Details

Time bar (total: 1.3m)

sample232.0ms

Algorithm
intervals
Results
89.0ms65×body1280valid
59.0ms79×body640valid
46.0ms255×body80valid
15.0ms28×body320valid
5.0ms17×body160valid

simplify160.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
159.0ms
(+ (* (/ (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: 0.3b

localize40.0ms

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))

rewrite79.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg associate-*r* associate-*l/ *-commutative
Counts
4 → 180
Calls
4 calls:
Slowest
36.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
24.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
8.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series492.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
153.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
95.0ms
(/ (cos th) (sqrt 2))
77.0ms
(/ (cos th) (sqrt 2))

simplify8.5s

Counts
180 → 192
Calls
180 calls:
Slowest
634.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
625.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
578.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
531.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
361.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.4s

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

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
44×times-frac
43×add-sqr-sqrt
37×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
28×sqrt-prod
25×associate-*l*
14×pow1
12×associate-/r* prod-exp cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* add-log-exp unswap-sqr
3×div-inv
2×clear-num frac-2neg associate-*r* *-commutative
1×associate-*l/
Counts
4 → 144
Calls
4 calls:
Slowest
32.0ms
(* (cos th) (* a1 a1))
31.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
28.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
17.0ms
(/ (cos th) (sqrt 2))

series459.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
177.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
139.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
100.0ms
(/ (cos th) (sqrt 2))
43.0ms
(* (cos th) (* a1 a1))

simplify6.9s

Counts
131 → 156
Calls
131 calls:
Slowest
861.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
536.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
365.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
336.0ms
(/ (* (* (* (cos th) (* a1 a1)) (* (cos th) (* a1 a1))) (* (cos th) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
285.0ms
(- (pow a1 2) (* 1/2 (* (pow a1 2) (pow th 2))))

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.3b
(/ (* (* (cos th) a1) a1) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.1b
(* (cos th) a1)

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
44×times-frac
38×*-un-lft-identity add-cube-cbrt
29×add-cbrt-cube add-exp-log
28×sqrt-prod
25×associate-*l*
12×associate-/r*
11×pow1
10×prod-exp cbrt-unprod
6×cbrt-undiv div-exp
4×expm1-log1p-u associate-*r* pow-prod-down insert-posit16 log1p-expm1-u associate-/l* add-log-exp unswap-sqr
3×div-inv
2×clear-num frac-2neg *-commutative
1×associate-*l/
Counts
4 → 143
Calls
4 calls:
Slowest
44.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
42.0ms
(/ (* (* (cos th) a1) a1) (sqrt 2))
18.0ms
(/ (cos th) (sqrt 2))
15.0ms
(* (cos th) a1)

series498.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
161.0ms
(/ (* (* (cos th) a1) a1) (sqrt 2))
96.0ms
(/ (cos th) (sqrt 2))
70.0ms
(* (cos th) a1)

simplify6.6s

Counts
130 → 155
Calls
130 calls:
Slowest
626.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
623.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
345.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1))
332.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
285.0ms
(/ (* (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* a1 a1) a1)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.8s

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

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
94×times-frac
68×add-exp-log
65×add-sqr-sqrt
60×*-un-lft-identity add-cube-cbrt
49×add-cbrt-cube
40×sqrt-prod
36×cbrt-prod
24×prod-exp cbrt-unprod
22×cbrt-undiv div-exp associate-*l*
16×associate-/r*
14×div-inv
9×pow1 associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 205
Calls
4 calls:
Slowest
54.0ms
(/ (/ (* (* (cos th) a1) a1) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
51.0ms
(/ (* (* (cos th) a1) a1) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
43.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
24.0ms
(/ (cos th) (sqrt 2))

series881.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
508.0ms
(/ (* (* (cos th) a1) a1) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
148.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
141.0ms
(/ (/ (* (* (cos th) a1) a1) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
84.0ms
(/ (cos th) (sqrt 2))

simplify31.7s

Counts
230 → 217
Calls
230 calls:
Slowest
1.1s
(/ (/ (* (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* a1 a1) a1)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt 2))
1.0s
(/ (/ (* (* (* (* (cos th) a1) a1) (* (* (cos th) a1) a1)) (* (* (cos th) a1) a1)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt 2))
998.0ms
(/ (/ (* (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (* (* a1 a1) a1)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt 2))
978.0ms
(/ (* (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (* (* a1 a1) a1)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
967.0ms
(/ (* (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* a1 a1) a1)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))

prune3.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes532.0ms

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
3.9s2529×body1280valid
1.9s2077×body640valid
1.7s8081×body80valid
627.0ms1080×body320valid
256.0ms517×body160valid