Details

Time bar (total: 1.0m)

sample98.0ms

Algorithm
intervals
Results
54.0ms256×body80valid
19.0ms256×pre80true

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
done2093
42093
31567
2267
158
017

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize37.0ms

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))))
37.3b
(/ (/ (* (* 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))
46.6b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite667.0ms

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:
169.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
93.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
206.0ms
(/ (/ (* (* 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))
192.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.8s

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
132.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s
(/ (/ (* (* 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))
228.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.1s

Counts
216 → 216
Iterations
IterNodes
done2012
22012
11313
0360

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.7b

localize50.0ms

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)))
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))))
33.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite973.0ms

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×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r/
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 308
Calls
4 calls:
152.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
608.0ms
(* (/ (/ (* 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))))
64.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
142.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.3s

Counts
4 → 12
Calls
4 calls:
315.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
2.8s
(* (/ (/ (* 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))))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
127.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.5s

Counts
320 → 320
Iterations
IterNodes
done2000
22000
11621
0465

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 33.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
0.0b
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))
0.1b
(* (/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
34.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
8083×times-frac
5713×*-un-lft-identity
3113×add-sqr-sqrt
2900×add-cube-cbrt
1551×distribute-lft-out
1162×associate-*l*
325×div-inv
263×associate-/r/
191×add-exp-log
137×add-cbrt-cube
128×div-exp
118×flip3-+ flip-+
96×associate-*r*
95×associate-/r*
83×cbrt-undiv
30×prod-exp difference-of-squares unswap-sqr
21×cbrt-unprod associate-/l*
15×sqrt-prod distribute-lft-out--
12×1-exp
6×pow1
5×associate-/l/
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
1×frac-times flip3-- pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 2711
Calls
4 calls:
84.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
155.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))
664.0ms
(* (/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
122.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.4s

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
307.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))
2.9s
(* (/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
154.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.0s

Counts
2723 → 2723
Iterations
IterNodes
done2359
02359

prune15.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
8063×times-frac
5816×*-un-lft-identity
3015×add-sqr-sqrt
2911×add-cube-cbrt
1618×distribute-lft-out
1162×associate-*l*
324×div-inv
260×associate-/r/
133×add-exp-log
116×flip3-+ flip-+
113×associate-/r*
97×add-cbrt-cube
86×div-exp
56×cbrt-undiv
24×associate-*r*
22×associate-/l*
20×prod-exp unswap-sqr
14×cbrt-unprod
9×1-exp
6×pow1 difference-of-squares
5×associate-/l/
4×insert-posit16 add-log-exp
3×clear-num frac-2neg sqrt-prod distribute-lft-out--
1×frac-times flip3-- pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 2707
Calls
4 calls:
669.0ms
(* (/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))) (/ (+ (* 1/2 i) (+ (* 1/4 beta) (* 1/4 alpha))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
298.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
101.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
235.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
634.0ms
(* (/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))) (/ (+ (* 1/2 i) (+ (* 1/4 beta) (* 1/4 alpha))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
260.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
120.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
379.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))

simplify3.1s

Counts
2719 → 2719
Iterations
IterNodes
done2225
02225

prune16.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.3b

regimes698.0ms

Accuracy

46.2% (8.9b remaining)

Error of 10.9b against oracle of 2.0b and baseline of 18.5b

bsearch66.0ms

Steps
ItersRangePoint
4
1.651674450270093e+130
3.0418911771928126e+130
2.736160234700738e+130

simplify14.0ms

Iterations
IterNodes
done59
159
041

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.4s8000×body80valid
415.0ms8000×pre80true