Details

Time bar (total: 1.8m)

sample349.0ms

Algorithm
intervals
Results
58.0ms256×body80valid
25.0ms256×pre80true

simplify7.0s

Counts
1 → 1
Iterations
IterNodes
done5020
31576
2267
158
017

prune80.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.5b

localize315.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.9b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
47.5b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
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×associate-*l* pow-prod-down add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 200
Calls
4 calls:
470.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
405.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.1s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
472.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series3.9s

Counts
4 → 12
Calls
4 calls:
121.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
332.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
2.6s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
834.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify3.9s

Counts
212 → 212
Iterations
IterNodes
done5000
11307
0358

prune4.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 33.7b

localize114.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
34.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.7s

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-exp-log add-cbrt-cube
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 frac-2neg clear-num add-log-exp
2×associate-*r/ prod-exp cbrt-unprod
1×flip3-- flip--
Counts
4 → 252
Calls
4 calls:
501.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
721.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
145.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
281.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series1.6s

Counts
4 → 12
Calls
4 calls:
496.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
678.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
208.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
258.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify5.6s

Counts
264 → 264
Iterations
IterNodes
done5031
24490
11123
0398

prune4.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.7b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
34.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
4160×times-frac
3009×*-un-lft-identity
1593×add-sqr-sqrt
1529×add-cube-cbrt
810×distribute-lft-out
171×div-inv
147×associate-/r/
101×associate-/r*
67×flip3-+ flip-+
43×add-exp-log
36×associate-/l*
34×add-cbrt-cube
32×difference-of-squares
29×div-exp
20×cbrt-undiv
16×sqrt-prod distribute-lft-out--
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
3×1-exp
1×flip3-- flip--
Counts
4 → 1484
Calls
4 calls:
664.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
203.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
898.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
604.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series1.8s

Counts
4 → 12
Calls
4 calls:
593.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
247.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
748.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
233.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify7.7s

Counts
1496 → 1496
Iterations
IterNodes
done5001
01720

prune31.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

localize117.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
0.2b
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

rewrite2.7s

Algorithm
rewrite-expression-head
Rules
4175×times-frac
3109×*-un-lft-identity
1550×add-sqr-sqrt
1534×add-cube-cbrt
877×distribute-lft-out
169×div-inv
142×associate-/r/
119×associate-/r*
65×flip3-+ flip-+
43×add-exp-log
34×add-cbrt-cube
29×div-exp
25×associate-/l*
20×cbrt-undiv
8×difference-of-squares
7×associate-/l/
4×pow1 frac-2neg clear-num sqrt-prod distribute-lft-out-- add-log-exp
3×1-exp
1×flip3-- flip--
Counts
4 → 1494
Calls
4 calls:
696.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
509.0ms
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
777.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
238.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

series1.3s

Counts
4 → 12
Calls
4 calls:
334.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
283.0ms
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
505.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
128.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

simplify4.4s

Counts
1506 → 1506
Iterations
IterNodes
done5000
01621

prune12.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

regimes577.0ms

Accuracy

40.9% (9.6b remaining)

Error of 11.7b against oracle of 2.1b and baseline of 18.3b

bsearch134.0ms

Steps
ItersRangePoint
6
5.49638027382935e+110
3.514303845479213e+111
3.464835701411268e+111

simplify26.0ms

Iterations
IterNodes
done60
160
042

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.9s8000×body80valid
456.0ms8000×pre80true