Details

Time bar (total: 1.1m)

sample80.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
10.0ms256×pre80true

simplify3.3s

Counts
1 → 1
Iterations
IterNodes
done5007
31614
2280
160
017

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.7b

localize189.0ms

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))))
36.0b
(/ (/ (* (* 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))))

rewrite1.9s

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:
228.0ms
(* i (+ (+ alpha beta) i))
362.0ms
(* (* 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))
477.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series3.1s

Counts
4 → 12
Calls
4 calls:
48.0ms
(* i (+ (+ alpha beta) i))
208.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
2.4s
(/ (/ (* (* 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))
463.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify3.7s

Counts
213 → 213
Iterations
IterNodes
done5000
11289
0360

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.8b

localize229.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* 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))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
33.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite3.7s

Algorithm
rewrite-expression-head
Rules
264×times-frac
191×add-sqr-sqrt
178×*-un-lft-identity
110×add-cube-cbrt
96×associate-*r*
74×add-cbrt-cube add-exp-log
42×associate-*l*
40×associate-/r/
35×cbrt-undiv div-exp
30×difference-of-squares
21×flip3-+ flip-+
20×div-inv
19×distribute-lft-out
17×prod-exp cbrt-unprod
15×sqrt-prod distribute-lft-out--
13×associate-/l*
10×associate-/r*
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/
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 316
Calls
4 calls:
627.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.3s
(* (/ (/ (* 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))))
193.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
490.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series5.9s

Counts
4 → 12
Calls
4 calls:
429.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
5.0s
(* (/ (/ (* 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
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
260.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify4.4s

Counts
328 → 328
Iterations
IterNodes
done5000
11652
0475

prune4.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 33.7b

localize270.0ms

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))))
33.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite5.3s

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 insert-posit16 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 → 254
Calls
4 calls:
1.6s
(* (/ (/ (* 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))))
3.0s
(* (* (/ (/ (* 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))))
257.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
379.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series6.7s

Counts
4 → 12
Calls
4 calls:
1.2s
(* (/ (/ (* 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))))
5.1s
(* (* (/ (/ (* 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))))
166.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
247.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify4.3s

Counts
266 → 266
Iterations
IterNodes
done5000
11407
0421

prune3.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 33.7b

localize995.0ms

Local error

Found 4 expressions with local error:

33.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
34.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
18×add-cbrt-cube add-exp-log
12×associate-/r*
8×flip3-+ associate-/r/ flip-+ associate-/l* associate-/l/
6×cbrt-undiv div-exp
4×expm1-log1p-u pow1 clear-num frac-2neg associate-*r/ insert-posit16 log1p-expm1-u div-inv add-log-exp
2×prod-exp cbrt-unprod
Counts
4 → 124
Calls
4 calls:
223.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
210.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
440.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
524.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series859.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
160.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
239.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
285.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify4.0s

Counts
136 → 136
Iterations
IterNodes
done5000
21896
1389
0130

prune2.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 33.7b

regimes952.0ms

Accuracy

36.2% (2.5b remaining)

Error of 36.9b against oracle of 34.4b and baseline of 38.3b

bsearch79.0ms

Steps
ItersRangePoint
7
1.5185210340582453e+216
6.531618038873483e+217
1.605441052792236e+216

simplify24.0ms

Iterations
IterNodes
done37
137
026

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.1s8000×body80valid
261.0ms8000×pre80true