Details

Time bar (total: 37.3s)

sample58.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
10.0ms256×pre80true

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5001
31615
2280
160
017

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.7b

localize71.0ms

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))))
38.5b
(/ (/ (* (* 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))
46.9b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite663.0ms

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 insert-posit16 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 → 201
Calls
4 calls:
82.0ms
(* i (+ (+ alpha beta) i))
114.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
306.0ms
(/ (/ (* (* 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))
155.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
32.0ms
(* i (+ (+ alpha beta) i))
172.0ms
(* (* 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 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))))

simplify1.9s

Counts
213 → 213
Iterations
IterNodes
done5001
11299
0359

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 37.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
36.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
366×times-frac
300×add-sqr-sqrt
235×*-un-lft-identity
155×add-cube-cbrt
96×associate-*r*
70×add-cbrt-cube add-exp-log
62×difference-of-squares
44×associate-/r/
42×associate-*l*
33×cbrt-undiv div-exp
31×sqrt-prod distribute-lft-out--
22×flip3-+ flip-+ div-inv
19×associate-/l*
16×prod-exp cbrt-unprod
12×associate-/r*
9×distribute-lft-out
6×pow1 unswap-sqr
5×associate-/l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r/
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 376
Calls
4 calls:
254.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
772.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
98.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
200.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.7s

Counts
4 → 12
Calls
4 calls:
410.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.0s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
114.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
190.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.8s

Counts
388 → 388
Iterations
IterNodes
done5000
11744
0511

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
0.1b
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
36.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.0s

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/ insert-posit16 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 → 203
Calls
4 calls:
421.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
364.0ms
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
84.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
146.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.5s

Counts
4 → 12
Calls
4 calls:
768.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
3.5s
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
109.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
142.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.9s

Counts
215 → 215
Iterations
IterNodes
done5000
11181
0349

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 37.3b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
33.0b
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
36.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite999.0ms

Algorithm
rewrite-expression-head
Rules
104×times-frac
85×add-sqr-sqrt
81×*-un-lft-identity
78×add-cbrt-cube add-exp-log
41×add-cube-cbrt
39×cbrt-undiv div-exp
22×associate-/r/ difference-of-squares
17×prod-exp cbrt-unprod
16×associate-/r*
15×associate-/l*
12×flip3-+ flip-+
11×sqrt-prod div-inv distribute-lft-out--
9×distribute-lft-out
8×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r/
1×frac-times flip3-- associate-*l/ flip--
Counts
4 → 211
Calls
4 calls:
479.0ms
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
263.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
82.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
168.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.4s

Counts
4 → 12
Calls
4 calls:
3.2s
(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
894.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
135.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
208.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.0s

Counts
223 → 223
Iterations
IterNodes
done5000
24964
11030
0348

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 37.3b

regimes267.0ms

Accuracy

29.5% (1.9b remaining)

Error of 35.7b against oracle of 33.7b and baseline of 36.5b

bsearch34.0ms

Steps
ItersRangePoint
3
1.363363468595541e+178
1.6449521655465905e+178
1.447602491634548e+178

simplify20.0ms

Iterations
IterNodes
done33
133
024

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.4s8000×body80valid
401.0ms8000×pre80true