Details

Time bar (total: 55.8s)

sample244.0ms

Algorithm
intervals
Results
107.0ms67×body1280valid
55.0ms83×body640valid
41.0ms275×body80valid
17.0ms33×body320valid
6.0ms19×body160valid

simplify133.0ms

Calls
1 calls:
Slowest
133.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize43.0ms

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))

rewrite48.0ms

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))
14.0ms
(/ (cos th) (sqrt 2))
11.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
8.0ms
(/ (cos th) (sqrt 2))

series228.0ms

Calls
4 calls:
Slowest
89.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
80.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
30.0ms
(/ (cos th) (sqrt 2))
29.0ms
(/ (cos th) (sqrt 2))

simplify4.3s

Calls
98 calls:
Slowest
586.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
542.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
242.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
237.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
200.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

series256.0ms

Calls
4 calls:
Slowest
87.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
85.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
42.0ms
(* (cos th) (* a1 a1))
42.0ms
(/ (cos th) (sqrt 2))

simplify3.8s

Calls
74 calls:
Slowest
541.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
329.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
252.0ms
(- (pow a1 2) (* 1/2 (* (pow a1 2) (pow th 2))))
225.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
213.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
294×times-frac
171×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
144×sqrt-prod
28×associate-/l*
18×add-cbrt-cube add-exp-log
15×associate-/r*
13×associate-*l*
11×div-inv
6×pow1 cbrt-undiv div-exp
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
2×prod-exp cbrt-unprod
1×associate-*r* pow-prod-down associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms
(/ (cos th) (sqrt (sqrt 2)))
8.0ms
(/ (cos th) (sqrt 2))
7.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))

series249.0ms

Calls
4 calls:
Slowest
77.0ms
(/ (cos th) (sqrt (sqrt 2)))
68.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
53.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
51.0ms
(/ (cos th) (sqrt 2))

simplify13.9s

Calls
397 calls:
Slowest
485.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
431.0ms
(/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt 1))
309.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
291.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
255.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune3.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
66×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
60×sqrt-prod
25×add-cbrt-cube add-exp-log
15×associate-/r*
14×associate-/l*
13×associate-*l*
11×div-inv
9×cbrt-undiv div-exp
6×pow1
4×prod-exp cbrt-unprod 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
11.0ms
(/ (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms
(/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2)))
7.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
4.0ms
(/ (cos th) (sqrt 2))

series259.0ms

Calls
4 calls:
Slowest
96.0ms
(/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2)))
71.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
59.0ms
(/ (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
32.0ms
(/ (cos th) (sqrt 2))

simplify14.3s

Calls
220 calls:
Slowest
481.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
465.0ms
(/ (/ (* (* (* (cos th) (* a1 a1)) (* (cos th) (* a1 a1))) (* (cos th) (* a1 a1))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
437.0ms
(- (- (+ (log (cos th)) (log (* a1 a1))) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2))))
388.0ms
(/ (/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
332.0ms
(/ (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))

prune2.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes353.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch6.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
3.8s2554×body1280valid
1.8s2133×body640valid
1.6s8029×body80valid
747.0ms1047×body320valid
217.0ms560×body160valid