Details

Time bar (total: 54.2s)

sample51.0ms

Algorithm
intervals
Results
28.0ms256×body80valid
9.0ms256×pre80true

simplify3.6s

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 49.3b

localize30.0ms

Local error

Found 4 expressions with local error:

43.4b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
33.2b
(/ (/ (* (* 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
(* i (+ (+ alpha beta) i))

rewrite504.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×associate-*l* pow-prod-down insert-posit16 add-log-exp
3×distribute-lft-out
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 193
Calls
4 calls:
Slowest
185.0ms
(/ (/ (* (* 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))
160.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
101.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
53.0ms
(* i (+ (+ alpha beta) i))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.1s
(/ (/ (* (* 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))
230.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
140.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
24.0ms
(* i (+ (+ alpha beta) i))

simplify3.3s

Counts
205 → 205

prune2.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 31.4b

localize51.0ms

Local error

Found 4 expressions with local error:

32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite596.0ms

Algorithm
rewrite-expression-head
Rules
216×times-frac
163×add-sqr-sqrt
151×*-un-lft-identity
99×add-cube-cbrt
32×associate-/r/ difference-of-squares
28×associate-/l*
25×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
11×cbrt-undiv div-exp
10×distribute-lft-out
6×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×prod-exp associate-*r/ cbrt-unprod
1×flip3-- flip--
Counts
4 → 256
Calls
4 calls:
Slowest
237.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
163.0ms
(/ (/ (* 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)))
53.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
451.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
355.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
187.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
93.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify2.9s

Counts
268 → 268

prune4.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 31.4b

localize64.0ms

Local error

Found 4 expressions with local error:

32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.4b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite653.0ms

Algorithm
rewrite-expression-head
Rules
192×times-frac
176×*-un-lft-identity
92×add-sqr-sqrt add-cube-cbrt
42×distribute-lft-out
32×sqrt-prod
30×associate-/r/
28×associate-/l*
25×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
15×associate-/r* div-inv
11×cbrt-undiv div-exp
6×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×prod-exp associate-*r/ cbrt-unprod
Counts
4 → 240
Calls
4 calls:
Slowest
267.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
198.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
132.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
50.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series7.8s

Counts
4 → 12
Calls
4 calls:
Slowest
7.2s
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
327.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
177.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
93.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify2.8s

Counts
252 → 252

prune4.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 31.4b

localize107.0ms

Local error

Found 4 expressions with local error:

32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.4b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))

rewrite595.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
138×*-un-lft-identity
74×add-sqr-sqrt add-cube-cbrt
32×sqrt-prod distribute-lft-out
21×add-cbrt-cube add-exp-log
20×associate-/r/ associate-/l*
14×associate-/r*
13×flip3-+ flip-+
10×div-inv
8×cbrt-undiv div-exp
7×associate-/l/
4×pow1 clear-num frac-2neg associate-*r/ insert-posit16 add-log-exp
2×prod-exp cbrt-unprod
Counts
4 → 197
Calls
4 calls:
Slowest
311.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
135.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
80.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
65.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series7.8s

Counts
4 → 12
Calls
4 calls:
Slowest
7.3s
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
175.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
143.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
122.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify2.1s

Counts
209 → 209

prune4.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 31.4b

regimes252.0ms

Accuracy

44.7% (1.3b remaining)

Error of 35.5b against oracle of 34.1b and baseline of 36.5b

bsearch122.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.8s8000×body80valid
387.0ms8000×pre80true