Details

Time bar (total: 38.4s)

sample87.0ms

Algorithm
intervals
Results
30.0ms256×body80valid
24.0ms256×pre80true

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5001
31807
2295
160
017

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.8b
(/ (/ (* (* 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))
45.1b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite628.0ms

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×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u 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 → 197
Calls
4 calls:
84.0ms
(* i (+ (+ alpha beta) i))
107.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
257.0ms
(/ (/ (* (* 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))
171.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.7s

Counts
4 → 12
Calls
4 calls:
31.0ms
(* i (+ (+ alpha beta) i))
163.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.2s
(/ (/ (* (* 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))
318.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify1.9s

Counts
209 → 209
Iterations
IterNodes
done5002
11307
0356

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 31.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
32.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.4s

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 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 → 268
Calls
4 calls:
90.0ms
(* i (+ (+ alpha beta) i))
932.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
209.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
91.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series3.5s

Counts
4 → 12
Calls
4 calls:
28.0ms
(* i (+ (+ alpha beta) i))
3.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
194.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
124.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.1s

Counts
280 → 280
Iterations
IterNodes
done5000
11652
0450

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 31.8b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
32.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
85×add-cbrt-cube add-exp-log
79×times-frac
63×*-un-lft-identity
61×add-sqr-sqrt
42×associate-*l*
41×add-cube-cbrt
40×cbrt-undiv div-exp
21×prod-exp cbrt-unprod
18×associate-/r/
15×associate-*r*
12×associate-/r*
10×flip3-+ flip-+
9×div-inv distribute-lft-out
7×associate-/l/
6×pow1
5×associate-/l*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp difference-of-squares unswap-sqr
3×clear-num frac-2neg
2×frac-times associate-*l/ sqrt-prod distribute-lft-out--
1×flip3-- pow-prod-down *-commutative flip--
Counts
4 → 199
Calls
4 calls:
372.0ms
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
648.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
129.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
69.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series4.6s

Counts
4 → 12
Calls
4 calls:
3.6s
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
740.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
193.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
128.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.5s

Counts
211 → 211
Iterations
IterNodes
done5001
11207
0347

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 31.8b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
0.2b
(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
32.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
220×add-exp-log
136×add-cbrt-cube
91×times-frac div-exp
87×prod-exp
73×add-sqr-sqrt *-un-lft-identity
54×cbrt-undiv
49×add-cube-cbrt cbrt-unprod
43×associate-*l*
39×associate-*r*
18×associate-/r/
11×pow1
10×flip3-+ flip-+
9×rec-exp 1-exp div-inv distribute-lft-out
6×frac-times associate-/r* associate-*l/ associate-*r/ difference-of-squares
4×expm1-log1p-u pow-prod-down log1p-expm1-u associate-/l* add-log-exp unswap-sqr associate-/l/
3×sqrt-prod distribute-lft-out--
2×clear-num frac-2neg *-commutative
1×flip3-- un-div-inv flip--
Counts
4 → 250
Calls
4 calls:
602.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
1.1s
(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
157.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
70.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series4.6s

Counts
4 → 12
Calls
4 calls:
887.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
3.4s
(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
177.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
140.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.1s

Counts
262 → 262
Iterations
IterNodes
done5000
11504
0417

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 31.8b

regimes406.0ms

Accuracy

34.1% (2.4b remaining)

Error of 37.0b against oracle of 34.6b and baseline of 38.3b

bsearch117.0ms

Steps
ItersRangePoint
9
2.633169120176745e+195
3.9600275033090194e+200
1.706379319752007e+196

simplify6.0ms

Iterations
IterNodes
done33
133
024

end0.0ms

sample1.9s

Algorithm
intervals
Results
933.0ms8000×body80valid
708.0ms8000×pre80true