Details

Time bar (total: 15.3s)

sample29.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify480.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01753
15853
225253
3126853
done500153

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.0b

localize15.0ms

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))))
37.5b
(/ (/ (* (* 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))
47.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite328.0ms

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:
74.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
53.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
117.0ms
(/ (/ (* (* 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))
73.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
116.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
791.0ms
(/ (/ (* (* 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))
184.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify440.0ms

Counts
212 → 212
Iterations

Useful iterations: done (430.0ms)

IterNodesCost
035812169
1120211261
done500010969

prune643.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 34.6b

localize18.0ms

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)))
35.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite359.0ms

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-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:
107.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
138.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
35.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
67.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series836.0ms

Counts
4 → 12
Calls
4 calls:
263.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
360.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
91.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
122.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.7s

Counts
264 → 264
Iterations

Useful iterations: 2 (598.0ms)

IterNodesCost
039811487
1109611156
2469710682
done500010682

prune862.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 34.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
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)))
36.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite400.0ms

Algorithm
rewrite-expression-head
Rules
336×times-frac
325×*-un-lft-identity
218×add-sqr-sqrt
154×add-cube-cbrt
79×distribute-lft-out
44×associate-/l*
32×associate-/r/ difference-of-squares
18×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
8×cbrt-undiv div-exp
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
1×flip3-- flip--
Counts
4 → 324
Calls
4 calls:
125.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
50.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
143.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
63.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series813.0ms

Counts
4 → 12
Calls
4 calls:
287.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
70.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
335.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
121.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.5s

Counts
336 → 336
Iterations

Useful iterations: 2 (611.0ms)

IterNodesCost
043414271
1114513883
2450013481
done500013481

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.4b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite513.0ms

Algorithm
rewrite-expression-head
Rules
400×*-un-lft-identity
339×times-frac
176×add-sqr-sqrt
151×add-cube-cbrt
136×distribute-lft-out
90×associate-*r*
29×associate-/l*
26×associate-/r/
22×add-exp-log add-cbrt-cube
14×flip3-+ flip-+
13×associate-/r* div-inv
8×cbrt-undiv div-exp difference-of-squares
6×pow1
5×associate-/l/
4×sqrt-prod distribute-lft-out-- add-log-exp
3×frac-2neg associate-*l* prod-exp clear-num cbrt-unprod unswap-sqr
1×flip3-- associate-*r/ pow-prod-down *-commutative flip--
Counts
4 → 320
Calls
4 calls:
232.0ms
(* i (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
126.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
85.0ms
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
49.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

series796.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(* i (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
290.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
173.0ms
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
73.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

simplify1.5s

Counts
332 → 332
Iterations

Useful iterations: 2 (552.0ms)

IterNodesCost
038611137
1105010706
2439510200
done500010200

prune950.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.3b

regimes189.0ms

Accuracy

43.4% (9.4b remaining)

Error of 11.4b against oracle of 2.0b and baseline of 18.6b

bsearch113.0ms

Steps
ItersRangePoint
6
2.1302782060339758e+130
1.0209381998641132e+131
5.444893654686351e+130
7
3.770398971022825e+122
6.076322687575861e+123
4.812957519652492e+123

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
042155
162155
done62155

end0.0ms

sample675.0ms

Algorithm
intervals
Results
352.0ms8000×body80valid
133.0ms8000×pre80true