
97×add-cbrt-cube
64×prod-exp
55×div-exp
41×associate-*l*
40×cbrt-unprod
30×cbrt-undiv
21×pow1
16×div-inv
15×associate-/r*
9×pow-prod-down
7×rec-exp 1-exp
5×associate-*l/ pow-flip
4×sqrt-pow1 insert-posit16 associate-/l* add-log-exp
2×frac-times clear-num frac-2neg pow1/2 associate-*r/ *-commutative
1×inv-pow
Counts
4 → 732
Calls
4 calls:
Slowest
139.0ms
(* (* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2))))) (* a1 a1))
60.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
17.0ms
(/ (* a2 (cos th)) (sqrt 2))
13.0ms
(/ 1 (sqrt (sqrt 2)))

series453.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
172.0ms
(/ (* a2 (cos th)) (sqrt 2))
154.0ms
(* (* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2))))) (* a1 a1))
127.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify1.8m

Counts
876 → 742
Calls
876 calls:
Slowest
923.0ms
(* (* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))) (/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
859.0ms
(* (* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))) (/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
820.0ms
(* (* (* (* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (cos th) (sqrt (sqrt (sqrt 2))))) (/ (cos th) (sqrt (sqrt (sqrt 2))))) (/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
781.0ms
(* (* (* (* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (cos th) (sqrt (sqrt (sqrt 2))))) (/ (cos th) (sqrt (sqrt (sqrt 2))))) (/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
736.0ms
(* (* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))) (* (* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2))))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))

prune13.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes517.0ms

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample7.9s

Algorithm
intervals
Results
2.6s2430×body1280valid
2.4s2037×body640valid
1.5s8003×body80valid
692.0ms976×body320valid
244.0ms572×body160valid