Details

Time bar (total: 54.3s)

sample197.0ms

Algorithm
intervals
Results
88.0ms90×body1280valid
37.0ms56×body640valid
35.0ms239×body80valid
13.0ms30×body320valid
7.0ms20×body160valid

simplify126.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
126.0ms
(+ (* (/ (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

localize45.0ms

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))

rewrite100.0ms

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
43.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
21.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
17.0ms
(/ (cos th) (sqrt 2))
16.0ms
(/ (cos th) (sqrt 2))

series455.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
132.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
84.0ms
(/ (cos th) (sqrt 2))
84.0ms
(/ (cos th) (sqrt 2))

simplify8.4s

Counts
180 → 184
Calls
180 calls:
Slowest
759.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
663.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
628.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
628.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
316.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.4b
(/ (* a2 (cos th)) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.2b
(* a2 (/ (* a2 (cos th)) (sqrt 2)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
50×times-frac
47×add-sqr-sqrt
40×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
31×sqrt-prod
25×associate-*l*
12×associate-/r*
11×pow1 associate-*r* prod-exp cbrt-unprod
7×cbrt-undiv div-exp
4×pow-prod-down insert-posit16 div-inv associate-/l* add-log-exp unswap-sqr
2×clear-num frac-2neg *-commutative
1×associate-*l/ associate-*r/
Counts
4 → 145
Calls
4 calls:
Slowest
35.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
31.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
11.0ms
(/ (* a2 (cos th)) (sqrt 2))
10.0ms
(/ (cos th) (sqrt 2))

series999.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
553.0ms
(/ (* a2 (cos th)) (sqrt 2))
185.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
160.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
100.0ms
(/ (cos th) (sqrt 2))

simplify6.9s

Counts
140 → 157
Calls
140 calls:
Slowest
684.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
670.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
342.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
289.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
258.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* a2 (cos th)) (sqrt 2))
0.2b
(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.2b
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
0.1b
(* a2 (cos th))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
29×add-cbrt-cube add-exp-log
22×add-sqr-sqrt
18×*-un-lft-identity times-frac add-cube-cbrt
15×sqrt-prod
13×associate-*r*
12×associate-/r*
9×prod-exp cbrt-unprod
8×pow1
7×cbrt-undiv div-exp
6×associate-*l*
4×insert-posit16 add-log-exp
3×div-inv
2×clear-num frac-2neg pow-prod-down *-commutative associate-/l* unswap-sqr
1×associate-*r/
Counts
4 → 108
Calls
4 calls:
Slowest
39.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
35.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
22.0ms
(/ (* a2 (cos th)) (sqrt 2))
15.0ms
(* a2 (cos th))

series506.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(/ (* a2 (cos th)) (sqrt 2))
145.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
130.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
62.0ms
(* a2 (cos th))

simplify4.2s

Counts
91 → 120
Calls
91 calls:
Slowest
309.0ms
(* (* (* a2 a2) a2) (* (* (cos th) (cos th)) (cos th)))
274.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
260.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
246.0ms
(/ (* (* (* (cos th) (* a1 a1)) (* (cos th) (* a1 a1))) (* (cos th) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
228.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (* a1 a1) (* a1 a1)) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
64×times-frac
56×add-sqr-sqrt add-exp-log
52×*-un-lft-identity add-cube-cbrt
45×add-cbrt-cube
42×cbrt-prod
38×associate-*r*
27×sqrt-prod
23×prod-exp cbrt-unprod
15×associate-/r*
14×cbrt-undiv div-exp
11×pow1
4×associate-*l* pow-prod-down associate-*r/ insert-posit16 div-inv associate-/l* add-log-exp
2×clear-num frac-2neg *-commutative unswap-sqr
1×frac-times associate-*l/
Counts
4 → 173
Calls
4 calls:
Slowest
73.0ms
(* (* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (cbrt (sqrt 2))))
30.0ms
(* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
20.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
8.0ms
(/ (cos th) (cbrt (sqrt 2)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
524.0ms
(* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
399.0ms
(/ (cos th) (cbrt (sqrt 2)))
186.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
129.0ms
(* (* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (cbrt (sqrt 2))))

simplify13.2s

Counts
178 → 185
Calls
178 calls:
Slowest
676.0ms
(* (* (* a2 a2) a2) (* (* (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))))
658.0ms
(* (* (* (* a2 a2) a2) (/ (* (* a2 a2) a2) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (* (* (/ (cos th) (cbrt (sqrt 2))) (/ (cos th) (cbrt (sqrt 2)))) (/ (cos th) (cbrt (sqrt 2)))))
461.0ms
(* (pow (/ 1 (sqrt 2)) 1/3) (cos th))
438.0ms
(* (* (* (* a2 a2) a2) (/ (* (* a2 a2) a2) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (/ (* (* (cos th) (cos th)) (cos th)) (sqrt 2)))
429.0ms
(* (* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (cbrt (sqrt 2))))

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes334.0ms

Accuracy

0% (0.5b remaining)

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

bsearch5.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
3.3s2577×body1280valid
2.4s2136×body640valid
1.5s8068×body80valid
661.0ms1062×body320valid
179.0ms502×body160valid