Details

Time bar (total: 8.0m)

sample256.0ms

Algorithm
intervals
Results
101.0ms101×body1280valid
72.0ms72×body640valid
41.0ms250×body80valid
20.0ms36×body320valid
4.0ms13×body160valid

simplify167.0ms

Calls
1 calls:
Slowest
167.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

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))
0.2b
(* (/ (cos th) (sqrt 2)) (* a2 a2))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
160×add-sqr-sqrt
92×times-frac
76×*-un-lft-identity add-cube-cbrt
58×sqrt-prod
50×associate-*l*
38×unswap-sqr
36×associate-*r*
32×add-cbrt-cube add-exp-log
24×associate-/r* associate-*l/
14×pow1
12×swap-sqr prod-exp cbrt-unprod associate-/l*
10×*-commutative
6×cbrt-undiv div-exp pow-prod-down
4×clear-num frac-2neg insert-posit16 div-inv add-log-exp
Calls
4 calls:
Slowest
49.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
34.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
16.0ms
(/ (cos th) (sqrt 2))
16.0ms
(/ (cos th) (sqrt 2))

series379.0ms

Calls
4 calls:
Slowest
131.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
106.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
80.0ms
(/ (cos th) (sqrt 2))
62.0ms
(/ (cos th) (sqrt 2))

simplify10.6s

Calls
274 calls:
Slowest
686.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
659.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
651.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
605.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
285.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune3.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize48.0ms

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)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
222×add-sqr-sqrt
194×times-frac
138×*-un-lft-identity
136×associate-*r* add-cube-cbrt
109×sqrt-prod
71×associate-*l*
40×unswap-sqr
32×add-cbrt-cube add-exp-log associate-/l*
24×associate-/r*
21×associate-*r/
20×*-commutative
12×associate-*l/
11×pow1 prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×swap-sqr
5×clear-num
4×frac-2neg pow-prod-down insert-posit16 div-inv add-log-exp
3×un-div-inv
Calls
4 calls:
Slowest
42.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
36.0ms
(/ (* a2 (cos th)) (sqrt 2))
31.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
17.0ms
(/ (cos th) (sqrt 2))

series492.0ms

Calls
4 calls:
Slowest
163.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
141.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
125.0ms
(/ (* a2 (cos th)) (sqrt 2))
62.0ms
(/ (cos th) (sqrt 2))

simplify13.6s

Calls
425 calls:
Slowest
689.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
532.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
326.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
293.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
268.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune4.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* a2 (cos th)) (sqrt 2))
0.3b
(/ (* a1 (* (cos th) a1)) (sqrt 2))
0.2b
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
0.1b
(* (cos th) a1)

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
280×times-frac
278×add-sqr-sqrt
226×associate-*r*
185×*-un-lft-identity
183×add-cube-cbrt
149×sqrt-prod
91×associate-*l*
50×unswap-sqr
48×associate-/l*
30×*-commutative
29×add-cbrt-cube add-exp-log
21×associate-*r/
18×associate-/r*
9×prod-exp cbrt-unprod
8×pow1
7×cbrt-undiv div-exp
4×clear-num insert-posit16 add-log-exp
3×frac-2neg un-div-inv div-inv
2×pow-prod-down
Calls
4 calls:
Slowest
40.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
40.0ms
(/ (* a1 (* (cos th) a1)) (sqrt 2))
15.0ms
(/ (* a2 (cos th)) (sqrt 2))
8.0ms
(* (cos th) a1)

series535.0ms

Calls
4 calls:
Slowest
172.0ms
(/ (* a2 (cos th)) (sqrt 2))
168.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
145.0ms
(/ (* a1 (* (cos th) a1)) (sqrt 2))
51.0ms
(* (cos th) a1)

simplify24.4s

Calls
598 calls:
Slowest
349.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
341.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
298.0ms
(/ (* a1 (* (cos th) (* (cbrt a1) (cbrt a1)))) 1)
282.0ms
(/ (* a1 (* (cos th) (sqrt a1))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
275.0ms
(/ (* (* (* a1 a1) a1) (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune5.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite281.0ms

Algorithm
rewrite-expression-head
Rules
2382×add-sqr-sqrt
1746×cbrt-prod
1240×associate-/r*
995×associate-*l*
959×times-frac
953×sqrt-prod
922×*-un-lft-identity
919×add-cube-cbrt
870×frac-times
612×unswap-sqr
578×associate-*r*
399×associate-/l*
348×swap-sqr
143×add-cbrt-cube
111×*-commutative
80×clear-num
78×frac-2neg
77×cbrt-unprod
61×add-exp-log
58×cbrt-undiv associate-*l/
36×associate-*r/
23×prod-exp
18×div-exp
8×pow1
5×un-div-inv div-inv
4×insert-posit16 add-log-exp
2×pow-prod-down
Calls
4 calls:
Slowest
124.0ms
(* (/ (* a1 (cos th)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ a1 (cbrt (sqrt 2))))
30.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
21.0ms
(/ (* a2 (cos th)) (sqrt 2))
10.0ms
(/ a1 (cbrt (sqrt 2)))

series996.0ms

Calls
4 calls:
Slowest
500.0ms
(/ a1 (cbrt (sqrt 2)))
173.0ms
(* (/ (* a1 (cos th)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ a1 (cbrt (sqrt 2))))
169.0ms
(/ (* a2 (cos th)) (sqrt 2))
154.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))

simplify6.3m

Calls
3051 calls:
Slowest
1.3s
(* (/ (* (* (* a1 a1) a1) (* (* (cos th) (cos th)) (cos th))) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (* (* a1 a1) a1) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))))
1.3s
(* (/ (* (* (* a1 (cos th)) (* a1 (cos th))) (* a1 (cos th))) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (* (* a1 a1) a1) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))))
1.2s
(* (/ (* (* (* a1 (cos th)) (* a1 (cos th))) (* a1 (cos th))) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))))) (/ (* (* a1 a1) a1) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))))
1.0s
(* (/ (* (* (* a1 (cos th)) (* a1 (cos th))) (* a1 (cos th))) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt 2))) (/ (* (* a1 a1) a1) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))))
1.0s
(* (/ (* (* (* a1 a1) a1) (* (* (cos th) (cos th)) (cos th))) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))))) (/ (* (* a1 a1) a1) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))))

prune29.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes407.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.0s2629×body1280valid
2.2s2111×body640valid
2.0s8011×body80valid
651.0ms1025×body320valid
181.0ms544×body160valid