Details

Time bar (total: 22.4s)

sample56.0ms

Algorithm
intervals
Results
13.0ms193×body80valid
9.0ms28×body1280valid
9.0ms256×pre80true
5.0ms19×body640valid
2.0ms10×body320valid
1.0ms6×body160valid

simplify3.4s

Counts
1 → 1
Iterations
IterNodes
done5001
324930
314722
304510
294301
284120
273916
263715
253502
243325
233117
222909
212698
202516
192291
182012
171763
161558
151364
141138
13931
12742
11607
10526
9431
8318
7267
6197
5124
469
350
233
120
010

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
26×add-sqr-sqrt
25×times-frac
19×distribute-lft-out
14×add-cube-cbrt
6×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-cbrt-cube add-exp-log add-log-exp
2×pow1 flip3-+ div-sub associate-/r/ flip-+ insert-posit16 associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- div-inv flip--
Counts
2 → 67
Calls
2 calls:
54.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
177.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series141.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
84.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts
73 → 73
Iterations
IterNodes
done5007
21126
1328
0126

prune320.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
2.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite896.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
34×add-sqr-sqrt
32×times-frac
24×add-cube-cbrt distribute-lft-out
11×add-log-exp
10×associate-/r*
8×add-cbrt-cube add-exp-log
6×associate-/l*
4×pow1 diff-log associate-/r/ insert-posit16 distribute-lft-out-- difference-of-squares
3×sub-neg flip3-- flip--
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp frac-sub flip-+ div-inv associate--r+
1×associate--r-
Counts
4 → 115
Calls
4 calls:
578.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
35.0ms
(/ alpha (+ (+ alpha beta) 2.0))
36.0ms
(/ beta (+ (+ alpha beta) 2.0))
245.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series306.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
63.0ms
(/ alpha (+ (+ alpha beta) 2.0))
68.0ms
(/ beta (+ (+ alpha beta) 2.0))
83.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts
127 → 127
Iterations
IterNodes
done5019
21580
1467
0197

prune670.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta)))
0.1b
(* (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))) (/ alpha (+ (+ 2.0 alpha) beta)))
0.1b
(/ (- (* (+ (* 1.0 (+ (/ alpha (+ (+ 2.0 alpha) beta)) 1.0)) (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta)))) beta) (* (- (* (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))) (/ alpha (+ (+ 2.0 alpha) beta))) (* (* 1.0 1.0) 1.0)) (+ (+ 2.0 alpha) beta))) (* (+ (+ 2.0 alpha) beta) (+ (* 1.0 (+ (/ alpha (+ (+ 2.0 alpha) beta)) 1.0)) (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))))))
2.1b
(- (* (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))) (/ alpha (+ (+ 2.0 alpha) beta))) (* (* 1.0 1.0) 1.0))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
210×*-un-lft-identity
119×times-frac
116×associate-*r/
110×associate-*l/
82×flip3-+ flip-+
81×distribute-lft-out
78×add-sqr-sqrt
76×frac-times
66×frac-add associate-/l/
64×frac-sub
63×add-cube-cbrt
62×add-cbrt-cube add-exp-log
42×associate-*r*
39×swap-sqr
36×associate-/r/
30×pow1
26×flip3-- flip--
23×prod-exp cbrt-unprod
22×associate-*l*
19×cbrt-undiv div-exp
7×pow-plus pow-prod-up
6×div-inv add-log-exp unswap-sqr
4×pow-prod-down insert-posit16
3×pow2 pow3 pow-sqr associate-/l*
2×*-commutative
1×difference-cubes clear-num associate-/r* sub-neg frac-2neg diff-log div-sub
Counts
4 → 310
Calls
4 calls:
187.0ms
(* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta)))
415.0ms
(* (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))) (/ alpha (+ (+ 2.0 alpha) beta)))
584.0ms
(/ (- (* (+ (* 1.0 (+ (/ alpha (+ (+ 2.0 alpha) beta)) 1.0)) (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta)))) beta) (* (- (* (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))) (/ alpha (+ (+ 2.0 alpha) beta))) (* (* 1.0 1.0) 1.0)) (+ (+ 2.0 alpha) beta))) (* (+ (+ 2.0 alpha) beta) (+ (* 1.0 (+ (/ alpha (+ (+ 2.0 alpha) beta)) 1.0)) (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))))))
265.0ms
(- (* (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))) (/ alpha (+ (+ 2.0 alpha) beta))) (* (* 1.0 1.0) 1.0))

series809.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta)))
99.0ms
(* (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))) (/ alpha (+ (+ 2.0 alpha) beta)))
486.0ms
(/ (- (* (+ (* 1.0 (+ (/ alpha (+ (+ 2.0 alpha) beta)) 1.0)) (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta)))) beta) (* (- (* (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))) (/ alpha (+ (+ 2.0 alpha) beta))) (* (* 1.0 1.0) 1.0)) (+ (+ 2.0 alpha) beta))) (* (+ (+ 2.0 alpha) beta) (+ (* 1.0 (+ (/ alpha (+ (+ 2.0 alpha) beta)) 1.0)) (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))))))
151.0ms
(- (* (* (/ alpha (+ (+ 2.0 alpha) beta)) (/ alpha (+ (+ 2.0 alpha) beta))) (/ alpha (+ (+ 2.0 alpha) beta))) (* (* 1.0 1.0) 1.0))

simplify4.0s

Counts
322 → 322
Iterations
IterNodes
done5005
12085
0498

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 3.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))
2.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite372.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
15×cbrt-prod
12×add-sqr-sqrt
9×distribute-lft-out
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×flip3-+ pow1/3 flip-+
2×difference-of-squares
1×sub-neg times-frac flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
21.0ms
(cbrt (+ (+ alpha beta) 2.0))
15.0ms
(cbrt (+ (+ alpha beta) 2.0))
26.0ms
(cbrt (+ (+ alpha beta) 2.0))
307.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series544.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(cbrt (+ (+ alpha beta) 2.0))
134.0ms
(cbrt (+ (+ alpha beta) 2.0))
142.0ms
(cbrt (+ (+ alpha beta) 2.0))
119.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.9s

Counts
76 → 76
Iterations
IterNodes
done5005
32443
2751
1284
0122

prune541.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 3.1b

regimes84.0ms

Accuracy

75.8% (3.2b remaining)

Error of 6.1b against oracle of 2.9b and baseline of 16.0b

bsearch85.0ms

Steps
ItersRangePoint
7
4728159102934193.0
3.643030813794801e+17
4.955254989703516e+16

simplify12.0ms

Iterations
IterNodes
done37
137
032

end0.0ms

sample1.4s

Algorithm
intervals
Results
392.0ms5837×body80valid
296.0ms8000×pre80true
243.0ms831×body1280valid
166.0ms712×body640valid
64.0ms410×body320valid
21.0ms210×body160valid