Details

Time bar (total: 1.2m)

sample312.0ms

Algorithm
intervals
Results
119.0ms68×body1280valid
76.0ms77×body640valid
57.0ms281×body80valid
24.0ms38×body320valid
12.0ms20×body160valid

simplify140.0ms

Calls
1 calls:
Slowest
140.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×associate-*l*
18×add-cbrt-cube add-exp-log
8×pow1
6×associate-/r* associate-/l*
4×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r* pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
14.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
8.0ms
(/ (cos th) (sqrt 2))
8.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
4.0ms
(/ (cos th) (sqrt 2))

series232.0ms

Calls
4 calls:
Slowest
81.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
75.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
41.0ms
(/ (cos th) (sqrt 2))
35.0ms
(/ (cos th) (sqrt 2))

simplify4.2s

Calls
98 calls:
Slowest
582.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
541.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
216.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
203.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
187.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.3b
(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.1b
(* (cos th) (* a1 a1))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×times-frac
18×add-cbrt-cube add-exp-log
16×associate-*l*
8×pow1
6×associate-/r*
4×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 associate-/l* add-log-exp
3×div-inv
2×clear-num frac-2neg associate-*r* pow-prod-down *-commutative
1×associate-*l/
Calls
4 calls:
Slowest
8.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
7.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
4.0ms
(* (cos th) (* a1 a1))
4.0ms
(/ (cos th) (sqrt 2))

series218.0ms

Calls
4 calls:
Slowest
78.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
62.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
43.0ms
(/ (cos th) (sqrt 2))
35.0ms
(* (cos th) (* a1 a1))

simplify3.9s

Calls
74 calls:
Slowest
625.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
310.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
259.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
258.0ms
(- (pow a1 2) (* 1/2 (* (pow a1 2) (pow th 2))))
214.0ms
(/ (* (* (* (cos th) (* a1 a1)) (* (cos th) (* a1 a1))) (* (cos th) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
0.3b
(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.3b
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a2 a2))
0.2b
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
129×times-frac
65×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
46×associate-*l*
45×cbrt-prod
37×add-exp-log
25×add-cbrt-cube
17×div-inv
14×cbrt-undiv div-exp
11×associate-/l*
10×associate-/r*
8×prod-exp cbrt-unprod
6×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
1×associate-*r* pow-prod-down associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
25.0ms
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
24.0ms
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a2 a2))
13.0ms
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
8.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))

series664.0ms

Calls
4 calls:
Slowest
450.0ms
(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
81.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
78.0ms
(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a2 a2))
54.0ms
(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

simplify10.4s

Calls
197 calls:
Slowest
637.0ms
(+ (log (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))) (log (* a2 a2)))
418.0ms
(/ (* (* (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt 2))
343.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
329.0ms
(- (+ (* 1/24 (* (pow (/ 1 (pow (sqrt 2) 2)) 1/3) (pow th 4))) (pow (/ 1 (pow (sqrt 2) 2)) 1/3)) (* 1/2 (* (pow (/ 1 (pow (sqrt 2) 2)) 1/3) (pow th 2))))
307.0ms
(+ (- (log (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (log (cbrt (sqrt 2)))) (log (* a2 a2)))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
371×times-frac
279×cbrt-prod
210×associate-*l*
194×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
122×add-exp-log
55×add-cbrt-cube
49×prod-exp
40×div-exp
30×cbrt-unprod
24×cbrt-undiv
16×div-inv
12×pow1
10×rec-exp
5×associate-/l*
4×associate-/r* pow1/3 pow-prod-down associate-*l/ insert-posit16 add-log-exp
2×clear-num frac-2neg associate-*r* *-commutative pow-prod-up pow-div
1×frac-times associate-*r/ pow-flip inv-pow associate-/l/
Calls
4 calls:
Slowest
49.0ms
(* (/ (/ 1 (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* a2 a2)))
25.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* a2 a2))
15.0ms
(/ (/ 1 (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))))
13.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))

series620.0ms

Calls
4 calls:
Slowest
448.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* a2 a2))
88.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
84.0ms
(* (/ (/ 1 (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* a2 a2)))
0.0ms
(/ (/ 1 (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))))

simplify32.8s

Calls
300 calls:
Slowest
1.1s
(* (/ (* (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (/ 1 (cbrt (sqrt 2)))) (* (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))))) (* (* (* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2))))
1.1s
(* (/ (* (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (/ 1 (cbrt (sqrt 2)))) (* (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))))) (* (* (* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* a2 a2)) (* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* a2 a2))) (* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* a2 a2))))
871.0ms
(* (/ (* (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (/ 1 (cbrt (sqrt 2)))) (* (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))))) (* (/ (/ (* (* (cos th) (cos th)) (cos th)) (sqrt 2)) (cbrt (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2))))
860.0ms
(+ (- (log (/ 1 (cbrt (sqrt 2)))) (+ (log (cbrt (cbrt (sqrt 2)))) (log (cbrt (cbrt (sqrt 2)))))) (+ (log (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (log (* a2 a2))))
795.0ms
(* (* (* (/ (/ 1 (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (/ (/ 1 (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))))) (/ (/ 1 (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))))) (* (* (* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* a2 a2)) (* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* a2 a2))) (* (/ (/ (cos th) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* a2 a2))))

prune5.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes576.0ms

Accuracy

0% (0.4b remaining)

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

bsearch8.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.8s2511×body1280valid
1.8s2134×body640valid
1.8s8116×body80valid
684.0ms1058×body320valid
251.0ms527×body160valid