Details

Time bar (total: 53.0s)

sample205.0ms

Algorithm
intervals
Results
69.0ms75×body1280valid
40.0ms63×body640valid
38.0ms256×body80valid
33.0ms39×body320valid
6.0ms19×body160valid

simplify179.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
179.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

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
42.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
24.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
22.0ms
(/ (cos th) (sqrt 2))
17.0ms
(/ (cos th) (sqrt 2))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
124.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
88.0ms
(/ (cos th) (sqrt 2))
76.0ms
(/ (cos th) (sqrt 2))

simplify8.7s

Counts
180 → 184
Calls
180 calls:
Slowest
629.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
589.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
578.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
576.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
390.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize37.0ms

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))

rewrite70.0ms

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
27.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
25.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
8.0ms
(/ (cos th) (sqrt 2))
4.0ms
(/ (sqrt 2) a1)

series417.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
119.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
77.0ms
(/ (cos th) (sqrt 2))
67.0ms
(/ (sqrt 2) a1)

simplify9.0s

Counts
216 → 203
Calls
216 calls:
Slowest
618.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
600.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
388.0ms
(/ 1 a1)
331.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
321.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize27.0ms

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) (* a2 a2))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
82×times-frac
51×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
36×sqrt-prod
32×add-cbrt-cube add-exp-log
31×associate-/r*
10×cbrt-undiv div-exp
9×pow1
8×prod-exp cbrt-unprod associate-/l*
5×div-inv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*l* pow-prod-down
1×associate-*r* associate-/r/ *-commutative unswap-sqr
Counts
4 → 155
Calls
4 calls:
Slowest
44.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
31.0ms
(* (cos th) (* a2 a2))
25.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
9.0ms
(/ (sqrt 2) a1)

series371.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
109.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2))
70.0ms
(* (cos th) (* a2 a2))
63.0ms
(/ (sqrt 2) a1)

simplify7.1s

Counts
167 → 167
Calls
167 calls:
Slowest
373.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
372.0ms
(- (pow a2 2) (* 1/2 (* (pow a2 2) (pow th 2))))
346.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
315.0ms
(/ (* (* (* (cos th) (* a2 a2)) (* (cos th) (* a2 a2))) (* (cos th) (* a2 a2))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
273.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (sqrt 2) a1) (/ (sqrt 2) a1)) (/ (sqrt 2) a1)))

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize50.0ms

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)
0.2b
(/ (* (cos th) a1) (/ (sqrt 2) a1))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
82×add-sqr-sqrt
74×*-un-lft-identity add-cube-cbrt
52×sqrt-prod
31×associate-/r*
25×add-cbrt-cube add-exp-log
22×associate-*l*
10×associate-/l*
9×cbrt-undiv div-exp
6×pow1 div-inv
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* unswap-sqr
1×pow-prod-down associate-*l/ associate-/r/ *-commutative
Counts
4 → 188
Calls
4 calls:
Slowest
25.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
23.0ms
(* (/ (cos th) (sqrt 2)) a2)
17.0ms
(/ (cos th) (sqrt 2))
9.0ms
(/ (sqrt 2) a1)

series465.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
177.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
154.0ms
(* (/ (cos th) (sqrt 2)) a2)
69.0ms
(/ (cos th) (sqrt 2))
66.0ms
(/ (sqrt 2) a1)

simplify7.4s

Counts
213 → 200
Calls
213 calls:
Slowest
361.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
326.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
300.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
296.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
280.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune2.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes640.0ms

Accuracy

0% (0.4b remaining)

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

bsearch5.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.6s2543×body1280valid
2.3s2084×body640valid
1.4s8065×body80valid
626.0ms1086×body320valid
190.0ms547×body160valid