Details

Time bar (total: 56.0s)

sample250.0ms

Algorithm
intervals
Results
113.0ms90×body1280valid
47.0ms56×body640valid
43.0ms239×body80valid
17.0ms30×body320valid
8.0ms20×body160valid

simplify552.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
552.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

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))

rewrite101.0ms

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
37.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
24.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
18.0ms
(/ (cos th) (sqrt 2))
17.0ms
(/ (cos th) (sqrt 2))

series444.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
137.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
78.0ms
(/ (cos th) (sqrt 2))
77.0ms
(/ (cos th) (sqrt 2))

simplify8.5s

Counts
180 → 192
Calls
180 calls:
Slowest
678.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
678.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
657.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
590.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
419.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

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)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
50×times-frac
47×add-sqr-sqrt
40×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
31×sqrt-prod
25×associate-*l*
12×associate-/r*
11×pow1 associate-*r* prod-exp cbrt-unprod
7×cbrt-undiv div-exp
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp unswap-sqr
2×clear-num frac-2neg *-commutative
1×associate-*l/ associate-*r/
Counts
4 → 153
Calls
4 calls:
Slowest
43.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
19.0ms
(/ (* a2 (cos th)) (sqrt 2))
16.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
12.0ms
(/ (cos th) (sqrt 2))

series485.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
134.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
131.0ms
(/ (* a2 (cos th)) (sqrt 2))
77.0ms
(/ (cos th) (sqrt 2))

simplify7.1s

Counts
140 → 165
Calls
140 calls:
Slowest
608.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
574.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
447.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
322.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
307.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

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-*r*
12×associate-/r*
9×prod-exp cbrt-unprod
8×pow1
7×cbrt-undiv div-exp
6×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×clear-num frac-2neg pow-prod-down *-commutative associate-/l* unswap-sqr
1×associate-*r/
Counts
4 → 116
Calls
4 calls:
Slowest
30.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
25.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
15.0ms
(* a2 (cos th))
11.0ms
(/ (* a2 (cos th)) (sqrt 2))

series473.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
128.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
119.0ms
(/ (* a2 (cos th)) (sqrt 2))
60.0ms
(* a2 (cos th))

simplify4.7s

Counts
91 → 128
Calls
91 calls:
Slowest
368.0ms
(* (* (* a2 a2) a2) (* (* (cos th) (cos th)) (cos th)))
333.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
303.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
282.0ms
(/ (* (* (* (cos th) (* a1 a1)) (* (cos th) (* a1 a1))) (* (cos th) (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
245.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 a2) a2) (* (* (cos th) (cos th)) (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
64×times-frac
56×add-sqr-sqrt add-exp-log
52×*-un-lft-identity add-cube-cbrt
45×add-cbrt-cube
42×cbrt-prod
38×associate-*r*
27×sqrt-prod
23×prod-exp cbrt-unprod
15×associate-/r*
14×cbrt-undiv div-exp
11×pow1
4×expm1-log1p-u associate-*l* pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
2×clear-num frac-2neg *-commutative unswap-sqr
1×frac-times associate-*l/
Counts
4 → 181
Calls
4 calls:
Slowest
106.0ms
(* (* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (cbrt (sqrt 2))))
47.0ms
(* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
41.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
17.0ms
(/ (cos th) (cbrt (sqrt 2)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
569.0ms
(* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
353.0ms
(/ (cos th) (cbrt (sqrt 2)))
168.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2))
146.0ms
(* (* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (cbrt (sqrt 2))))

simplify14.4s

Counts
178 → 193
Calls
178 calls:
Slowest
885.0ms
(* (* a2 (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (cos th) (cbrt (sqrt 2))))
666.0ms
(* (* (* a2 a2) a2) (* (* (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ a2 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))))
660.0ms
(* (* (* (* a2 a2) a2) (/ (* (* a2 a2) a2) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (* (* (/ (cos th) (cbrt (sqrt 2))) (/ (cos th) (cbrt (sqrt 2)))) (/ (cos th) (cbrt (sqrt 2)))))
527.0ms
(* (* (* (* a2 a2) a2) (/ (* (* a2 a2) a2) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (/ (* (* (cos th) (cos th)) (cos th)) (sqrt 2)))
490.0ms
(* (pow (/ 1 (sqrt 2)) 1/3) (cos th))

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes400.0ms

Accuracy

0% (0.5b remaining)

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

bsearch3.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.0s2577×body1280valid
2.1s2136×body640valid
2.0s8068×body80valid
646.0ms1062×body320valid
173.0ms502×body160valid