Details

Time bar (total: 29.9s)

sample216.0ms

Algorithm
intervals
Results
82.0ms80×body1280valid
53.0ms246×body80valid
46.0ms61×body640valid
14.0ms26×body320valid
4.0ms11×body160valid

simplify147.0ms

Calls
1 calls:
Slowest
147.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

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))

rewrite44.0ms

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×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg associate-*r* pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
15.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
14.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
8.0ms
(/ (cos th) (sqrt 2))
6.0ms
(/ (cos th) (sqrt 2))

series409.0ms

Calls
4 calls:
Slowest
123.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
121.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
101.0ms
(/ (cos th) (sqrt 2))
64.0ms
(/ (cos th) (sqrt 2))

simplify4.4s

Calls
98 calls:
Slowest
611.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
557.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
253.0ms
(- (+ (/ 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))))
196.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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))

rewrite51.0ms

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×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u 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
20.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
14.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
8.0ms
(/ (cos th) (sqrt 2))
8.0ms
(* (cos th) (* a2 a2))

series457.0ms

Calls
4 calls:
Slowest
176.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
143.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
74.0ms
(* (cos th) (* a2 a2))
64.0ms
(/ (cos th) (sqrt 2))

simplify4.0s

Calls
74 calls:
Slowest
614.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
495.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
250.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
248.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
241.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize8.0ms

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))

rewrite28.0ms

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×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg associate-*r* pow-prod-down *-commutative div-inv associate-/l*
Calls
4 calls:
Slowest
11.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
8.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
4.0ms
(* (cos th) (* a2 a2))
4.0ms
(* (cos th) (* a1 a1))

series413.0ms

Calls
4 calls:
Slowest
153.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
139.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
69.0ms
(* (cos th) (* a1 a1))
52.0ms
(* (cos th) (* a2 a2))

simplify3.3s

Calls
50 calls:
Slowest
373.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
305.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
264.0ms
(- (pow a1 2) (* 1/2 (* (pow a1 2) (pow th 2))))
252.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
195.0ms
(/ (* (* (* (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

localize21.0ms

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)))

rewrite39.0ms

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×expm1-log1p-u pow1 associate-*r* insert-posit16 log1p-expm1-u 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
17.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
13.0ms
(/ (* a2 (* a2 (cos th))) (sqrt 2))
5.0ms
(* a2 (* a2 (cos th)))
3.0ms
(* a2 (cos th))

series408.0ms

Calls
4 calls:
Slowest
155.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
135.0ms
(/ (* a2 (* a2 (cos th))) (sqrt 2))
63.0ms
(* a2 (* a2 (cos th)))
55.0ms
(* a2 (cos th))

simplify2.0s

Calls
41 calls:
Slowest
231.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
205.0ms
(/ (* (* (* (cos th) (* a1 a1)) (* (cos th) (* a1 a1))) (* (cos th) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
190.0ms
(/ (* (* (* a2 (* a2 (cos th))) (* a2 (* a2 (cos th)))) (* a2 (* a2 (cos th)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
183.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
150.0ms
(- (/ (pow a2 2) (sqrt 2)) (* 1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))

prune930.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes382.0ms

Accuracy

0% (0.5b remaining)

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

bsearch3.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
3.3s2509×body1280valid
1.7s2129×body640valid
1.6s7901×body80valid
663.0ms1059×body320valid
600.0ms563×body160valid