Details

Time bar (total: 29.6s)

sample261.0ms

Algorithm
intervals
Results
100.0ms80×body1280valid
62.0ms246×body80valid
56.0ms61×body640valid
17.0ms26×body320valid
5.0ms11×body160valid

simplify153.0ms

Calls
1 calls:
Slowest
153.0ms
(+ (* (/ (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: 0.4b

localize44.0ms

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))

rewrite53.0ms

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
20.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
14.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
8.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series458.0ms

Calls
4 calls:
Slowest
148.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
142.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
92.0ms
(/ (cos th) (sqrt 2))
76.0ms
(/ (cos th) (sqrt 2))

simplify4.4s

Calls
98 calls:
Slowest
594.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
518.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
263.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
259.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
219.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

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) (* a2 a2)) (sqrt 2))
7.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
4.0ms
(* (cos th) (* a2 a2))
4.0ms
(/ (cos th) (sqrt 2))

series417.0ms

Calls
4 calls:
Slowest
144.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
127.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
88.0ms
(/ (cos th) (sqrt 2))
58.0ms
(* (cos th) (* a2 a2))

simplify3.6s

Calls
74 calls:
Slowest
556.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
301.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
224.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
222.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
192.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) (* a2 a2)) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.2b
(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.1b
(* (cos th) (* a1 a1))
0.1b
(* (cos th) (* a2 a2))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1
6×associate-/r* times-frac associate-*l*
4×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 add-log-exp
2×clear-num frac-2neg associate-*r* pow-prod-down *-commutative div-inv associate-/l*
Calls
4 calls:
Slowest
16.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
16.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
9.0ms
(* (cos th) (* a2 a2))
8.0ms
(* (cos th) (* a1 a1))

series459.0ms

Calls
4 calls:
Slowest
172.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
143.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
75.0ms
(* (cos th) (* a2 a2))
69.0ms
(* (cos th) (* a1 a1))

simplify3.2s

Calls
50 calls:
Slowest
299.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
278.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
265.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
253.0ms
(- (pow a1 2) (* 1/2 (* (pow a1 2) (pow th 2))))
223.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* a2 (* a2 (cos th))) (sqrt 2))
0.2b
(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.1b
(* a2 (cos th))
0.1b
(* a2 (* a2 (cos th)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac
4×pow1 associate-*r* insert-posit16 add-log-exp
3×cbrt-undiv div-exp
2×clear-num frac-2neg *-commutative div-inv associate-/l*
1×prod-exp cbrt-unprod
Calls
4 calls:
Slowest
16.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
14.0ms
(/ (* a2 (* a2 (cos th))) (sqrt 2))
3.0ms
(* a2 (* a2 (cos th)))
3.0ms
(* a2 (cos th))

series433.0ms

Calls
4 calls:
Slowest
163.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
140.0ms
(/ (* a2 (* a2 (cos th))) (sqrt 2))
80.0ms
(* a2 (* a2 (cos th)))
50.0ms
(* a2 (cos th))

simplify2.0s

Calls
41 calls:
Slowest
255.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
202.0ms
(/ (* (* (* a2 (* a2 (cos th))) (* a2 (* a2 (cos th)))) (* a2 (* a2 (cos th)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
199.0ms
(/ (* (* (* (cos th) (* a1 a1)) (* (cos th) (* a1 a1))) (* (cos th) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
147.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
143.0ms
(- (+ (log (cos th)) (log (* a1 a1))) (log (sqrt 2)))

prune964.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes465.0ms

Accuracy

0% (0.5b remaining)

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

bsearch3.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.5s2509×body1280valid
2.1s2129×body640valid
1.5s7901×body80valid
725.0ms1059×body320valid
214.0ms563×body160valid