Details

Time bar (total: 47.6s)

sample66.0ms

Algorithm
intervals
Results
34.0ms256×body80valid
10.0ms256×pre80true

simplify5.3s

Counts
1 → 1

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.5b

localize101.0ms

Local error

Found 4 expressions with local error:

45.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
36.5b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
0.0b
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

rewrite656.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×*-un-lft-identity add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in *-commutative
1×pow2 pow-plus flip3-- pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 212
Calls
4 calls:
Slowest
261.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
162.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
133.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
94.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
279.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
172.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
91.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify4.3s

Counts
224 → 224

prune3.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 33.7b

localize85.0ms

Local error

Found 4 expressions with local error:

34.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
33.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
0.0b
(* i (+ (+ alpha beta) i))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
213×times-frac
175×add-sqr-sqrt
145×*-un-lft-identity
101×associate-*r*
92×add-cube-cbrt
67×add-cbrt-cube add-exp-log
45×associate-*l*
30×cbrt-undiv div-exp difference-of-squares
28×associate-/r/
17×prod-exp cbrt-unprod
16×flip3-+ flip-+
15×sqrt-prod distribute-lft-out--
14×div-inv
12×distribute-lft-out
8×pow1
7×unswap-sqr
6×associate-/r*
5×associate-*r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* add-log-exp associate-/l/
2×clear-num frac-2neg pow-prod-down *-commutative
1×distribute-rgt-in frac-times distribute-lft-in flip3-- associate-*l/ flip--
Counts
4 → 272
Calls
4 calls:
Slowest
779.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
133.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
94.0ms
(* i (+ (+ alpha beta) i))
74.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series3.5s

Counts
4 → 12
Calls
4 calls:
Slowest
3.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
172.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
111.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
41.0ms
(* i (+ (+ alpha beta) i))

simplify1.1s

Counts
284 → 284

prune5.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 33.6b

localize117.0ms

Local error

Found 4 expressions with local error:

33.9b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.9b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (* (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))

rewrite883.0ms

Algorithm
rewrite-expression-head
Rules
193×add-exp-log
145×add-cbrt-cube
98×div-exp
68×cbrt-undiv
65×prod-exp
58×times-frac
48×*-un-lft-identity
47×cbrt-unprod
42×associate-*l*
39×add-sqr-sqrt
28×add-cube-cbrt
14×associate-/r/
12×associate-*r*
9×flip3-+ flip-+ distribute-lft-out
8×pow1 1-exp
7×sqrt-prod div-inv
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*r/
2×rem-sqrt-square sqrt-pow1 pow1/2 difference-of-squares unswap-sqr associate-/l/
1×frac-times clear-num frac-2neg flip3-- pow-prod-down associate-*l/ *-commutative flip-- associate-/l* distribute-lft-out--
Counts
4 → 191
Calls
4 calls:
Slowest
787.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (* (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
66.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
14.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
13.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series3.6s

Counts
4 → 12
Calls
4 calls:
Slowest
3.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (* (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
151.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
100.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
90.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify2.9s

Counts
203 → 203

prune4.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 33.6b

localize113.0ms

Local error

Found 4 expressions with local error:

34.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
34.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
33.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
33.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

rewrite458.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
18×add-cbrt-cube add-exp-log
12×associate-/r*
8×flip3-+ associate-/r/ flip-+ associate-/l* associate-/l/
6×cbrt-undiv div-exp
4×expm1-log1p-u pow1 clear-num frac-2neg associate-*r/ insert-posit16 log1p-expm1-u div-inv add-log-exp
2×prod-exp cbrt-unprod
Counts
4 → 124
Calls
4 calls:
Slowest
152.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
114.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
97.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
160.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
137.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
127.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify669.0ms

Counts
136 → 136

prune3.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 33.6b

regimes719.0ms

Accuracy

43.7% (1.5b remaining)

Error of 35.2b against oracle of 33.6b and baseline of 36.4b

bsearch182.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.6s8000×body80valid
434.0ms8000×pre80true