Details

Time bar (total: 49.4s)

sample247.0ms

Algorithm
intervals
Results
88.0ms70×body640valid
72.0ms70×body1280valid
44.0ms251×body80valid
16.0ms30×body320valid
5.0ms16×body160valid

simplify165.0ms

Calls
1 calls:
Slowest
165.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

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))

rewrite84.0ms

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
Calls
4 calls:
Slowest
32.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
23.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
17.0ms
(/ (cos th) (sqrt 2))
10.0ms
(/ (cos th) (sqrt 2))

series424.0ms

Calls
4 calls:
Slowest
147.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
133.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
77.0ms
(/ (cos th) (sqrt 2))
67.0ms
(/ (cos th) (sqrt 2))

simplify8.1s

Calls
180 calls:
Slowest
650.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
630.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
595.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
570.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
312.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

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
Calls
4 calls:
Slowest
47.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
24.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
17.0ms
(/ (cos th) (sqrt 2))
9.0ms
(/ (sqrt 2) a1)

series417.0ms

Calls
4 calls:
Slowest
136.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
132.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
87.0ms
(/ (cos th) (sqrt 2))
62.0ms
(/ (sqrt 2) a1)

simplify8.9s

Calls
216 calls:
Slowest
591.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
542.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
392.0ms
(/ (cos th) (/ (sqrt (* (cbrt 2) (cbrt 2))) 1))
322.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
300.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (sqrt 2) a1) (/ (sqrt 2) a1)) (/ (sqrt 2) a1)))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
82×times-frac
53×add-sqr-sqrt
51×*-un-lft-identity add-cube-cbrt
36×sqrt-prod
31×associate-/r*
29×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
8×associate-/l*
6×pow1 prod-exp cbrt-unprod
5×div-inv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* associate-*l*
1×pow-prod-down associate-/r/ *-commutative unswap-sqr
Calls
4 calls:
Slowest
37.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
20.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
10.0ms
(/ (sqrt 2) a1)
8.0ms
(* (cos th) a1)

series432.0ms

Calls
4 calls:
Slowest
163.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
137.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
79.0ms
(/ (sqrt 2) a1)
53.0ms
(* (cos th) a1)

simplify6.8s

Calls
166 calls:
Slowest
354.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
342.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
332.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1))
332.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
262.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (sqrt 2) a1) (/ (sqrt 2) a1)) (/ (sqrt 2) a1)))

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

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-*l*
12×associate-/r*
9×prod-exp cbrt-unprod
8×pow1
7×cbrt-undiv div-exp
6×associate-*r*
4×insert-posit16 add-log-exp
3×div-inv
2×clear-num frac-2neg pow-prod-down *-commutative associate-/l* unswap-sqr
1×associate-*l/
Calls
4 calls:
Slowest
36.0ms
(* (/ (* (cos th) a1) (sqrt 2)) a1)
28.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
13.0ms
(* (cos th) a1)
11.0ms
(/ (* (cos th) a1) (sqrt 2))

series445.0ms

Calls
4 calls:
Slowest
136.0ms
(/ (* (cos th) a1) (sqrt 2))
127.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
126.0ms
(* (/ (* (cos th) a1) (sqrt 2)) a1)
55.0ms
(* (cos th) a1)

simplify5.1s

Calls
90 calls:
Slowest
369.0ms
(* (/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* a1 a1) a1))
360.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1))
329.0ms
(* (/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* a1 a1) a1))
305.0ms
(- (/ a1 (sqrt 2)) (* 1/2 (/ (* a1 (pow th 2)) (sqrt 2))))
278.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes476.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.8s2469×body1280valid
2.8s2147×body640valid
1.9s8065×body80valid
601.0ms1046×body320valid
212.0ms529×body160valid