Details

Time bar (total: 35.7s)

sample63.0ms

Algorithm
intervals
Results
35.0ms256×body80valid
10.0ms256×pre80true

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5011
31567
2267
158
017

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.6b
(/ (/ (* (* 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))
48.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite586.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×*-un-lft-identity add-cube-cbrt
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 insert-posit16 add-log-exp
3×swap-sqr
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in *-commutative
1×pow2 pow-plus flip3-- pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 204
Calls
4 calls:
121.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
122.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
207.0ms
(/ (/ (* (* 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))
132.0ms
(/ (* (* 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:
94.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
134.0ms
(* (* 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))
243.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.7s

Counts
216 → 216
Iterations
IterNodes
done5001
11313
0360

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 32.4b

localize75.0ms

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))))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
33.4b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.2s

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×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r/
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 368
Calls
4 calls:
289.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
725.0ms
(* (/ (/ (* 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))))
73.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
118.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.8s

Counts
4 → 12
Calls
4 calls:
479.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.1s
(* (/ (/ (* 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))))
111.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
166.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.4s

Counts
380 → 380
Iterations
IterNodes
done5001
11707
0503

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 32.4b

localize82.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
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))))
33.4b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
329×times-frac
285×add-sqr-sqrt
226×*-un-lft-identity
147×add-cube-cbrt
117×associate-*r*
70×add-cbrt-cube add-exp-log
62×difference-of-squares
36×associate-/r/
31×sqrt-prod distribute-lft-out--
29×cbrt-undiv div-exp
20×prod-exp cbrt-unprod
18×div-inv associate-/l*
17×flip3-+ flip-+
13×associate-*l*
10×distribute-lft-out
9×associate-/r*
8×pow1
5×unswap-sqr
4×insert-posit16 add-log-exp
3×associate-/l/
2×clear-num frac-2neg flip3-- pow-prod-down associate-*r/ *-commutative flip--
1×frac-times associate-*l/
Counts
4 → 348
Calls
4 calls:
108.0ms
(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
315.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
717.0ms
(* (/ (* 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))))
166.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.2s

Counts
4 → 12
Calls
4 calls:
135.0ms
(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
426.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
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))))
193.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.4s

Counts
360 → 360
Iterations
IterNodes
done5001
11571
0470

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.5b

localize78.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* 1/4 (+ alpha beta)) (* i 1/2)) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
0.0b
(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.0b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
0.0b
(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))

rewrite982.0ms

Algorithm
rewrite-expression-head
Rules
85×*-un-lft-identity
60×add-sqr-sqrt
58×times-frac
52×add-cbrt-cube add-exp-log
45×associate-*r*
38×add-cube-cbrt
24×distribute-lft-out
18×cbrt-undiv div-exp
16×prod-exp cbrt-unprod
13×associate-*l*
10×associate-/r/
8×pow1
7×associate-/r*
6×associate-/l* difference-of-squares
5×flip3-+ flip-+ div-inv
4×insert-posit16 add-log-exp unswap-sqr
3×associate-*r/ sqrt-prod distribute-lft-out-- associate-/l/
2×clear-num frac-2neg pow-prod-down *-commutative
1×frac-times flip3-- associate-*l/ flip--
Counts
4 → 175
Calls
4 calls:
611.0ms
(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* 1/4 (+ alpha beta)) (* i 1/2)) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
154.0ms
(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
93.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
121.0ms
(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
638.0ms
(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* 1/4 (+ alpha beta)) (* i 1/2)) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
314.0ms
(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
118.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
108.0ms
(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))

simplify2.9s

Counts
187 → 187
Iterations
IterNodes
done5002
24189
1888
0274

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.5b

regimes388.0ms

Accuracy

49.7% (8.2b remaining)

Error of 10.2b against oracle of 2.0b and baseline of 18.3b

bsearch78.0ms

Steps
ItersRangePoint
5
5.4039666828126895e+146
1.5043712263133658e+147
6.263709625600619e+146

simplify9.0ms

Iterations
IterNodes
done51
151
035

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.4s8000×body80valid
316.0ms8000×pre80true