Details

Time bar (total: 52.8s)

sample292.0ms

Algorithm
intervals
Results
92.0ms77×body1280valid
71.0ms261×body80valid
66.0ms79×body640valid
28.0ms43×body320valid
7.0ms19×body160valid

simplify124.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
124.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

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))

rewrite118.0ms

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
46.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
37.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
17.0ms
(/ (cos th) (sqrt 2))
16.0ms
(/ (cos th) (sqrt 2))

series453.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
136.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
81.0ms
(/ (cos th) (sqrt 2))
76.0ms
(/ (cos th) (sqrt 2))

simplify8.4s

Counts
180 → 184
Calls
180 calls:
Slowest
670.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
644.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
609.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
607.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
325.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.5b
(/ (sqrt 2) a1)
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.2b
(/ (* (cos th) a1) (/ (sqrt 2) a1))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
78×add-sqr-sqrt
73×*-un-lft-identity add-cube-cbrt
52×sqrt-prod
32×add-cbrt-cube add-exp-log
31×associate-/r*
22×associate-*l*
10×cbrt-undiv div-exp associate-/l*
9×pow1
8×prod-exp cbrt-unprod
6×div-inv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ associate-/r/ *-commutative
Counts
4 → 191
Calls
4 calls:
Slowest
36.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
22.0ms
(/ (cos th) (sqrt 2))
12.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
9.0ms
(/ (sqrt 2) a1)

series392.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
111.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
92.0ms
(/ (cos th) (sqrt 2))
59.0ms
(/ (sqrt 2) a1)

simplify8.4s

Counts
216 → 203
Calls
216 calls:
Slowest
623.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
537.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
391.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
306.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
304.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (sqrt 2) a1) (/ (sqrt 2) a1)) (/ (sqrt 2) a1)))

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
50×times-frac
47×add-sqr-sqrt
40×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube associate-*l* add-exp-log
31×sqrt-prod
12×associate-/r*
11×pow1 prod-exp cbrt-unprod
7×cbrt-undiv div-exp
4×associate-*r* pow-prod-down insert-posit16 div-inv associate-/l* add-log-exp unswap-sqr
2×clear-num frac-2neg associate-*l/ *-commutative
Counts
4 → 145
Calls
4 calls:
Slowest
30.0ms
(* (/ (* (cos th) a1) (sqrt 2)) a1)
27.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
12.0ms
(/ (* (cos th) a1) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series547.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
143.0ms
(* (/ (* (cos th) a1) (sqrt 2)) a1)
135.0ms
(/ (* (cos th) a1) (sqrt 2))
87.0ms
(/ (cos th) (sqrt 2))

simplify6.8s

Counts
140 → 157
Calls
140 calls:
Slowest
706.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
512.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
364.0ms
(* (/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* a1 a1) a1))
321.0ms
(* (/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* a1 a1) a1))
305.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
95×times-frac
85×add-sqr-sqrt
73×*-un-lft-identity add-cube-cbrt
44×cbrt-prod sqrt-prod
32×associate-*r* add-exp-log
25×add-cbrt-cube
23×associate-*l*
14×pow1
12×prod-exp cbrt-unprod associate-/l*
9×associate-/r*
7×unswap-sqr
6×cbrt-undiv div-exp pow-prod-down
4×insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg *-commutative
1×associate-*l/ associate-*r/
Counts
4 → 194
Calls
4 calls:
Slowest
57.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (cbrt (sqrt 2)) a1))
42.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms
(/ (cos th) (sqrt 2))
10.0ms
(/ (cbrt (sqrt 2)) a1)

series854.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
509.0ms
(/ (cbrt (sqrt 2)) a1)
182.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
81.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (cbrt (sqrt 2)) a1))
81.0ms
(/ (cos th) (sqrt 2))

simplify7.5s

Counts
212 → 206
Calls
212 calls:
Slowest
701.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
659.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
457.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (/ (cbrt (sqrt 2)) a1) (/ (cbrt (sqrt 2)) a1)) (/ (cbrt (sqrt 2)) a1)))
453.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (sqrt 2) (* (* a1 a1) a1)))
287.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (/ (cbrt (sqrt 2)) a1) (/ (cbrt (sqrt 2)) a1)) (/ (cbrt (sqrt 2)) a1)))

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes413.0ms

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
4.0s2576×body1280valid
1.5s2050×body640valid
1.3s7868×body80valid
571.0ms1008×body320valid
213.0ms502×body160valid